The effects of chip-shaped solids on valve head loss characteristics
by David Allan Johnson
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Civil Engineering
Montana State University
© Copyright by David Allan Johnson (1968)
Abstract:
The main purpose of this study was to determine the head loss characteristics of different valves in a
pipe line carrying a mixture of water and chip-shaped solids. Since the head loss caused by a valve is
given by HL = KL (v^2)/(2g), this study involved determining values of the loss coefficient, KL, for
each valve at different flow conditions. Observations were also made on the efficiency of each valve
with respect to use in a solid-liquid pipe line.
The following four valves were tested in this study: ball valve, plug valve, v-ball valve, and pinch
valve. Tests were conducted on each valve for various closures at velocities of 4, 6, 8, and 10 fps with
chip concentrations of 0, 10, and 20 percent.
The loss coefficient was observed to (1) be approximately constant with respect to velocity at velocities
greater than 6 fps for a given closure and percent concentration, (2) increase with increasing chip
concentration, and (3) increase with increasing valve closure. For design purposes, empirical
relationships of the following forms were derived for each valv6: ((KL)c)/((KL)0) = e^bC and
((KL)c)/((KL)0) = 1+mC These equations give the loss coefficient (KL)C for a given concentration as
a function of the concentration C and the clear water loss coefficient (KL)0 for a given valve closure.
THE E F F E C T S OF C H I P - S H A P E D SOLIDS ON
VALVE HEAD LOSS C H A R A C T E R I S T I C S
>
by
DAVID A L L A N J OH NSON
A thesis sub mitt ed to the Gra duat e Faculty in partial
ful fill ment of the req uire ments for the degree
of
MASTER OF SCIENCE
in
Civil E n g i n e e r i n g
Approved:
H e a d , Major D e p a r W e n t
C h a i r m a n , E x a m i n i n g Com mittee
Gr a d u a te^Dean
MON T A N A STATE U N I V E R S I T Y
Bozeman, Montana
December,
1968
iii
ACKNOWLEDGEMENT
This study was one phase of a project inv es t i g a t i n g
the hyd raul ics of t r a n s p o r t i n g wood chips by pipe line
spo ns o r e d by the Int er m o u n t a i n Forest and Range Exp erim ent
Station, U. S 0 Forest Service, and the Department of Civil
E n g i n e e r i n g and E n g i n e e r i n g Mechanics, Montana State Un i v e r ­
sity.
The valves used in this study were provided by:
Rockwell M a n u f a c t u r i n g Company
Grove Valve and R e g u l a t o r Company
Fisher G o v erno r Company
Farris Flexible Valve Corporation.
The author wishes to express his gratitude to
Dr. Wil l i a m A. Hunt, who provided the guidance for this s t u d y .
A special thanks is ext ende d to Mr. Ronald Schmidt, who p r o ­
vided con s i d e r a b l e effort and advice in the app aratus con­
str uction and data col lect ing phases of this project.
The
a u t h o r ’s a p p r e c i a t i o n is also e x t e n d e d to Mr,. Gary Hen drix for
his ass ista nce in this study.
Notable contrib ution s to this
study were made by members of the Mechanical E n g i n e e r i n g
Dep artm ent mac hine shop at Montana State Uni vers ity and
mem bers of the stgff of the Montana State U n i vers ity Computing
Center,
R e c o g n i t i o n is also due to und ergr aduat e assistants,
Mr. Clyde Wolf, M r 0 Larry Neal, and Mr. Tom Hedges, who were
r e s p o n s i b l e for r e d u c i n g data from film strips to F O R T R A N
coding s h e e t s .
Special r e c o g ni tion is extended to the author's
wife, P a t , for her pat ience and effort spent in the typing and
p r o o f r e a d i n g of the manuscript.
TABLE OF CONTENTS
Page
List of Tables
............
. . . . . . . . . . . . . .
List of Figures
. . . . . . . , ............ . .
vii
. . . . . viii
List of S y m b o l s . . . . . . . . . . . . . . . . . . . . . . . . .
Abs trac t
I.
Int r o d u c t i o n
A.
B.
C.
II.
III.
VII.
..
I
Ba c k g r o u n d mat e r i a l . . . . . . . . . . . . . .
Obj ecti ves of s t u d y .........
L i t e r a t u r e review . . . . . . . . . . . . . . . . . . . .
I
2
4
7
A.
B.
. . . . . .
7
Basic head loss m e c h a n i s m . . . . . . . .
Effects of valve closure, chip
concent ratio n, and vel ocit y
E x p e r i m e n t a l Methods
.
. . . . . . . . . . . . . . .
8
13
D e t e r m i n a t i o n of loss coe ffic ient
. . . . .
D e t e r m i n a t i o n of valve areas
. . . . . . . . .
D e t e r m i n a t i o n of velocity and con cent ratio n . .
App arat us Des c r i p t i o n . . . . . . . . .
13
16
18
.
21
Ope ra t i o n of the pipe line system . . . . . . .
System components . . . . . . . . . . . . . . .
Test section and components . . . . . . . . . . . .
Valves tested . , . .. . . . . . . . . . . . . . . . . . . . . . .
.
21
23
26
31
Test Pro cedu re
A.
B.
C.
VI.
..
. xiii
. . . . . .
A.
B,
C.
D,
V.
. .................. . .
Theory of Head Losses Caused by Valves
A.
B.
C.
IV.
. . . .. . . . . . . . . . . . .
x
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
P r e p a r a t i o n of equ ipment
........ . . . . . .
34
Data col lect ion procedure . . . . . . . . . . .
36
Data r e d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Data Ana lysis
...
. . . . . . . . . .
40
A.
B.
Computer operati ons . . . . . . . . . . . . . .
40
P r e s e n t a t i o n of
data ...................... 44
C.
D.
Flow pictures . . ...................... . . . .
Summary of valve c h a r a ct erist ics
. . . . . . .
Co n c l u s i o n s and R e c o m m e n d a t i o n s ...............
.
52
55
57
vi
A p p endi ces
A.
B.
C.
D.
E.
. . . . . . .
..........
, ................
Error Ana lysi s ........................ . .
M a n o met er Board
. . . . . . . . . . . . . . . .
S t a t i st ical Equ ations
..............
Com pute r P r o g r a m . . . . . . . . . . . . . . . . . . .
Summary of C o m pute d Results
................
Li t e r a t u r e Cited . . . . . .................. . .
. . . .
60
61
65
70
78.
88
92
vi i
LIST OF TABLES
Table
I.
II.
III.
Page
Summary of Com pute d R e s u l t s ,
Emp ir i c a l Con stants for
Valve C h a r a c t e r i s t i c s
V-Ball Valve . . . , . 45
Equ atio ns
. . . . . . .
50
..............
. . . . . . .
56
IV.
Summary of C o m pute d Results,
Plug Valve . . . . . .
88
V.
Summary of C o m p u t e d Results,
Ball Valve . . . . . .
89
VI.
Sum mary of C o m p u t e d Results,
Pinch Valve
90
VII.
. . . . .
Sum mary of C o m p u t e d Results, Gate Valve . . . . . .
91
viii
LIST OF FIGURES
Page
Figure
1.
Grade lines sho w i n g effect of constri ction
..
. . .
2.
Pipe and typical hyd raul ic grade line
. . . . . . .
14
3.
Plot of dim en s i o n l e s s grade line . . . . . . . . . .
15
4.
Plot of ind icator rea ding versus percent closed
19
5.
Sch emat ic of pipe line system
6.
Control console
7.
Plan view of test s e c t i o n ......... ....
. .
. . .
27
8.
Loc atio n of pre ssure taps intest
..
. . .
28
9.
Typical pre ssure tap c o n s tru ction
. .
9
. . . . . . . . . . .
22
.. . . . . . . . . . . . . . ...................
24
section
.............. .
30
10.
Dif f e r e n t i a l m a n o m e t e r b o a r d ..............
11.
S c h e mat ic dia gram of valves tes ted . . . . . . . . .
32
12.
F O R T R A N coding sheet and sample data . . . . . . . .
41
13.
Sample computer output . . . . . . . .
............
43
14.
Plot of
versus vel ocity .............. . . . . . . . . . .
46
15.
Plot of
versus c o n c e n t r a t i o n . . . . . . . . . .
47
16.
Plot of (Kr ) / ( K r )
versus c o n c e nt ratio n . . . . . .
49
17.
Plot of (K l ) q versus percent closure . . . . . . . .
51
18.
Pic ture of sliding bed . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
19.
T u r b u l e n c e d o w n s t r e a m from plug v a l v e ,
4.4 percent closed . . . .................... . .
53
20.
21.
.. . .
29
. . . .
. .
T u r b u l e n c e d o w n s t r e a m from plug valve,
50. 0 percent closed
. . ............ . . ...........
54
Pic ture of b e g i n n i n g of " p l u g - u p ”
54
. . . . . . . . .
ix
22.
S c h e m a t i c of d i f f ere ntial m a n o m e t e r board
. . . . .
23.
Sample linear t w o - d i m e n s i o n a l data . . . . . . . . . . . . . .
65
„
70
X
LIST OF SYMBOLS
A
- Any c r o s s - s e c t i o n a l a r e a .
a
- S t r a i g h t liffe y-intercept.
b
- Slopd of straight line.
C
- V o l u m e t r i c chip concentration.
CVAL
- Valve dlosure in percent of constriction.
COEF
- C o r r e l a t i o n coefficient.
CCl^
- Carbon tet rachloride.
D
- Pipe diameter.
DPHD
- Dif f e r e n t i a l pre ssure head between tap I and any
. other tap.
E
- Sum of s qu ared e r r o r s .
e
- Base of Nap erian logarithms.
E^
- Energy loss.
EVAR
- E s t imat e of var ianc e about regression.
f
- F r i ctio n factor.
fps
- Feet per second.
g
- Gravitational acceleration.
gpm
- Gallons per minute.
Hl
- Valve head loss.
Hg
- Mercury.
HGL
- H y d r a u l i c grade line.
ID
- Inside dia m e t e r of any pipe.
Kl
- Valve head loss c o e f f i c i e n t .
L
- Length of any reach of pipe.
xi
mm
- Millimeter.
n
- Number of observations.
OD
- Outside dia mete r of pipe.
P
- Pressure.
pcf
- Pounds per cubic foot.
Q
- Flow rate in g p m .
S
- Spe cific gravity of any fluid.
S
- St a t i s t i c a l variance.
V
- Nominal v e l ocit y in fps.
XVAL
- X - d i s t a n c e c o r r e s p o n d i n g to center of valve in
test s e c t i o n .
X
- Distance from first pre ssure tap in test section
to any other t a p .
y
- Level of fluid in m a n o m e t e r tubes.
Z
- Height of water above fluid in m a n o m e t e r tubes.
A
- Dif fere nce in any rea ding or measurement.
- Spe cific weight in pcf of any fluid.
- T h e o r e t i c a l mean of infinite population.
>
- Gre ater t h a n .
C
- Any + error.
b p/d* -- Change in pre ssur e with res pect to distance.
Subscripts
i - Pressure tap n u m b e r .
u - Upstream.
d
Downstream.
xi i
v - Valve area.
p - Pipe a r e a .
m - Mixture flow rate.
w - Clear water supply flow rate.
f - Fluid flowing.
c - Carbon t e t r a c h l o r i d e .
m - Mercury.
n - Some pre ssure tap d o w n str eam of tap I.
o - Loss coe ffic ient for clear water,
c - Loss coe ffic ient for a given concentration.
xiii
ABSTRACT
The main purpose of this study was to det ermine the
head loss c h a r a c t e r i s t i c s of dif ferent valves in a pipe line
car ryin g a mi x t u r e of water and ch i p - s h a p e d solids.
Since
2
the head loss caused by a valve is given by
, this
study inv olved d e t e r m i n i n g values of the loss c o e f f i c i e n t „
K^, for each valve at different flow c o n d i t i o n s . O bs erva tions
were also made on the e f f icie ncy of each valve with respect
to use in a s o l i d - l i q u i d pipe line.
The fol lo w i n g four valves were tested in this study:
ball valve, plug valve, v-ball valve, and pinch valve.
Tests
were con duct ed on each valve for various closures at v e l o c ­
ities of 4 , 6, 8 , and 10 fps with chip c o n c ent ratio ns of 0 ,
10, and 20 p e r c e n t .
The loss coe ffic ient was o b s erve d to (I) be a p p r o xi matel y
constant with respect to vel ocity at velocities gre ater than
6 fps for a given closure and percent concentration,
(2 ) increase with in c r e a s i n g chip concentration, and
(3) increase with i n c r eas ing valve closure.
For design
p u r p o s e s , emp irical r e l a t i o n s h i p s of the fol lowing forms
were der ived for each v a l v 6 :
c k L-1C
bC
c k L-1C
r
— r— = e
and 77;— %— = I + mC.
CKL 0
'.
CKL 0
These equ ations give the loss coeffic ient (K^ )c for a given
c o n c e n t r a t i o n as a function of the con cent ratio n C and the
clear water loss co e f f i c i e n t (Kr ) for a given valve closure.
CHAPTER
I
INTRODUCTION
A.
B a c k g r o u n d mat eria l
The t r a n s p o r t a t i o n of solids by pipe line is not n e w .
For man y years chemical, mining, and dredging operations
have inc luded sho rt-h aul slurry pipe lines.
years, however,
In the past few
inc reas ed att ention has been given to the
hyd raul ics of t r a n s p o r t i n g solids by pipe lines over longer
distances.
Cur rently,
con side rable research is being done on
solids pipe lines in the United States, Canada, and other
fdreign countries.
Also, several long distance pipe line
t r a n s p o r t a t i o n systems have been built and ope rated s u c c e s s ­
fully .
It is g e n e r a l l y con clud ed that because of continuous
ope rati on and low ope ra t i n g costs, pipe lines can compete
e c o n o m i c a l l y with other exi s t i n g methods.
Govatos
Zandi and
(12) discuss solids pipe lines and give 30 ref erences
to articles d i s c u s s i n g solids t r a n s p o r t a t i o n and industrial
pipe line installations.
A f e a s i bi lity study in 1965 by Hunt (4) showed that a
pipe line system could also be used to convey woo d c h i p s ,
eco no m i c a l l y ,
from forest to pulp mill.
As a result, a
res e a r c h pro ject was ini tiated at Mon tana State Univers ity
to inv esti gate the hyd raul ics of such a t r a n s p o r t a t i o n system
The project was spo ns o r e d through a cooperative agreement by
the I n t e r m o u n t a i n Forest and Range Exp erim ent Station,
—2"
United States Forest Service, and the Department of Civil
E n g i n e e r i n g and E n g i n e e r i n g Mec hanics at Montana State
University.
Up to this date studies have been completed
under the above c o o p e ra tive agreement on the fol lo w i n g s ub­
jects ;
specific gra vity of sat urat ed wood c h i p s , pump p e r ­
formance c h a r a ct erist ics+ head losses in a x i - s y m m e t r ic pipe
expansions, head losses of a m o d i f i e d gate valve, pipe line
frictio nal l o s s e s , and a water h am mer analysis of a high
pressure chip injection system.
A study of the head loss cha rac t e r i s t i c s of four
dif fere nt types of valves in a pipe line carrying a mixture
of water and chips is pre sent ed in this paper.
Results of
this study will pro vide design informa tion on valve head
losses and hence power req u i r e m e n t s for con stru ction of a
ful l-sc ale ope ra t i n g system.
Tests were conducted on a v-ball
valve, a ball valve, a plug valve, and a pinch valve.
Results
of the m o d i f i e d gate valve study m e n t i o n e d above are also
pre se n t e d in this paper.
The tests were per fo r m e d in the
civil e n g i n e e r i n g section of Ryon L a b orat ory on the campus
of Mon tana State University.
B.
Obj ecti ves of study
Flow thr ough a valve is a r e l a t i v e l y com plex phenomenon
and head losses gen er a l l y cannot be det ermi ned analytically.
Because of the variety of flow pas sage ways in different
valves, head loss cha rac t e r i s t i c s must be d e t e rmi ned
-3-
experimentalIy.
The energy equ atio n for a liquid written
between points ups trea m (subscript I) and d o w nstr eam
(subscript 2) of a valve is
T + 2i
+
Z.
Pg
v2
z0 +' *''**"*a
losses i_2
if +' --2g +' "2
I
where p is pre ssure in psf,
(I)
ft is the specific weight of the
fluid flowing in pcf, v is the nominal velocity, z is the
e l e v a t i o n above a datum, g is the g r a v ita tiona l acceleration,
and the loss term includes the loss due to pipe line friction
and the loss caused by the valve.
For a horizontal,
constant
dia mete r pipe this sim plif ies to
l o s s e s 1_2
Pl ~_J2
(2 )
a
where p^ and p^ must be d e t ermi ned experim ental ly.
losses for a given flow condition are determined,
Once the
it is
des irab le to equate them to a fun ction of some commonly
known par am e t e r such that head losses may be e s t i m a t e d for
similar flow conditions.
The D a r c y - W e i s b a c h equation, giving
the head loss as a fun ction of velocity, was d e v e l o p e d for
pipe line friction losses.
Similarly, head losses caused by
valves and other fittings are e x p r e s s e d as
lL 2g
where K. is an emp iric al head loss coefficient
(3)
—4—
The main obj ective of this study, t h e n , was to determine
exp e r i m e n t a l Iy the values of the loss coefficient,
each valve at dif ferent flow conditions.
, for
Velocity, valve
closure, and chip con ce n t r a t i o n were varied and the effects
on
determined.
Flat r e c t a n g u l a r plastic chips with a
spe cifi c gravity sli ghtly greater than that of water were
used to simulate wood chips.
In add ition to head loss data,
o b s e r va tions were also made on the m e c hani cal e f f icie ncy of
each valve with res pect to use in a s o l i d -l iquid pipe line.
C.
L i t e r a t u r e review
A literature survey was con duct ed in an attempt to find
inf orma tion on head losses caused by valves in s o l i d-l iquid
lines for Com pari son with values obt aine d in this study.
V i r t ual ly no i n f o r ma tion was found on valve head losses in
s o l i d - l i q u i d pipe lines.
In fact, very little recent inf or­
ma t i o n was found on valve head losses in general.
Pub lished
ana lyti cal and e x p e r i m e n t a l inf orma tion on valve head losses
tends to be the result of work done several years ago and on
the older types of valves.
More recent work has apparently
been done by valve m a n u f a c t u r e r s and pri vate firms and not
rel e a s e d for public consumption.
The fol lowi ng inf orma tion was found on the effect of
closure,
concent ratio n, and vel o c i t y on the loss coefficient.
Rouse (8 ) gives the fol lowi ng loss coefficients,
, for
various valves at dif ferent valve closures for clear water flow.
—5—
Gate Valve
Fully Open
3/4 Open
1/2 Open
1/4 Open
Plua Globe or Stop Valve
0. 19
I .15
5.6
24.0
D i a p hra gm Valve
Fully Open
3/4 Open
1/2 Open
I /4 Open
Fully Open
3/4 Open
1/2 Open
1/4 Open
4.0
4.6
6.4
78.0
Plua Valve with Scr ewed Ends
2.3
2 *6
4.3
21.0
Fully Open
90% Open
80% Open
70% Open
0.77
2.86
9.6
28.0
No i n f o r ma tion about the effect of con cent ratio n on the
head loss c o e f f ic ient was found.
However, Charley (I) did
some work on the effect of ch i p - s h a p e d solids on head losses
in pipe expansions.
He found t h a t , for flow rates greater
than 226 g p m , the loss' coeffic ient for a pipe exp ansi on
app e a r e d to dec rease with an increase in chip concentration.
The Crane Com pany (2) implies that the loss coefficient,
K l ,. does not vary with Reynolds number and hence velocity for
fully tur bulent clear water flow.
The valve head loss
2
equ a t i o n H l
L Tj^.
v2
H l = f-jj
L 2g
is similar to Darcy's equation
TThus
h u s , a log-log plot of loss coefficient.
coefficient, K 1
l,
versus R e y n o l d s number would be e x p e c t e d to yield a graph
similar to the w e l l - k n o w n Moody dia g r a m for pipe friction
losses.
The Crane Com pany claims that in the f u l l y - d e v e l o p e d
tur bulent region of a log-log plot of K l versus R g or velocity,
the loss coefficient, K l , for clear water would be constant
- 6-
as is the friction factor for M o o d y ’s diagram.
i n f o r ma tion was given on how
flow of water and s o l i d s .
However, no
varies with vel o c i t y for
CHAPTER
II
T H E O R Y OF HEA D LOSSES CA U S E D BY VALVES
Some knowledge of the cha ract erist ics of flow through a
valve is nec essa ry before d e v e l o p i n g the exp erim ental methods
used to det ermine the loss c h a r a ct erist ics of the various
valves.
Flow of a fluid through a valve is a rel ativ ely
c om plex phenomenon.
The addition of solid particles to the
fluid further complic ates the c h a r a ct erist ics of the flow.
As ind icat ed in the p r e c e d i n g c h a p t e r , no pub lish ed t h e o r e t ­
ical work on flow of s o l i d - l i q u i d mix tures through valves was
found.
Thus* the fol lowi ng d i s cuss ion gives a general des­
cription of (I) the head loss mec hani sm, as d e v e lop ed by
app l i c a t i o n of the basic laws of fluid mec hanics, and (2) the
effects of valve closure, chip concentration, and velocity on
head losses as r e p o r t e d in rel ated sol id-l iquid tra nsp o r t a t i o n
studies,
A.
Basic head loss m e c h a n i s m
A valve is e s s e n t i a l l y an irr egul ar c o n s t ri ction in a
pipe line.
For any given flow condition, the e q u a t i o n of
con tinu ity requires an acc e l e r a t i o n of the fluid through the
con s t r i c t i o n and a dec e l e r a t i o n d o w n s t r e a m from the valve.
At the same time, the energy equ atio n requires a reduction
in pressure, head to coincide with the inc reasing velocity
through the valve.
In other words*, the con stri ction caused
by the valve results in a con vers ion of pressure head or
-8-
pot ential energy to vel ocit y head or kinetic energy.
In the
region d o w n s t r e a m from the v a l v e , the energy con vers ion is
r e v e r s e d and pre ssure head is r e c o v e r e d as the fluid slows
and again assumes uni form flow conditions.
Howeverbecause
of energy losses * this t r a n s f o r m a t i o n is less than IOO percent
eff icie nt and the initial pressure head is not com pletely
recovered.
A certain amount of energy is dis sipa ted by turbulence
and friction in the valve and in the region d o w n s t r e a m from
the valve.
Since the continuity equ atio n requires the v e l o c ­
ity head to return to its initial value during the recovery
process, this d i s s i p a t e d energy is lost at the exp ense of
pre ssure head o n l y .
loss.
The r e s u l t i n g Ap/fr
is known as the head
The m a g n i t u d e of this head loss is aff ected by valve
closure, chip c o n c e n t r a t i o n , and vel ocity as dis cu s s e d below.
A section of pipe line with a valve is shown in Fig.
I with
the c o r r e s p o n d i n g vel ocit y ^ hydraulic, and energy grade lines.
B.
Effects of valve closure, chip con centration, and
vel ocity
As seen in the above discussion, valve head losses are
a result of energy d i s s i p a t e d by tur bule nce and friction.
Spe cifi c causes of this energy d i s s i pa tion are given below.
The con s t r i c t i o n or closure of the valve causes turbule nce in
three ways.
The r e d u c t i o n in area through the valve causes
an a c c e l e r a t i o n of the fluid.
As a result of the increased
-9-
velocity, zones of high shear form which in turn disturb the
vel ocity d i s t r i b u t i o n or cause turbulence.
con s t r i c t i o n is increased,
hence t u r bule nce increase.
As the degree of
the velocity, shear forces, and
The geo metr ic shape of the
p a s sage way through the valve also aids in the formation of
tur bule nce by d i s r u p t i n g the streaml ines of flow in the pipe
line.
Tu r b u l e n c e also forms in the region just dow nstr eam from
the valve as a result of the constriction.
As seen in Fig.
I,
the c o n s tri ction in the pipe line results in a positive
pressure gradient
valve.
^ ^ >0 in the region dow nstr eam from the
A c c o r d i n g to V. L . Str eeter (IO) this positive
pressure gradient induces boundary layer separation along the
Total Energy Grade Line
£_
+
V_
Hyd raulic Grade Line
Velocity Grade Line
Fig.
I.
Grade lines showing effect of constri ction
-10-
pipe walls in this region which results in back flow and the
for mati on of add itio nal eddies.
The turbulence caused by
the valve is e v e ntua lly damped out and the flow is e s s e n ­
tially u ni form again at the point where the h y d r aul ic grade
line becomes a slo ping straight line.
The dis tance between
the valve and this point is r e f erre d to as the settling
length.
The set tlin g length increases with the amount of
t u r bule nce or energy dissipated.
A c c o r d i n g to the above discussion, then, tur bule nce and
the c o r r e s p o n d i n g di s s i p a t i o n of energy are direct Iy related
to the degree of con s t r i c t i o n caused by the valve.
Therefore,
head loss and hence the loss coeffic ient can be pre dict ed to
increase as the valve closure is increased.
This is in
agr eeme nt with the clear water loss coefficients given by
Rouse (8).
The presence of c h i p - sh aped solids in the fluid also
affects the flow cha ract eristics.
H o w e v e r , the effect of
solids on valve head losses is not nearly as obvious as that
of valve closure.
Solid particles have both ben efic ial and
det rime ntal effects.
A c c o r d i n g to the results of experiments
on the flow of s o l i d - l i q u i d mix ture s in pipes by J. W. Daily
and T „ K . Chu as r e p o r t e d by M. Hino (3), app ro x i m a t e l y
neu tral ly buo yant particles cause (I) an increase in the
t u r bule nce int ensity over that for clear water, and (2) a
r e d u cti on in the set tlin g length.
In other words, solid
— 11 —
par ticles break up large eddies into smaller, high velocity
eddies which,
turbulence.
in effect,
increase the intensity of the
A l t h o u g h the int ensity of turbulence is increased,
the red u c e d set tlin g length caused by the presence of solid
par ticles indicates that the t u r bule nce is damped out quicker
than for clear water.
This in turn indicates that less
energy is d i s s i p a t e d and hence, the head losses are smaller.
A c c o r d i n g to B . W. C ha rley (I), these facts account for the
o b s erve d decrease in the head losses caused by a x i - s y m m e t r ic
pipe e x p ansi ons for flow of a s o l i d - l i q u i d mixture.
However, S . L , Soo (9) reports that because of physical
contact bet ween the particles and the walls, the addition of
solid par ticles to the flow causes an increase in friction and
flow r e s i s t a n c e along the bou ndar ies of a conduit.
Energy
di s s i p a t i o n and hence head losses wou ld app aren tly increase
with an i n c reas ing volume of par ticles or chips in the fluid
flowing.
In a p a r t i a l l y closed valve, chips tend to collect
in pockets and crevices, r e s u l t i n g in a sort of "semi-p lugge d"
con dition and inc reas ed flow resistance.
Fri ction between
the chips and t u r b ule nce caused by the relative mo t i o n of the
chips also dis sipa te small amounts of e n e r g y .
In summary,
t h e n , the pre sence of chips appears to cause a red uc t i o n in
head losses by i n c reas ing the tur bule nce intensity which in
turn reduces the set t l i n g length.
On the other h a n d , chips
ap p a r e n t l y also increase the head losses because of energy
— 12 —
d i s s i p a t e d by inc reas ed friction and flow resistance.
Thus ,
without further evidence, a theoretical pre dict ion of the net
effect of chips on the head loss cannot be made.
P r e l i m i n a r y analysis of the data from the previously
m e n t i o n e d gate valve tests indicates that for a given v e l o c ­
ity and valve closure,
chi p-sh aped solids increase the head
loss over that for clear w a t e r , contrary to the conclusions
of Charley (I).
The refore,
on the basis of trends shown by
the gate valve tests, it can be pre di c t e d that the net effect
of ch i p - s h a p e d solids should be that of inc reas ing the head
loss and the loss c o e f f i c i e n t ,
„
As r e p o r t e d by Rouse (8 ) and others, the clear water
valve head loss coefficient,, K^, is generally ass umed to be
constant for any velocity.
In other w o r d s , the head loss
increases with velocity but the ratio
remains approxiv2/2g
m a t e Iy constant.
In conclusion, t h e n , it can be pre dicted that the valve
head loss coe ffic ient should increase with i n c reas ing valve
closure and chip con ce n t r a t i o n but remain constant with
i n c reas ing velocity.
CHAPTER
III
E X P E R I M E N T A L METHODS
In order to ach ieve the objectives of this study, the
fol lo w i n g e x p e r i m e n t a l pro cedu res were followed:
m i n a t i o n of the head loss coefficient,
(I) d e t e r ­
, (2) d e t e r mi natio n
of valve areas, and (3) d e t e r m i n a t i o n of the m i x t u r e velocity
and percent concentration.
A.
D e t e r m i n a t i o n of loss coefficient,
The head loss, in feet of fluid f l o w i n g , o c c u r r i n g at a
valve in a pipe line is m e a s u r e d as the differe nce between
the ups trea m and d o w n s t r e a m portions of the h y d r a u l i c grade
line when both lines are pro je c t e d to a point over the valve.
Fig, 2 shows a typical h y d r aul ic grade line, H G L , and the head
loss, H^, caused by a valve.
To det ermine the head loss and
hence the effect of velocity, closure, and c o n c e nt ratio n on
the loss coe fficient, K^,. the hyd ra u l i c grade lines for the
various flow conditions must be est ablished.
A series of pre ssur e taps a l o n g the test section, as
d i s c u s s e d in Cha pter IV, and a d i f f e re ntial m a n o m e t e r board
(Ap pend ix B) pro v i d e d information needed to est ab l i s h the
h y d r a u l i c grade line.
The m a n o m e t e r board gave the pressure
head differences, DPHD., between the first pre ssur e tap in
the test section and the other pre ssur e taps at distances x^
d o w n s t r e a m of the first tap as shown in Fig. 2. , A set of
t w o - d i m e n s i o n a l data (x^, D P H D .) was thus obtained where the
-14-
subscript i refers to the pressure tap number.
Plo ttin g this
data would give a curve with the exact shape of the true
hyd ra u l i c grade line but upside down and with a y - i ntercept
of z e r o .
Div iding each of the d i f f e re ntial pressure heads, D P H D ^ ,
by the vel ocity head gives a set of dim ensi onles s differential
pressure heads, DIMPH., which are dependent on distance along
the pipe line,
.
The data (x_, D I M P H ^ ) thus establi shes an
upside d o w n , d i m e n si onles s hyd raulic grade line.
However,
the d i f f e re ntial pressure heads dis cuss ed above are the head
losses occ urri ng between the points indicated.
P r o ject ing
the straight line portions of the dimensi onles s hydraulic
grade line as shown in Fig. 3 to a point coi ncid ing with the
center of the valve (x = X V A L ) gives the loss coefficient,
DPHD
Fig. 2.
Pipe and typical hyd raul ic grade line
,
-15-
f or the valve because K
A n /x
I.
, as pre viou sly
shown.
Once the data (x_, DIMPH.) was calculated, the loss
coe ffic ient could be d e t ermi ned by using linear reg ress ion
met hods to fit straight lines to the data for the linear
portions of the dim e n s i o n l e s s grade line.
These fitted lines
are given by the equ ation y = a + bx where the variables
(x, y) c o r resp ond to the data (x., DIMPH^), a is the y-intercept, and b is the slope of the line.
By using linear
regression, a and b were d e t e r m i n e d such that the establi shed
lines were the lines of "best fit."
The equations used to
cal culate a and b for each line are dev eloped in A p p e n d i x C .
The loss coe fficient,
, is then given by the difference
bet ween the ups tream and do w n s t r e a m lines or, in other words,
the dif fere nce between the y values given by the equations
AP/tf
v2/2g
x - d ista nce dow nstr eam
Fig. 3.
Plot of d i m e nsi onles s grade line
— 16—
y = a + bx at some common x.
The re f o r e f
K L = y d “ y u = ' ( a + b x ) d “ (a+ bx)u
(4)
where x = XVAL and the subscripts d and u refer to the
d o w n s t r e a m and ups t r e a m portions of the d i m e nsi onles s grade
line as shown in Fig. 3.
A computer program (Ap pendix D) was
d e v e l o p e d to per form the above operations.
T h e o r e t i c a l l y the ups trea m y-i ntercept, a^, should be
zero and the slopes of both lines should be equal.
However,
the r e g r e s s i o n analysis gave values of a^ that varied
slightly from zero and slopes that were not quite the same.
A d i s cuss ion of the r e s u l t i n g errors is given in A p p e n d i x A.
B.
D e t e r m i n a t i o n of valve areas
Because the head loss varies with the amount of con­
str iction in the pipe line caused by the v a l v e , some means
of gau g i n g the closure of each valve was needed before testing
could begin.
Valve closure is usually exp ressed as a p er­
centage of stem travel or angle of turn of the ope rating
m e c h a n i s m on the valve.
In this study valve closure was
c a l cula ted as a fun ction of the area of the ope ning through
the valve and the c r o s s -s ectio nal area of the pipe line.
In
other w o r d s , the term valve closure indicates the percent age
of con s t r i c t i o n in the pipe line caused by the valve.
valve closure in p e r c e n t , C V A L , is exp ressed as
The
-17-
CVAL = 100 - -Tjl (100)
P
where
(5)
is the area of the opening of the valve at a given
position, and A^ is the area of the 4-in. diameter pipe.
An
indicator, as dis cu s s e d in Chapter IV, was ins talled on the
o p e r ati ng m e c h a n i s m of each valve for gauging the closure.
The scale on the ind icator ranged from 16 at the wide open
pos ition of the operator to zero for the fully closed
position.
In order to det ermi ne the valve closure cor r e s p o n d i n g to
a given indicator reading, a plot of indicator r e a d i n g versus
closure was made for each valve.
This plot was made from
data obt aine d by ca l c u l a t i n g the areas and p e r cent age closed
of a few openings c o r r e s p o n d i n g to equally spaced positions
on the ind icator scale between 16 and the 100 per cent closed
reading.
The areas of the openings thr ough the various valves
were d e t e r m i n e d in dif fere nt ways.
Pictures were taken of
the v-ball and ball valves from whi ch drawings of the areas
of ope ning were made.
These drawings were then pla n i m e t e r e d
to det ermi ne the areas in square feet.
The openings in the
plug and pinch valves were not e n t i r e l y . v i s i b l e through the
inlet of the valve and pictures could not be taken.
Instead,
calipers were used to obtain the dimensions of the openings
and a p p r o x i m a t e sketches were made.
Areas of the openings
— 18—
were then c a l cula ted by p l a n i m e t e r i n g the sketches.
The
s i m plic ity of the shape of the o pe ning in the gate valve
made it possible to calculate the areas mat hema tical ly.
The plot of ind icat or r ea ding versus per cent age closed
for each valve is shown in Fig. 4.
From this plot, the
indicator setting for any closure chosen for tes ting could be
determined.
The curves for the v - b a 11, plug, and pinch valves
in Fig. 4 do not reach 0 percent closed at an indicator
rea d i n g of 16 because the areas through the valves when in
the wide open pos ition are less than the area of the 4-in.
pipe.
Thus, these valves cause a constri ction of the pipe
line when in the wide open position.
The curves for the
v - b a 11, plug, and ball valve reach 100 percent closed at an
ind icat or rea d i n g other than zero.
This is bec ause the ind i­
cator scale was con nect ed to the o p e r ati ng m e c h a n i s m and
ranged from 16 to 0 between the wide open stop and the .closed
stop of the operator.
For these three valves, the area of
opening was red uced to zero before the operator rea ched the
closed stop which cor r e s p o n d e d to a zero indicator reading.
A plot of ind icator rea d i n g versus percent age closed is known
as the "control c h a r a c t e r i s t i c " of the valve.
C.
D e t e r m i n a t i o n of vel ocity and c o n c ent ratio n
The actual nominal vel ocity of the flow dur ing each test
was d e t e r m i n e d from the average v o l u m e t r i c flow rate of the
mixture,
, which was m e a s u r e d in gallons per minute, g p m .
-19-
1.
2.
3.
4.
5.
V-Ball Valve
Plug Valve
Ball Valve
Pinch Valve
Gate Valve
Ind icator
reading
Percent closed
Fig. 4.
Plot of indicator r ea ding versus percent closed
The vel ocity in feet per second was det ermi ned by converting
Qm from gallons per min ute to cubic feet per second and
div i d i n g by the area in square feet, or
gpm
448.8
x 4 x 144
".ELHl1x
„cf s.
'in I
.TtzI
x D2
W
where D is the dia mete r of the pipe in inches.
In this study chip con ce n t r a t i o n was exp ress ed as a
ratio of the volume of solids to the total mix ture volume.
(6)
-20-
C o n c e n t r a t i o n of the mi x t u r e was de t e r m i n e d from the clear
water flow.rate, Q , and the flow rate of the mixture, Qfflt as
shown below.
The volume of water in the mixture is equal to
the total volume of the mix ture minus the volume of chips in
the mix ture, or
Volume HgO = Volume Mixture - C o n c e n t r a t i o n x Volume Mixture.
Since the flow rates are in terms of volume per unit of time,
this can be e x p r e s s e d in terms of the flow rates, Qffl and Q ,
or
= Qm - CQm
where C is the con centration.
R e a r r a n g i n g gives
QL
M u l t i p l y i n g by 100 gives C as the vol umet ric c o n c e nt ratio n as
a p e r c ent age of the total volume, or
Q r.,
100.
(7)
CHAPTER
IV
APPARATUS DESCRIPTION
The apparatus de s c r i p t i o n will be given in four parts:
(I) ope rati on of the pipe line system,
maj or com pone nts of the system,
(2) d e s c r ip tion of the
(3) des crip tion of the test
section and its components, and (4) des crip tion of the valves
tested.
A.
O p e r a t i o n of the pipe line system
A sch ematic di a g r a m of the pipe line system is shown in
F i g . 5.
Because of the need for var y i n g the con cent ratio n of
wood chips in the mixture,
two sep arate systems are required
to supply chips and water.
Water is initially pumped from a
sump under the l a b orat ory floor to a constant head tank on
the roof by an aux il i a r y 6-in. centrif ugal pump.
A 3-in.
dia meter line from the tank feeds water to the m i x tank as
shown in Fig. 5.
The clear water flow rate is m e a s u r e d by a
3-in. m a g n e t i c flow met er in the supply line.
is used for co n t r o l l i n g the clear water supply.
A gate valve
O ve rflo wing
of the tank is pre ve n t e d by an a u t o m a t i c shutoff valve o p e r ­
ated by a float sensing the level of water in the tank.
The plastic chips are stored in the chip bin as s h o w n .
They are fed into the m i x tank via a short conveyer belt.
The supply of chips is reg ulat ed by a sliding gate on the
storage bin.
C o n c e n t r a t i o n of the m ix ture can thus be
-
22-
11
I.
2.
3.
4.
5.
6.
7.
8.
Long Branch
Short Branch
3-Way Valve
R o t atin g Screen
Water Col lect ion
Chip Storage
Mix Flow Meter
Supply Gate
F i g . 5.
9.
10.
11.
12.
13.
14.
15.
16.
Control Valve
Pump and Motor
Console
Conveyer
Mix Tank
Ove rflo w Valve
Control Valve
Water Flow Meter
Sch emat ic of pipe line system
— 23 ”
r e g u l a t e d by c o n t r o l l i n g the amounts of water and chips fed
into the m i x t a n k .
A hor izon tal 4-in. alu minu m pipe carries the mixture
from the m i x tank to the main p u m p .
A vertical section
connects the pump dis charge to the pipe line which hangs near
the roof of the laboratory.
The dis charge of the mix ture of
wat er and chips from the main pump was con trol led by varying
the speed of the pump motor,
A d i a p h r a g m valve in the
ver tical section was also used for control purposes.
Flow
rate of the mi x t u r e is m e a s u r e d by a 4-in. m a g n e t i c flow
met er above the control valve.
The pipe line is made up of
two parallel branches con nect ed to the pumping apparatus by
t h r e e - w a y valves as shown in Fig. 5,
The valves tested in
this study were ins tall ed in the short branch.
The pipe line dischar ges into the upper end of a tilted^
rotating,
c yl indr ical screen which separates the chips from
the water.
Water is col lect ed in a bin beneath the screen
and r e t u r n e d to the lab orat ory sump for recircu latio n.
Chips
are tumbled out of the lower end of the screen and into the
chip storage bin from which they are fed into the system
again.
B.
Sy s t e m components
All operations of the system are con trolled from the
control console which is shown in Fig. 6.
main pump motor,
Switches for the
c o n v e y e r , rot a t i n g separation screen, flow
-24-
Fig.
6.
Control console
charts , and a rheostat for varying the speed of the main pump
motor are mou n t e d at the left on the console top.
Fuse and
starter boxes for the motor are m o u n t e d below the console
top.
The two large radial charts are Foxboro Dyn alog recorders
which give a direct reading in gallons per minute (gpm) of the
flow rate of the clear water in the supply line and the flow
rate of the mixture of chips and water being di s c h a r g e d from
the p u m p .
-25-
To the right of the flow charts is a m a n o m e t e r tube
showing the level of water in the m i x tank.
Also to the
right in Fig 6, within easy reach of the o p e r a t o r , are the
gate on the chip storage bin and the clear water control
valve.
The control valve on the dis charge side of the pump
is vis ible in the picture to the left and rear of the console.
The i n s t r u m e n t a t i o n below the flow charts is part of a system
linked to a Hew lett Pac k a r d 211 6 Com pute r used in other
studies.
The main pump used in the system is an All is - C h a l m e r s
4 x 4 x 9.5-in. cen trif ugal p u m p .
The pump was equ ipped
with a f l a t - b I a d e d i o p e n -fa ced imp eller (NSX t y p e ) which is
e s p e c i a l l y suited to h a n d l i n g s o l i d - l i q u i d mixtures.
Power
to the pump was sup plie d by a 15 hp I 150/2600 rpm General
E l e c t r i c 240 volt, d-c shunt wound motor.
Flow rates of the clear water supply and the mixture
were m e a s u r e d by 3- and 4-in. Fox boro D y n a l o g , m a g n e t i c flow
t r a n s mi tters con nect ed to the Fox boro model 9 6 5 OC recorders
on the console.
O p e r a t i o n of the flow meters is based on
Far aday 's law of e l e c t r o m a g n e t i c induction.
Flu id moving
through a m a g n e t i c field in the m e t e r induces a voltage
pro p o r t i o n a l to the velocity.
This voltage is t r a n s mi tted
to the rec o r d e r which is c a l i bra ted to give a r e a d i n g from
O to 400 gallons per minute.
cent of full scale accuracy.
The m a n u f a c t u r e r claims +1 p e r ­
-26-
The plastic chips used in the study were made by
Com merc ial Plastics of Chicago.
The nominal dimensions of
the chips are 1/2 by 3/8 by I/IO in.
chips were used.
Two types of plastic
One type, red in color, had a specific
gravity of 1.04 and was made of Cycolac.
The other, blue in
color, had a spe cific gravity of 1.05 and was made of
Ethocel.
The pipe used in the system had a nominal inside diameter
of 4 inches.
Clear acrylic plastic pipe was used extensively,
but a l u m i n u m pipe was used where higher strength was needed.
V i c t a u l i c couplings were used to join sections of pipe.
C.
Test section and components
The valve test section was located on the p r e v i ou slym e n t i o n e d "short b r a n c h " of the pipe line system.
of the test section is shown in Fig. 7.
ope ra t i n g pla t f o r m
A plan view
The test section,
m a n o m e t e r b o a r d , and camera were all hung
from the roof trusses of the laboratory.
The entire test
section was made of 4-in. ID clear, plastic pipe.
The re­
mai nder of the short branch was made up of a 4-ih. ID flexible
rubber hose on each end of the test section con nect ed by 4-in.
S m i t h - B l a i r flexible couplings.
The section ups t r e a m of the
valve con tain ed four pressure taps spaced as shown in Fig. 8.
The d o w n s t r e a m section contained 10 pressure taps.
Data from
taps I through 4 were used to e s t a b l i s h the ups trea m linear
por tion of the dim en s i o n l e s s h y d r aul ic grade line and from
-27-
Valve
a
O=
6
O
Ope rating
platform
Camera
Man ometer
board
Fig. 7.
Plan view of test section
taps 9 through 14 for the d o w nstr eam section.
The pipe was
jo i n e d to the test valves with 4-in. Smith-B lair universal
flanged c o u p l i n g s .
A typical pre ssure tap is shown in Fig. 9.
pressure vents,
pipe,
The three
1/8 inch in diameter, are located around the
120 degrees apart.
Two -inch square plastic blocks were
shaped to fit the cur vature of the pipe and glued over the
pressure vents.
These blocks were drilled and threaded to
accept I m p e r i a l - E a s t m a n 1/4-in. brass tee sections.
The three
tee sections were then con nected by l/4-in. OD tygon tubing.
A fourth tee con nected the pressure tap to the line from the
m a n o m e t e r board.
Fig.
10 shows the differe ntial man ometer board used in
this study for d e t e r m i n i n g the h y d r aul ic grade line along the
test section.
A dev elop ment of the man omet er board equations
is given in A p p e n d i x B.
Tubing from the pressure taps in the
test section was con nect ed at the top of each tube of the
Upstream Section
i
to
CD
I
5 6 7 8
Q Q Q Q
s
k
3
0.5 '
Q
Q
- 3 S1 .0 '
Q
G
- I @
4.5'
Q
2 @
5.0’
D o w nstr eam Section
Fig. 8.
Loc ation of pressure taps in test section
-29-
Brass
Tygon
r" tubing
Fig. 9.
Typical pressure tap construction
m a n o m e t e r board through an Imp e r i a l - E a s t m a n brass needle
valve ( H ) .
The tubes of the m a n o m e t e r board were 48 inches
long and made of l/4-in. OD glass tubing.
At the top of each
tube was a tee section, one branch connected to the tube, one
branch con nect ed to the pressure inlet valve, and the third
con nect ed to a 1/4-in.
air from the tubes.
5/8-in.
Nupro purge valve used for bleeding
The m a n i f o l d was made up of a section of
ID copper tubing with silver soldered Swage Iok fittings
c o n n ect ing to the glass tubing.
Sta ndar d globe valves (C) and
(D) are used to divide the m a n i f o l d when either or both of the
-30-
Fig.
10.
Dif fere ntial man om e t e r board
me r c u r y loops (F) and (G) were in u s e .
The two mer c u r y loops
were con nect ed in a separate stainless steel m a n i f o l d (E).
Tank (A) is a res er v o i r for the carbon t e t r ach lorid e used
in the m a n o m e t e r tubes.
The carbon tet rach lorid e was colored
with red Sudan III dye for easy visibility.
m a n i f o l d through a globe valve ( B ) .
Fluid enters the
-SiSim u l t a n e o u s readings of all tubes on the m a n o m e t e r board
were made by taking photogr aphs of the manometer.
The camera
used in this study for r e c o r d i n g data was a Leica MS with
35 mm lens and light met er attachment.
an ASA number of 400 was u s e d ,
Kodak T r i - X film with
The high speed of the film
a ll owed a shutter speed of I/60 sec at lens openings of
f5.6 to f 16.
No art ific ial light was u s e d ; the natural light
in the laboratory, though somewhat variable, was sufficient.
D.
Valves tested
Four commercial valves were tested in this study:
ball, t ap ered p l u g , and pinch t y p e „
v-ball,
The previous Iy-me ntio ned
gate valve was con s t r u c t e d of ple xigl ass in the laboratory.
Fig.
11 shows the pri ncip le of ope rati on of each valve and the
general shape of the ope ning through the valve.
The ball valve m e c h a n i s m consists of a ball with a 4-in.
dia mete r cylindr ical hole through it.
Rotation of the ball is
about an axis p e r p e n d i c u l a r to the flow and in a horizontal
direction.
The plug valve operates in the same way as the
ball valve, the d i f fere nce being that a plug in the shape of a
t r u n c a t e d cone with a tapered r e c t a n g u l a r hole through it
replaces the ball.
The pinch valve m e c h a n i s m consists of a
heavy rubber sleeve, the bottom half of which is forced to the
shape of a smooth weir.
The upper half of the sleeve moves
v e r t i c a l l y in operation, p r o v idi ng a pinching a c t i o n .
The
v-ball valve m e c h a n i s m consists of a portion of a spherical
-32-
P r i n c i p l e of Ope ration
Flow Area
Ball Valve
Fig.
11.
Sch em a t i c diagrams of valves tested
-33-
shell with a V - s h a p e d notch in one side.
Rot ation of the
V - n otched shell is about an axis p e r p e n d i c u l a r to the flow
and in a vertical direction.
The gate valve consists of a
cir cular gate o p e r a t i n g in a vertical direction p e r p end icula r
to the flow.
All of the com merc ial valves except the plug valve were
p r o vide d with p n e u mat ic operators.
For simplic ity of o p e r ­
ation, the p n e u mat ic operators were removed and some form of
man ual operator installed.
A radial ope rating lever was in­
sta lled on the v-ball and ball valves similar to the one
r e c e i v e d with the plug valve.
All three were closed from the
wide open pos itio n by r o t atin g the ope rati ng lever through an
arc of about 90 degrees.
The pinch valve r e q uire d a screw-
type ope rato r with a stem travel of 2.5 in.
An indicator was ins talled on each valve for gauging the
area of opening^
Each of the indicators read from O to 16,
in 16 equal divisions from closed stop to open stop.
The
pinch valve ind icator ope rated v e r t i c a l l y with res pect to the
stem travel of the screw operator.
The indicators on the
other three valves were con nected to the ope rati ng lever and
had radial scales.
The gate valve tested in 1965 had a screw-
type operator and indicator similar to the ones used on the
pinch valve.
CHAPTER V
TEST P R O C EDU RE
The test p r o c edu re was made up of three parts:
(I) p r e p ­
aration of e q u i p m e n t , (2) data collection, and (3) data r e ­
duction.
A.
P r e p a r a t i o n of equipment
Data from the m a n o m e t e r board des crib ed in the preceding
chapter was used in d e t e r m i n i n g
„
T h u s , it was one of the
most important pieces of equ ipment used in c o l l ect ing data and
as such it r e c e i v e d con side rable attention.
Before each valve
t e s t , the m a n o m e t e r tubes were drained, partial Iy d i s a s s e m ­
bled, and scr ubbe d with a small nylon brush.
At every other
cleaning, the tubes were flushed with acetone to remove
har d e n e d deposits before being rin sed with water.
The mercury
tubes were d i s a s s e m b l e d and cleaned in a similar m a n n e r .
Before r e f i l l i n g the m a n o m e t e r board, the carbon tet rach lorid e
and m e r c u r y were fil tered to remove impurities.
After cleaning, the tubes were rea s s e m b l e d on the m a n o m ­
eter board and all tubes filled with water to eli mi n a t e air
from the, system.
The r e s e rvo ir tank was then filled with
colored carfron tetrach lorid e.
By ope ning the valve
(B , Fig. 10) below the reservoir,
fluid was all owed to enter
the m a n i f o l d and rise in the glass tubes, d i s p l a c i n g the
water.
The tubes were filled to a level of app ro x i m a t e l y
-35-
24 i n c h e s .
Mer cury was added to the two mer cury loops through
a sta ndpipe att ache d to the mid dle of the mer cury manifold.
Air bubbles in the m a n o m e t e r system affect the level of
fluid in the m a n o m e t e r tubes which results in incorrect values
of d i f f e re ntial pressure.
T h u s , after all tubes in the
m a n o m e t e r were filled to the des ired level with fluid, flow
was e s t a b l i s h e d in the test section which caused air bubbles
to be driven from the manometer.
By opening the purge valves
at the top of each m a n o m e t e r tube, any air bubbles in the
system were forced out by the pressure.
Tes ting began after
all air bubbles were e l i m i n a t e d from the system.
Air bubbles
which p e r i o d i c a l l y ent ered the m a n o m e t e r system during the
testing were removed, when discovered, by the a f o r e m e n t i o n e d
method.
Acc urat e flow rate m e a s u r e m e n t was essential to the test
p r o c e d u r e . . The a c c u r a c y of the flow rate r e a d i n g s , from
whi ch values of c o n c e n t r a t i o n and actual vel ocity were d e t e r ­
mined, was dep ende nt on the cal ibra tion of the flow m e t e r s .
T h u s , before each valve test, the pipe line was div erte d to
dis char ge into a c a l ibra ted tank to check the flow recorders.
Clear water was used for cal ibra tion p u r p o s e s .
The procedure
inv olved c o n v e r t i n g the dis charge from pounds of water for a
m e a s u r e d time interval to a gallons per minute flow rate.
The
m e a s u r e d flow rate and the flow rec orde r reading were then
com pare d and the rec orde rs adj uste d accordi ngly and re c h e c k e d .
-36-
C a l i b r a t i o n checks were made at flow rates of app ro x i m a t e l y
350, 250, and 100 g p m .
With little effort the flow charts
could be made to agree to within about one gallon per minute
of the cal cula ted discharge.
The laboratory water supply system was also cleaned
per iodically.
Twice during the testing, the laboratory sump
was drained, hosed clean, and r e f i l l e d with fresh water.
C o l l e c t i o n screens were cleaned of chips and other debris
w as hed into the sump from the laborat ory floor.
Screens above
the water col lect ion bin ^ under the discharge end of the pipe
line, were also cleaned of spilled chips and foreign m a t e r i a l .
B.
Data col lect ion procedure
The testing phase of this study involved col lect ing valve
head loss data for dif ferent flow conditions set up by varying
the velocity, valve closure, and chip concentration.
Data was
col lect ed at nominal vel ocit ies of 10, 8, 6, and 4 fps for
each valve tested.
These velocities correspond to flow rates
of 382, 305, 229, and 153 g p m .
For each vel ocity the valves
were tested at three or four dif fere nt closures.
All valves
were tested in the wide open and 50 percent closed position
for purposes of c o m p ari ng the eff ec t i v e n e s s of the different
valves in passing a mi x t u r e of wood chips and water.
Each
valve was also tested at one or two other closures, depending
on the ch a r a c t e r i s t i c s of the valve.
Tests were run with
O i 10, and 20 percent chip con c e n t r a t i o n for each given
-37-
v e l ocit y and valve c l o s u r e .
The 1965 gate valve tests were
c o n d uct ed at con ce n t r a t i o n s of O 6 5, 10, 15, and 20 percent.
The data col lect ion p r o c edu re involved two m-en.
One man
ope rate d the system and r e c orde d flow rates from the control
console.
The other man ope rate d the camera, m a n o m e t e r board,
and valve.
velocities.
Tests were run in order of high vel ocit ies to low
The valve was ini tially set in the wide open
pos itio n as the ope rato r e s t a b l i s h e d a flow of 10 fps at zero
concent ratio n.
While the flow con dition was stabilizing, the
cam eraman p r e p a r e d i d e n t i f i c a t i o n tags and placed them at the
bot tom of the m a n o m e t e r board.
These tags ind icated valve
type, date of test, m a n o m e t e r board arrangement, velocity,
valve closure, and con centration.
Each pho togr aph of the
m a n o m e t e r board was thus identified.
When a steady flow was est ablished, the ope rato r signaled
the cam eraman and began r e c o r d i n g ten observa tions of mix and
clear water flow rates on p r e v i o u s l y - p r e p a r e d data sheets.
As each ob s e r v a t i o n was made, the cameraman was not ifie d and
a picture of the m a n o m e t e r board was taken.
When ten o b s e r ­
vations were com plet ed for 0 p er cent concentration, the
ope rato r added chips to the system and reduced the clear water
flow to get 10 percent con ce n t r a t i o n at the same velocity while
the cam eraman changed the c o n c e n t r a t i o n ide nt i f i c a t i o n tag on
the man omet er.
When steady flow at 10 percent con cent ratio n
was establi shed* another series of ten observa tions were
-38-
re c o r d e d .
The chip con ce n t r a t i o n was next inc reased to 20
percent by the ope r a t o r and ten more observa tions were made.
The system was then cleared of chips as the cameraman set the
valve to the next closure and changed i d e n tif icati on tags.
A
series of ten o b s e r va tions were then made at that valve
set ting for O 1 10, and 20 percent concentrations.
This process
was r e p e a t e d for each desired valve closure.
After tests were made for each valve closure at 10 fps,
the valve was opened to its wide open position.
The flow
rate was then red u c e d to 8 fps and the test pro cedure repeated.
Tests were run at 6 and 4 fps in the same manner.
At the end
of each valve test, three reruns at some given velocity, valve
closure, and c o n c e n t r a t i o n were made as a check on r e p e a t ­
ability.
Values of
obt ained from the rerun data were
gen er a l l y found to agree with those obtained from the regular
test data.
During tire testing of each v a l v e , observations
wer e also made on the general ope ration of the valve and the
ch a r a c t e r i s t i c s of the flow imm edia tely upstream and dow n­
stream of the valve.
C.
Data red uc t i o n
All of the tests on each valve were com pleted in about
two days.
At the end of each day's testing, the exposed film
was taken to a local p h o t o g r a p h i c shop for ove rnight p r o c ­
essing.
In this way any data lost due to pho t o g r a p h i c errors
could be rerun the next d a y .
The films were d e v e lop ed into
—
39
—
35 mm neg ativ e strips which were p r o j ect ed onto a screen with
a film strip projector.
Two und er g r a d u a t e assistants read the
m a n o m e t e r levels in each frame of the film strips and rec orde d
the l e v e l s , along with c o r r e s p o n d i n g m i x and clear water flow
rates from the console operator's data sheets on FOR T R A N
coding f o r m s .
A sample coding sheet with data is shown in
Chapter 6.
The data was then pun ched on standard data pro cess ing
cards.
These cards and a F O R T R A N source program (Appendix D)
d e v e l o p e d for data r e d u c t i o n were sub mitted for pro cess ing
on the SDS Sigma 7 com puter in the Montana State Uni vers ity
C o m p u t i n g Center.
The computer output for one test run at
a given velocity, valve closure, and chip con cent ratio n is
shown in Chapter 6.
Generally, two or three runs were re­
quired before all m i s t a k e s and bad data were e l i m i n a t e d and
final head loss results were obtained. . Bad data was dis­
covered by the m et hods dis cu s s e d in A p p e n d i x C .
CHAPTER VI
DATA ANALYSISThe analysis of data col lect ed in this study includes the
following:
data,
(I) com puter operations,
(2) p r e s e nt ation of
(3) flo w pictures, and (4) summary of valve c h a r a c t e r ­
istics.
A.
C o m pute r operations
Data from the sheets pre pare d by the console operator and
from the pictures of the m a n o m e t e r board was rec o r d e d on
F O R T R A N coding sheets as shown in Fig.
12.
The sample data
shown is for one ball valve test at 10 fps, 25 percent valve
closure, and 0 percent concentration.
The first six lines
contain m i s c e l l a n e o u s inf orma tion as exp lained by the comment
cards in the computer pro gram (Ap pend ix D ) .
The next 18 lines
contain obs erve d data, each pair of lines being one o b s e r ­
vation.
Columns I through 12 of the first line of each pair
contain the flow rates Q
the flow recorders.
and Q
in gpm which were read from
Columns 13 thr ough 72 are filled with
the m a n o m e t e r tube fluid levels for pressure taps I through
10.
The first 24 columns of the second line contain man ometer
levels for taps 11 through 14 while columns 25 through 36
contain the levels of fluid in two mer cury tubes.
A computer p r o g r a m , written in F O R T R A N II l a n g u a g e , was
d e v e l o p e d for ana ly z i n g the above d a t a .
The com puter was
Party
Date
/g
Col Sc.
5
Soi - B all Ihnze
CSfimfiL e )_____
10
15
20
35
30
25
40
45
50
55
60
7
[5
/,.,8 ,3 ,3 1 4", ,4 / lo , , , , I , , , , I , , . , I . , , . j
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. ■ /.0 .3 .8 3 --M .L .L V ,ft,L V ,- . 7
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18
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• * , • ,0, , Iflz, 7,. m5 i , , J.YI * IY,5*, I Y3, • ,3*I ,
Fig. 12.
, /,9, .lv. . . .
3^1» 12 I 1Si 6, e, 7, A, I , I I I I I I • I I I I I , I I I
F O R T R A N coding sheet and sample data
, ,/,f i.lv . . . .
— 42 —
thus p r o g r a m m e d to per f o r m the f o l l o w i n g sequence of operations
in.the c o m p u ta tion of K^:
(a)
read the m i s c e l l a n e o u s information and observed
data for a given v e l o c i t y , closure, and concentration,
(b)
compute the average m a n o m e t e r r ea ding for
each tap and the average c o n c ent ratio n from the observed
flow rates,
(c)
compute the statist ical probable error of
each average m a n o m e t e r rea ding and the average con­
centration,
(d )
compute d i m e nsi onles s differe ntial heads
from average m a n o m e t e r readings,
(e)
compute slopes and y - i ntercepts of upstream
and d o w n s t r e a m portions of the dimensi onles s grade line
using regression,
(f)
compute the c or rela tion coefficient and
est imat e of var iance about reg ress ion for each line,
(g)
compute the loss coefficient,
, as the
d i f fere nce b et ween the two lines at x = X V A L , and
(h)
print out the input data and .results of
all c a l c u la tions and recycle to (a) for the next set
of test data.
The computer output for the data shown in Fig.
shown in Fig.
13.
12 is
Two pages of output were req u i r e d for each
test at a given velocity, valve closure, and concentration.
— 43 —
-»..' .... . -.«d_
$i^***^^* x«*<r8
%:,%%%:,
"»
-K *"
5*T *•v t-«x
" *- '
- " ' "» '*
-
■
■
WItItf
■
'
.
■
.
.
.
.
.
■
■
-
,
,%.» C-I
*».*
i».» I)'* w«» '*«?
. ««,. %».. ,.,e, U f I* «M T M.» *.» **«# $#«#W«* *»«» **«»W,' *»» ** » I* *#«»M T
T
'M,
T
m .
*
.
M
r.' M.T .
M.T c*.
-s««..*.fcj»
S i.* t» .? 8 * . r » *.» »»«* i i . s s»*« i*« » »*<’ t»«» «»<* *»•» « » * ♦»*’ * * • * w *
.5.5
* i*«9
„.
WM. f . M T
n.$ tt.t «.» 0,1%».$ « «** )M »
*»!?
%'* *" '*"* " * **"'
U « tT .» M t W .« I * . * l» * M l M M IT M I * . * # * M * ' » * * , »
*TMMt T M 4 « T M
I .T r . T
M m/I#
M T M .T , M M M M M M M ,T M
T M M «« #MT
;
T ,.,
.,M
„ . ,
M .T
'
TW
.2
:
%
'
MTMfTt — TTTMTi*
..
-!-,rrnr-T
.VO MW# T T k T C liT
I
I T M M TT T M TCC
"Mkw* "VUfiy
Fig.
^ I* «:*m%
13.
'***
Sample computer output
-44-
Input data and averages are pri nted on the first sheet while
the loss c o e f f ic ient results are p ri nted on the second sheet
as s h o w n „
B„
P r e s e n t a t i o n of
data
E x p e r i m e n t a l values of
and cor re s p o n d i n g actual v e l o c ­
ities and c o n c e n t r a t i o n s for tests run on the v-ball valve are
s u m m a r i z e d in Table I.
The same data for the plug, ball,
pinch and gate valves is given in Tables IV through VII in
Appendix E .
Raw data, computer output lists, and other i n f o r ­
ma t i o n p e r t a i n i n g to this study may be found on file in the
D e p artm ent of Civil E n g i n e e r i n g and En g i n e e r i n g Mechanics,
Montana State University, B o z e m a n , Montana.
The v a r i a t i o n of the loss coefficient with velocity at
0, 10, and 20 percent con ce n t r a t i o n s for the various valves
is shown by the log-log plots in Fig.
14.
The clear water
loss coe ffic ient for each valve tends to be constant with
res pect to vel o c i t y except for the gate v a l v e .
also indicate that
The graphs
appears to vary somewhat with velocity
for higher chip con centrations.
H o w e v e r , for each valve,
tends to app roach some constant value for vel ocit ies greater
than about 6 fps.
For design purposes, t h e n ,
can be
ass umed constant with respect to vel ocit y for a given closure
and per cent chip concentration.
The loss coefficient,
, was also observed to increase
with i n c r e a s i n g v o l u m e t r i c chip c o n c e nt ratio n for a given
TABLE
Valve
V
4 fps
C
I
Summary of Com pute d Results - V-Ball Valve
8 fps
6 fps
V
C
V
C
KL
KL
KL
V
10 fps
C
KL
3.932 0.00 1.033 5.903 0.00
9.68
43. 3% 3.9 56 10.17 1.320 5.911
5.885 19.59
.972 7.877 0.00
1.089 7.861
9.88
1.303 7.869 19.63
.901 9.880 0.00
.981
1.023
1.166 9.867 20.50 1.198
0.00 1 .661 5.903 0.00
9.36
9.93 1.949 5.895
5.877 19.48
1.693 7.840 0.00
1.851 7.877 10. 19
2.2 62 7.911 20.36
1 .663
1.864
2.121
62.5%
5.908 0.00
5.92 7 10. 10
5.909 19.91
4.764 7.859 0.00
4.700 7.846 9.36
5.838 7.914 20.38
4.592 9.843 0.00 4.853
5.011
5.498 9.872 20.55 5.769
75.0%
5.916 0.00 20.104 7.888 0.00 19.951
5.924 10.33 19.801 7.835 9.24 19.197
5.897 19.85 22.604 7.856 20.07 21.305
3.940
50. 0% 3.948
Repeat
Repeat
5.867 9. 18 1.867 7.856 20.07 5.885
62.5% Closed
5 0 . 0 % Closed
10.0
10.0
50. O K
Ball
50. 0%
Gate
Pinci
I .Ol-7
8 9
10
Vel ocity (fps)
8 9 10
Velocity (fps)
Fig.
14.
Plot
of
versus
velocity
at different
concentrations
10.0
a. Ball A
Gate (a8.9
2 . 0< r
Ba 1 1»
i
nch +
Percent Concent ratio n
Fig.
15.
Plot
of
versus
concentration
at 50 percent
closure
-
48-
valve closure as shown by the s e m i-lo g plots in Fig.
15.
Similar trends were obs erved for each valve at any given
percent closed.
For any set of t w o - d i m e n s i o n a l data (x , y)
that plots as a str aight line on a sem i-log graph, an equation
of the form y = ae I)X can be derived where a is the y-inter cept
and b is the slope of the line.
A set of data (C ,
) was
obt aine d at each valve closure for the valves tested in this
study.
P l o t t i n g this data gave a set of straight lines for
each valve similar to and inc luding those in Fig.
15.
By
a v e r a g i n g the slopes of these lines, an empirical equation of
the f o l l owi ng e x p o n en tial form was dev eloped for each valve:
(KL ) c _
" V o
bC
(8 )
= "
In this equ atio n b is the average slope, C is the variable
c o n c e n t r a t i o n in decimal form,
( K ^ ) q is the clear water head
loss c oe ffic ient or y-i n t e r c e p t for any valve c l o s u r e , and
( K ^ ) c is the loss c oe ffic ient for a given concentration.
In
other words, this equ atio n gives the approximate value of the
loss coe ffic ient as a function of con cent ratio n and the clear
water loss c o e f f ic ient at some valve closure.
Values of b
are given in Table II.
Ano t h e r ap p r o x i m a t e r e l a t i o n s h i p for p r e d i c t i n g
also developed.
Values of (K^) / ( K l )
was
computed from the
e x p e r i m e n t a l data for each valve are plotted against con­
cen trat ion in Fig.
16.
Straight lines fitted to this data
2.0
2.0
tV-Ball
I
vO
Ball
Fig.
16.
Plot
of I V c
c k L 1O
versus
c o n c en t ra tion
— 5 0—
can be e x p r e s s e d by linear equations of the form
I V c
ckL
1.0 + mC
(9)
jO
where m is the slope of the line.
Values of m for this
equ atio n are also tab ul a t e d in Table II.
T h u s „ once the clear
water loss coeffic ient for a given closure is determined
either an e x p o n en tial or linear r e l a t i o n s h i p can be used to
app r o x i m a t e the c o r r e s p o n d i n g loss coefficient for any con­
centration.
Table II.
Emp iric al values of b and m for K l e q u a t i ons
Valve Type
E x p o n en tial
Equation
Linear
Equation
V-Ball
Ball
Plug
Pinch
Gate
1.00
0.83
1.02
1 .78
1.57
1.30
1.40
. 92
1.80
2.30
S e m i - l o g plots of (K l ) q versus percent valve closure for
the various valves are given in Fig.
17.
These curves , when
used with the r e l a t io nship s dev el o p e d above, provide a p p r o x i ­
mate values of the loss coefficient, K L , at a given valve
closure and chip con ce n t r a t i o n for design purposes.
These
methods give values of K l that gen er a l l y agree to within
10 percent of the empirical d a t a .
Gite
10.0
Ball
10.0
—
51
—
Percent Closure
Fig.
17.
Plot
Percent Closure
of
(K l )q versus
percent
closure
-52-
C.
Flo w pictures
Fig. 18 is a picture of the test section car rying a flow
of 153 gpm (4 fps) with a chip c o n c ent ratio n of about 5 percent
just ups t r e a m of the plug valve.
the picture.
Flow is from left to right in
Under these conditions, the chips settle and
move along the bot tom of the pipe in what is r e f erre d to as a
"sl iding bed."
The picture in Fig.
19 shows app ro x i m a t e l y the
same flow conditions just d o w n s t r e a m of the plug valve, which
was in the wide open position (4.4 percent constriction).
Since the sli ding bed is only slightly disturbed, minor
t u r bule nce is evident.
For comparison, Fig. 20 shows the
effect on the flow caused by the plug valve when 50 percent
closed.
The sli ding bed is com plet ely disrupted,
a high degree of turbulence.
indicating
This turbulence was observed to
increase with v e l ocit y as well as valve closure.
At 75 percent closed, the ope ning through the plug valve
was in the shape of a na r r o w slit.
The width of this slit
was slightly greater than the largest dimension of the chips
used.
As a result, plu gging of the pipe line occ urre d for
flows with r e l a t i v e l y low chip concentrations.
Fig. 21 shows
the b e g i n n i n g of a plu g-up just u p s trea m of the plug valve at
4 fps, 75 percent closed, and about 8 percent concentration.
A mass of chips can be seen in the picture piled up in the
pipe just to the left of the valve coupling.
-53-
Fig.
Fig. 19.
18.
Picture of sliding bed of
chips ups trea m from valve
Pic ture of tur bule nce dow nstr eam from
plug valve, 4.4 percent closed
-54-
Fig. 20.
Fig. 21.
Picture of turbule nce dow nstr eam from
plug valve, 50 percent closed
Picture of b e g i n n i n g of "plug-up"
-55-
D„
Summary of valve cha ract erist ics
A chart of valve cha rac t e r i s t i c s is given in Table III
for purposes of c o m p ari ng the valves tested in this study.
The "control curve" refers to the plot of indicator reading
versus p e r cent age closed given in Fig. 4.
A perfect control
curve would be linear from the wide open position to the
100 percent closed position.
"Wide open per cent age closed"
is the amount of c o n s t ri ction in the pipe line caused by the
valve when in the wide open position.
self e x p l a n a t o r y .
The r e m a ini ng items are
TABLE
III
Valve Charact erist ics
Ball
Valve
Plug
Valve
V-Ball
Valve
Pinch
Valve
Gate
Valve
Control curve
Good
Good
Good
Poor
Fair
Wide open % closed
0.0%
4.4%
43.3%
28. 5%
0.0%
K l @ wide o p e n , 0% chips
0.020
0. 100
0.970
0. 120 0.014
K l @ 5 0 % c l o s e d , 10% chips
6.60
6.10
1.70
0.90
O b s t r u c t e d str eaml ine flow
Yes
Yes
Yes
No
Yes
Pockets or shoulders
Yes
Yes
Yes
No
No
Flow in either direction
Yes
Te s
No
Ye s
Yes
Tight shutoff
Yes
Yes
Yes
Ye s
Yes
Chip she arin g ability
Yes
Yes
Yes
No
No
4.30
5 6-
CHAPTER VII
C O N C L U S I O N S AND R E C O M M E N D A T I O N S
As predicted,
an increase in the loss coefficient,
,
was obs erve d for each valve as the degree of con stri ction in
the pipe line or valve closure was i n c r e a s e d .
values of
The observed
for clear water flow through the gate valve are
a p p r o x i m a t e l y the same as those rep o r t e d by H . Rouse (8).
R o u s e ’s plug valve
values are c o n s i de rably higher than the
plug valve data obt a i n e d in this study.
This probably is due
to dif fere nces in the geo metric c o n f igu ratio n of the p a s s a g e ­
ways through the valves.
At a given closure and flow rate,
was found to in­
crease with chip c o n c e n t r a t i o n as predicted.
For the various
valves tested, the loss coe ffic ient at 20 percent chip c on­
cen trat ion was obs e r v e d to be gre ater than that for clear
water by factors ran g i n g from 1.18 to 1.46 times.
This is
contrary to the effects R . W . Ch a r l e y (I) observed for flow
through pipe expansions.
The valve head loss coeffic ients for clear water were
obs erve d to be constant with vel ocit y for a given valve
closure as predicted.
At higher concentrations,
increase sli ghtly with d e c r e a s i n g velocity.
greater than 6 f p s , h o w e v e r ,
tended to
For velocities
a p p r o a c h e d some constant value.
Thus, K l can be ass u m e d constant for design purposes „
-58-
The fol lowi ng r e c o m m e n d a t i o n s are made as a result of
e x p e rie nce gained in this study.
Improvements i^i this p a r ­
ticular study could be made by
(a) e l i m i n a t i n g v i c t aul ic couplings in the test
section which cause extra und esir able t u r b u l e n c e ,
(b )
using filters on the pressure inlets of
the m a n o m e t e r board to keep foreign mat erial from
e n t erin g the s y s t e m ,
(c )
using fluid in the m a n o m e t e r board that
has a p p r o x i m a t e l y the same spe cific weight as carbon
t e t r a c h l o r i d e but which is n o n c o rr osive and does not
dissolve the pla stic chips used for testing purposes,
(d )
c o n d uct ing tests with chips of different
specific gravities,
(e)
using different sizes of chips and/or pipe
and valves to check if the ratio of particle size to
pipe diameter is a factor, and
(f)
tes ting the various valves ins talled in
n o n c o n v e n t i o n a l positions.
To further enhance the technical knowledge of t r a n s ­
por ting c h i p - sh aped solids by pipe lines, the fol lowing
res earc h projects should be initiated:
(a)
a study in which the results of all prior
tests using pla stic chips are checked with tests using
actual wood c h i p s ;
-59-
(b)
a study aimed at d e t e r m i n i n g critical factors
such as flow rate and con ce n t r a t i o n for p r e d i c t i n g
"pl ug-u ps" caused by v a l v e s , e x p a n s i o n s , c o n t r a c t i o n s ,
e l b o w s , and other f i t t i n g s ;
(c )
a study to det er m i n e the corrosive effects
of wood chip brine on the pipe line, p u m p s , v a l v e s ,
and other c o m p o n e n t s ;
(d)
a study to develop a me t h o d for sep arat ing
the wood chi p-wa ter m ix ture at the pipe line t e r m i n a l ;
and
(e)
a study to det ermine methods for disposal
of the p o l lute d wood chip brine at the pipe line
terminal,.
60-
APPENDICES
APPENDIX A
ERROR ANA L Y S I S
The accuracy of e x p e r im ental work is limited by errors
inherent in the pro cedu res and app aratus used.
A dis cussion
of the errors a f f e c t i n g the results of this study will be
given in three parts:
(I) the effect of errors in m e a s u r e ­
ments , (2) errors due to regression,
and (3) sum mary of error
effects.
A.
The effect of errors in mea s u r e m e n t s
M e a s u re ments of flow rates were made to est ab l i s h con­
cen trat ion and vel o c i t y and of m a n o m e t e r fluid levels to
e s t a bli sh the loss coefficient.
I.
Flow rate mea s u r e m e n t s
Flow rate obs erva tions ave rage d less than +5 gpm
v a r i a t i o n from the des ired mean values.
The m a x i m u m flu ctu­
ations were obs erve d for low flow rates (+15 gpm) because of
pump instability.
Flu c t u a t i o n s also had a ten dency to in­
crease with i n c r eas ing chip concentration.
A c c o r d i n g to a
sta tist ical analysis (Ap pend ix C ) , the probable error in the
average c o n c e n t r a t i o n d e t ermi ned from ten flow rate o b s e r ­
vations was usually less than +0.5 percent (percent con­
centration) .
L a b o r a t o r y c al ibra tion of the flow recorders provided
acc urac y of +1 g p m .
An error of I gpm in the o b s erve d clear
water and mix t u r e flow rates would cause the computed 20 p e r ­
cent c o n c e n t r a t i o n to vary by +1 percent (percent concentration)
—
62
—
for 4 fps (153 g p m ) and +0.5 percent for 10 fps (362 gpra).
A
+1 gpm error in the mi x t u r e flow rate would cause an error of
+.03 fps in a vel ocit y of 4 fps and +.02 fps at 10 fps.
2.
Man om e t e r level m e a s u r e m e n t s
F l u c t u a t i o n of the levels of fluid in the man omet er
tubes was obs erve d to increase with valve closure and chip
con centration.
A c c o r d i n g to a s ta tist ical a n a l y s i s , the
probable errors in the average m a n o m e t e r readings were about
+.05 in.
The pro babl e errors in the observed fluid levels of
m a n o m e t e r tub.es con nect ed to pressure taps in the highly
tur bule nt region just d o w nstr eam from the valve were +.2 in.
Errors in the obs erved m a n o m e t e r fluid levels
r e s ulte d from couplings in the test section cau sing extra
t u r b u l e n c e , air bubbles in the m a n o m e t e r , small leaks in the
m a n o m e t e r , dirt in the m a n o m e t e r , and human errors.
An error of +.1 in. in the difference between the
o b s erve d fluid levels of two m e r c u r y tubes would cause the
dim e n s i o n l e s s d i f f e re ntial pressure head, D I M P H , to vary
by + . 4 1 6 at 4 fps and +.0 68 at 10 fps.
Mercury man omet er
tubes were used for high dif f e r e n t i a l pressures just dow n­
stream of the valve.
Thus, as shown by the equation developed
in A p p e n d i x B , the d o w n s t r e a m portion of the dimensi onles s
h y d r aul ic grade line is rel ated to the upstream line by the
DIMPH givten by the mer c u r y loop.
Any error in the DIMPH given
by the m e r c u r y loop raises or lowers the d o w n s t r e a m grade line
- 63-
with respect to the ups tream line causing
to be in error by
the same a m o u n t .
An error of +.1 in. in the difference between the
o b s erve d fluid levels for two carbon tet ra c h l o r i d e tubes would
cause the DIMPH to vary by + . 0 1 9 6 at 4 fps and +.0 032 at
10 f p s .
The effect on
of such an error in one DIMPH would
be small since the grade lines are es t a b l i s h e d by regression
with several points
B.
( ,
DIMPH^).
Errors due to regress ion
A c o r r e la tion coefficient, C O E F , and an estimate of
var ianc e about regress ion, E V A R , were cal cula ted as a measure
of the acc urac y of the straight lines fitted by reg ress ion to
the linear portions of the dim e n s i o n l e s s grade line upstream
and d o w n s t r e a m of the valve.
cussed in A p p e n d i x C .
The COEF and the EVA R are d i s ­
In this study values of the COEF for
the e m p i r i c a l l y e s t a b l i s h e d grade lines varied b e t w e e n 0.98
and 1.00.
A COEF of 1.00 indicates a perfect linear r e l a t i o n ­
ship bet ween the data, x. and DIMPH^.
Values of the EVAR
com puted for the grade lines ave rage d about .15 which indi­
cates the grade lines fitted the data quite well.
An EVAR of
0.00 indicates a perfect fit.
T h e o r e t i c a l l y the slopes of the two straight line p o r ­
tions of any given dim en s i o n l e s s grade line should be equal.
However, values of the two slopes varied at most by .002
because of e x p e r i m e n t a l errors in the data.
The upstream
— 64 —
y - i n t e r c e p t s should have always been 0.0 , but the actual
values varied by +.005.
The loss coefficient is given as
= (a + b x ) ^ - (a+bx)
From this equation it can be seen
.
that any error in either intercept, a, will directly affect
.
Likewise, any error in either slope, b, will cause an
error of bx in
C.
where x = X V A L .
Error summary
From the for eg o i n g discussion, the fol lowing max imum
error est imates can be tabulated:
Loss C o e f f ic ient
Percent C o n c e n t r a t i o n
0.5 % Pro babl e error
I .0% R e c orde r error
.416 Hg m a n o met er error
.020 CCl^ m a n o met er error
1.5% Total
.030 Reg ress ion slope error
.005 R e g ress ion intercept error
+.471 Total
The error in c o n c e n t r a t i o n was found to increase with de­
cre asin g vel ocity while the error in
crease with d e c r e a s i n g velocity,
in c r e a s i n g chip concentration.
was obs erve d to in­
inc reas ing valve closure, and
APPENDIX B
MAN OM E T E R BOARD
Ap/ $ i
Fluid
Flo wing
Fig. 22.
Carbon
Tetrachloride
-Ma ni fold
Mercury
S c h e m a t i c of d i f f ere ntial m a n o m e t e r board
—
6 6-
The m a n o m e t e r board used in this study was designed for
m e a s u r i n g dif f e r e n t i a l pressure heads between the first
pre s s u r e tap in the test section and other pressure taps d o w n ­
stream of the first.
Fou rteen pre ssur e taps were located
along the test section as shown in Chapter 4.
Fig. 22 shows
a sch em a t i c dif f e r e n t i a l m a n o m e t e r board and its rel a t i o n s h i p
to a typical section of pipe line and the hyd ra u l i c grade line
Bas ic a l l y two m a n o m e t e r board arr ange ments were used.
One
con figu ratio n, using carbon t e t r a c h l o r i d e (CCl^) in all
m a n o m e t e r tubes, was used when the
were all small.
A p / $ . as shown in Fig. 22
Because of the r e l ativ ely light weight of
CCl^ (specific gra vity = 1.59), dif fere ntial pre ssure heads
gre ater than 3 ft of water (1.3 psi) caused deflect ions ( A y )
too great for the length of m a n o m e t e r tubes used.
When high
dif f e r e n t i a l pre ssure heads occurred between two pressure
taps, such as across the valve or between points 2 and 3 in
Fig. 22, a' second a r r a n g e m e n t was used in which a U-tube
filled with m er cury was con nected to the two pre ssure taps.
D e f l e ct ions thus obt ained were smaller because of the greater
weight of mer c u r y (specific gravity = 13.55).
The man omet er
board used in this study was d e s igne d so that one or two
mer c u r y loops could be v a Ived into the carbon t e t r a ch lorid e
system when needed.
-
A.'
67
-
Dif f e r e n t i a l m a n o m e t e r board for low A p/g-
With flow from left to right in Fig. 2 2 ? the pressure is
gre ates t at the left end or point I and decreases with d i s ­
tance to the right.
T h u s , P ^ > P2 > P3 > P4•
pre ssure is constant,
Since the m a n ifol d
the dif ferent pressures at taps I through
4 force the m a n o m e t e r fluid to the levels s h o w n .
With valves A and B closed and valve C o p e n , the d i f f e r ­
ential pressures bet ween the pre ssure taps in the pipe line
are given directly by the levels of the carbon t e t r a ch lorid e
tubes and the m e r c u r y loop is isolated from the system.
Since the m a n i f o l d pressure is c o n s t a n t , the following
is true:
(IO)
R e a r r a n g i n g Eq.
10 gives:
Pl-P2 =
*f(%2-=l) +
( 11 )
Bc(^-Fl)
where p^-pg is the d i f f e re ntial pressure between taps' I and
2.
Also note that z 2_ z i = ~ ^ 2 " ' Srl ^ °
E g . 11 can now be
rew ri t t e n a s :
APl-2 = y2-?l (
#c-
( 12 )
Bf)'
The head loss for steady flow in a hor izon tal pipe of
constant diameter is e x p r e s s e d as a change in pre ssure head
where
Ap
is the change in pressure in psf and
^
is the
—
68
-
specific weight in pcf of the fluid flowing in the pipe.
T h u s , div idin g
A p 1_2 by
to give the head loss ,
, and
c o n v ert ing the m a n o m e t e r readings from, inches to feet gives;
A P 1-S
'
O 2- V
^c"
(13)
1-2
The spe cific weight of any fluid may be exp ress ed as ■
I
W
(S4,) where
t
^
W
is the specific weight of water and
is the spe cific gravity of the fluid.
r e a r r a n g e d and
T h u s „ Eg. 13 can be
can celed giving
HL
(14)
1-2
In this study the fluid flowing was w a t e r .
T h u s , with
= 1.0 , the head loss between tap I and any d o w n s t r e a m tap n
is given by
H
Y n- Y 1
tlL 1
=
(S -I).
1-n
12
c
B.
(15)
D i f f e r e n t i a l m a n o m e t e r with mer cury loop for
high
Ap/ft
With valves A and B open and valve C closed in Fig. 22,
the m e r c u r y loop is inserted and gives the pressure dif ference
bet ween tap 2 and tap 3.
The m a n i f o l d pressure for tubes I
and 2 is now dif fere nt from that for tubes 3 and 4.
Eg. 15 holds for the head loss between taps I and 2:
HL
Ya-Y1
1-2
12
(S -I).
c
(16)
— 69Likewise,, the head loss between 2 and 3 is given by
Hr
2 -3
- T T jl lV
(17)
n
which is similar to E q „ 16 except for the use of mercury
rather than carbon t e t r a c h l o r i d e .
The head loss between taps I and 3 is thus
Hr
_ Hr
, Hr
L l-3
L l-2 + L 2-3
1-3
Y2- Y 1
- T T j - (sc - n
Yi-Ys
+ -TTj
(s„ - n
(18)
E q 0 15 can then be used again to find the head loss
between tap 3 and any other d o w n s t r e a m t a p , n, or
(19)
J3-n
Using Eq.
18 and E q 0 19 the head loss between tap I and any
tap d o w n s t r e a m from tap 3 can be found by
Vn “V 2+V 3+Vn
1-n
Y 2- Y 1
Yi-Yc
- T T j (s c - 1 > + - T T j
cV
Y n- Y 3
li + - T 2
cs C-15
(2 0 )
R e a r r a n g i n g E q 0 20 gives the final m a n o m e t e r equ ation
v.-
(21)
APPENDIX C
STATISTICAL EQUATIONS
S t a t i st ical analysis was used to find:
(I) the slope and
intercept of the d i m e nsi onles s hyd raulic grade lines,
(2) the
c o r r e la tion coe ffic ient and estimate of variance about r e g r e s ­
sion of the fitted dim ensi onles s hyd raul ic grade lines, and
(3) the probable error in the average man om e t e r readings and
concentration.
A.
Slope and intercept of grade lines
The dim en s i o n l e s s hyd raulic grade line for fluid flowing
in a pipe is r e p r e s e n t e d by the line that best fits a plot of
Ap/ft
—5--- versus distance along the pipe.
The linear regression
v /2g
methods for d e t e r m i n i n g this line are developed below.
A
sample set of typical t w o - d i m e n s i o n a l data points (x ., y .) for
n obs e r v a t i o n s are shown plotted in Fig. 23.
The equation of
the straight line fitted to this data is y = a+bx where a is
the y - i n t e r c e p t and b is the slope.
y
Fig. 23.
Sample linear t w o - d im ensio nal data
-71-
To make this line the "line of best fit," a and b must be
d e t e r m i n e d such that the error,
€ ^
is a minimum.
The error,
€., is the d i f f e r e n c e between the e xp erim ental y. value
c o r r e s p o n d i n g to a given
equ ation y = a + b x . .
and the y value pre di c t e d by the
Therefore* ' £. = a+bx.-y^.
Any single
C. cannot be m i n i m i z e d without a f f e c t i n g the others.
Thus,
n
the sum
€ . must be made as close to zero as possible.
This
i= l 1
sum can be made equal to zero by many choices of straight lines
for which the pos itiv e and negative errors cancel.
the sum of the squares of the
However,
if
£. is minimized, the effect of
sign on the error is eliminated.
The refore, a and b must be
d e t e r m i n e d such that the sum of the squares given by E in the
equation
n
Y
E=
9
(a+bx.-y.)
(22)
A
is a m i n i m u m .
This pro cedu re is known as the m e t h o d of least
squares.
E x p a n d i n g E q . 22 gives:
E =
X j (a^+2abxj-2ayj+b^x.^-2bx.y.+y.^).
i= I
(23)
The m i n i m i z a t i o n cri terion requires setting the partial
d e r ivat ive with respect to a and b equal to zero giving:
-
f
1—1
and
(2a+2bXj-2y.) = 0,
(24)
-72-
£
C2a x . + 2bx. - 2x^y^)
i= l
db
(25)
R e a r r a n g i n g and div i d i n g both equations by 2 and noting that
n
^ a = an gives the fol lo w i n g e q u a t i o n s :
i= I
n
n
(26)
E V i = an+b E x i
1=1 ^
i=l
n
n
0
a E x i + b E (xi ) •
i=l 1
i=l
(27)
These two equations are known as the normal equations.
Sim u l t a n e o u s solution of the normal equations gives the values
of a and b for the line that best fits the data acc ording to
the cri teria of least squares or
n
o
n
n
n
(28)
n
(x ) i= l
(2 9 )
n
I (x.)2 i
i= l
Li=*!
These equ ations for a and b are rel ativ ely c u m b e r s o m e .
E q . 28, h o w e v e r , can be r e a r r a n g e d and sim plif ied to give:
a = y+bx
(30)
where y and x are the average values of y and x, and b is the
slope com pute d by E q . 29.
-73-
E q 1 29 and E q „ 30 were used in the computer pro gram dis cussed
in A p p e n d i x D to det ermine the equ atio ns of the dimensi onles s
h y d r aul ic grade lines ups t r e a m and dow nstr eam of the valve
being tested.
Values of y c o r resp ond to dim ensi onles s d i f f e r ­
ential pre ssure heads (DIMPEL) and values of x to distance
along the test section (x
EL
.
C o r r e l a t i o n coe ffic ient and estimate of variance
about r e g r e s s i o n
It is des irab le to have some m ea sure of how well the
exp e r i m e n t a l data est abli shes the d i m e nsi onles s hyd raulic grade
line.
One such indicator is known as the correla tion c o e f f i ­
cient ( C O E F ) .
Ano t h e r is the est imat e of var iati on about
regression (EVAR).
The c o r r e la tion c oe ffic ient is a statistical mea sure of
the degree to which two variables
relatio nship .
(x^, y .) form a linear
The COEF varies between -I and +1, depending
on the increase or decrease of one variable as the other
increases.
A c o r r e la tion of -I or +1 indicates a perfect
linear rel atio nship .
In other w o r d s , a straight line fitted
to the data would pass through every point (x ., y .) .
There­
fore, a COEF gre ater than -I or less than +1 indicates that not
all data points ( x .„ y ^ ) form a linear rel ationship.
Since the
hyd raul ic grade line should be linear in the regions upstream
and d o w n s t r e a m of the valve on a plot of pressure versus d i s ­
tance, a COEF much gre ater than -I or less than +1 would
' -74-
indicate bad data.
Mis read or incorrect data were determined
by inc ludi ng a c o r r e la tion coe ffic ient calcula tion in the
com puter pro gram used in r e d ucin g the data.
to det er m i n e the COEF is dev elop ed below.
The equation used
Steele and Torrie (10)
give the cor rela tion coefficient as
COEF =
E
xy
-/E(X)2
E(Y)2
(31)
where
Z
Z
xy
(x-x.)(y-y.),
i= l
Z<x)2
Z Ii-Xi)2.
i= I
Z(Y)2 - Z Ci-Yi)2.
i=l
S u b s t i t u t i n g for
^ X Y , E x , and
EY
in E q „ 31 and exp anding
gives the final equation:
COEF
(32)
The est imat e of variance about regression is a st a t i s ­
tical m e a s u r e of the degree to which the data points deviate
from the line fitted to the data by reg ress ion methods.
In
other w o r d s , the EVAR is a mea s u r e of the amount of e r r o r , ( .
as shown in Fig. 23.
Therefore, the smaller the value of
-75E V A R , the closer the data points are to the fitted line.
An
EVAR of zero wou ld mean the line passes through every point,
(Xj, y.).
A mea s u r e of how acc urat ely the exp e r i m e n t a l data
e s t a b l i s h e d the hyd ra u l i c grade line was provided by including
a c a l c u la tion of the EVAR in the data reduction program.
equ atio n used to det er m i n e the EVAR is developed below.
The
Steele
and Torrie (10) give the est imate of variance about reg ress ion
as
E y5
EVAR
( E x y )2
E x 2
(33)
n— 2
Making the same s u b s t it ution s as those leading to Eq. 32
and r e a r r a n g i n g gives the final equation:
n
EVAR
n
Ln1?iXiyi"1?1Xi i?/*
I
n (n-2)
C.
n
(34)
n
0 r n
n y (x .) - y. x
i=I
Li=I
Variance of m a n o m e t e r readings and con cent ratio ns
In this s t u d y , readings were made of m a n o m e t e r levels
and flow rates and the averages used to est ablish the d i m e n s i o n ­
less hyd ra u l i c grade line and c o n c ent ratio n of the mixture.
An
infinite number of such readings wou ld be req u i r e d to obtain
the true means.
Thus,
it is des irable to have some mea sure of
how closely the o b s erve d averages predict the true means that
wou ld be obt ained from an infinite number of observations.
Use
— 7 6—
of the S t u d ent -t d i s t r i b u t i o n as dis cu s s e d by Miller and
Fre und (6) provides such an indicator.
The process of ass igni ng a + error to an average, x,
used to pre dict a true m e a n , yd , such that yU = x + £ , is
known as interval estimation.
Miller and Freund (6) show that
interval e s t i m a t i o n met hods give the error in p r e dict ing the
true mean as:
(35)
in nearly all m a t h e m a t i c a l handbooks and statistics texts as a
function of the des ired confidence interval and the number of
o bs erva tions n .
S u b s t i t u t i n g the equ atio n for the variance of
n o b s e r v a t i o n s , x . , into E q . 35 gives the probable error as
(36)
Previous work by Cha rley (I) d e t e r m i n e d that ten observations
for a 90 percent confident interval were needed to reduce this
error to less than .1 in.
In add ition to p r e dict ing the accuracy of the average
m a n o m e t e r r e a d i n g , the probable error was also used to find
m i s r e a d or m i s p u n c h e d data.
The probable error of each average
m a n o m e t e r rea ding was cal cula ted in the computer pro gram used
-77-
to reduce the d a t a „
One or more bad readings would noticeably
increase the error value.
Bad data could thus be found by
stu d y i n g the error output rather than all of the individual
readings.
APPENDIX D
COMPUTER PROGRAM
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
WOODCHIP PIPELINE VALVE STUDY
HEADLOSS CALCULATION PROGRAM (FORTRAN II)
FROM READ-IN EMPIRICAL,DATA THIS PROGRAM CALCULATES THE AVERAGE MANOMETER READING,THE PROBABLE ERROR IN THE AVERAGE USING A 90 PERCENT CONF IDENC E LIMIT,THE DIFFERENTIAL PRESSURE HEAD OF EACH TAP RELATIVE TO
THE FIRST UPSTREAM TAP, THE DIMENSIONLESS PRESSURE HEAD AT EACH TAP
DEFINED AS (D IFF HD)/(V**2/2G ),THF REGRESSION LINES AND CORRELATION
COEFFICIENTS OF THE DIMENSIONLESS HYDRAULIC GRADE LINE UPSTREAM AND
DOWNSTREAM OF THE VALVE,THE PRESSURE DROP THROUGH THE VALVE AND THE
HEAD LOSS COEFFICIENT AND PROVIDES PUNCHED OUTPUT OF X-DI STANCES,
DIMENSIONLESS PRESSURE HEADS, CONCENTRATIONS, AND HEAD LOSS COEFFICIEN
TS FOR USE IN OTHER PROGRAMS
INPUT DATA ARRANGEMENT
CARD I SGC,SGM,D,NS,T90,NTA,NTB,NFV
CARD 2,3 X-D ISTANCES
CARD 4 NVEL,RIDENT,NVO
CARD 5 KVO,CVAL,MB,KU I,KUF,KD I,KDF,
NTU,NTD,XVAL
CARD 6 NOBS,NC,NML
CARD 7+ QM,QW,14Y,0-4YM
(FORMAT I )
(FORMAT 2 )
(FORMAT 3 )
(FORMAT 4 )
(FORMAT 5 )
(FORMAT 2)
NOTE....PROGRAM WORKS WITH ONE SET OF VALVE DATA AT A TIME.
EACH SET OF VALVE DATA MUST BE RUN SEPARATELY.
DIMENSION SUY(IS) ,YB II8) ,YA(5) ,SSQY(IS) ,RIDENT(S) ,AYBRO(IS) ,SYSARf
118) ,YERR(18),SUYMI 18 I,SSQYMf18) ,AMBRQt18) ,SYMBRi 18) *YAERR!18) ,DPHD
2(18),DIMPHI I8), X ( 18) ,Y(18,10), Q M ( 10),QW(10),YM(5,10),CONf18 I
DIMENSION B (2), A(2I,EVAR(2),COFT(2),HL(2)
1 FORMAT(2F6.2,F6.3,14,F8.3,312)
2 FORMAT (12F6.2)
3 FORMAT (I4,5A4,12)
4 FORMAK 13,F5.1,714,F6.2)
5 FORMAT (314)
4F FORMAT (IHl)
46 FORMAT(3 X ,I B H RUN IDENT IF ICAT ION,5 X ,5A4,5 X ,I2 , 2 IH FPS NOMINAL VELOC
I IT Y,4X,6HVALVE , F 5 . I,15H PFRCENT CLOSED«4X,4HC0NC^F7.2,BH PERCENT)
47 FORMAT (2OX,49HDISTANCE FROM FIRST UPSTREAM PRESSURE TAP IN FEET)
48 FORMAT (27X,68H Xl
X2
X3
X4
X5
X6
X7
X8
X9 XlO X
111 Xl2 X13 X14)
49 FORMAT (26X,2?F6.I)
50 FORMAT (2 O X,2 5HMANOMET ER READING OF Y(M)
Y2
Y3
Y4
YS
Y6
QW
CONC
Yl
51 FORMAT (IX,11IHRUN QM
HGl
HG
2
HG3
H
G
4
)
YG
Y9
YlO
Yll
Y12
Y13
Y14
I
Y7
(I3,2F6.0,F6.3,1X,22F5.I)
40 FORMAT
41 FORMAT (IX)
52 FORMAT(21X,19HAVERAGE VALUES FOR ,13,5H RUNS)
53 F0RMAT(3X,2r6»0,F6.3,lX,22F5.1)
54 FORMAT (20X,47HPROBABLE ERROR WITH 90 PERCENT CONFIDENCE LIMIT)
55 FORMAT (IX, 5HERR0R, 9X,F6.2,2X,22F5.2)
56 FORMAT (20X,26HDIFFERENTIAL PRESSURE HEAD)
Yl
Y2
Y3
Y4
Y5
Y6
Y7
57 FORMAT (3X , 9TH
Y9
YlO
Yll
Yl 2
Y13
Yl 4)
I YB
58 FORMAT (3X,18F7.3)
59 FORMAT (20X,27HDIMENS IONLESS PRESSURE HEAD)
(I3,2F6.0,F6.3,1X,7F5.1,5X,14F5.1)
60 FORMAT
61 FORMAT(3X,2F6.0,F6.3,1X,7F5.I»5X»14FB. I)
62 FORMAT (IX ,5HERR0R, 9X,F6.2,2X,7F5.2,5X,14F5.2)
63 FORMAT (3X ,7F7.3,7X,10F7.3)
64 FORMAT t3X,I2,21H FPS NOMINAL VELOCITY,10X,SHVALVE ,I3,15H PERCENT
I CLOSED)
19 READ I,SGC,SGM,D ,NS,T90,NT A ,NTB,NFV
READ 2,(X(I), 1=1,NS)
20 READ 3, NV E L , RIDENT , NVO
PUNCH 175,RIDENT,NVEL
175 FORMAT{5 X ,2OHRUN IDENTIFICATION
I 3HFPS)
PUNCH 176,(X(I),1=1,NS)
,5A 4 ,2X ,I5HN0MINAL VELOC
, I2,lX,
I
NO
I
c
C
C
C
C
C
C
C
C
C
C
C
C
C
C
176 FORMAT(5X .I3HX-DISTANC ES ,9F6.2/(5X»9F6.2) )
21 RFAD 4,KVO,CVAL,MB,KUI,KUF,KDI,KDF,NTU,NTD,XVAL
PUNCH I77,CVAL
177 FORMAT(5X,15HVALVE CLOSURE ,F5.1,8H PERCENT)
22 READ 5, NOBS, NC, NML
x (I)=d i s t a n c e f ro m u p s t r tap (f t ) n v e l =n o m i n a l v e l o c i t y
RIDENT =RUN IDENT IF ICAT KVO=VALVE OPENING IDENTIFICATION CODE
CVAL=VALVE CLOSE IN PERCENT MS=MERC LOOP CODE KUI=INIT UPSTR TAP FOR
SLOPE KUF=FINAL UPSTR TAP KDI=INIT DNSTR TAP FOR SLOPE KDF=FINAL
DNSTR TAP
NTU=NO OF TAPS UPSTR SLOPE
NTD NO OF TAPS DNSTR SLOPE
NOBS =NO OF OBSERVATIONS PER RUN NC=CONCENTRAT ION CODE NML =NO OF
MERCURY TUBES USED SGC=SP GR CARB TET SGM=SP GR MERC D=DIAM
NS=NUMBER OF TAPS
T90=PR08 ERROR TEST VALUE
NVO=MAX NO. OF VALVE SETTINGS PER NOMINAL VELOCITY
NFv =FINAL VELOCITY OF THE SERIES
DO 23 J=I ,NOBS
23 READ 2, QM(J), QW(J), (Y(I,J ),I= I ,NS), (YM(L ,J ),L= I,NML)
QM =M IX FLOW QW =CLEAR WATER FLOW Y(I)=CARB TFT MAMOM READINGS
YM=MERC MANOM READINGS C AND CC CONVERT MANOM READINGS TO PRESSURE
HEADS-CARB TET AND MERC RESPECTIVELY
C=(SGC-I.)/12.
CC=(SGM-I.1/12.
OBS=NORS
SSQC=O.OO
SUCON=O.00
SUQM=O.OO
SUQW=O.OO
INITIALIZATION FOR SUMATION
DO 24 II= I ,NS
SSQY(II)=0.00
24 SUY(II )=0.00
DO 26 JJ = I ,NOBS
SUQm =SUQM + QM(JJ)
SUQw =SUQW + QW(JJ)
SUMMING QMIX AND QWATER
DO 26 N= I, NS
25 SUY(N)= SUY(N) + Y(N,JJ)
a
f
C
C
C
C
C
-81
C
SSOY(N)=SSQYtN)+Y(N,JJ)**2.
YB(N)=SUYtN)/OBS
AYBRQtN)=ABSF((SSQY(N )-SUY(N )#*2./OBS>/(OBS*(OBS-I.)))
SYBAR(N)=SQRTF!AYBRQ(N))
SUY(N)=SUM OF MANOM READ SSQY=SUM OF READ SQUARED YB=AVG READING
AYBRQ=VARIANCE OF Y SYBAR =STD DEVIAT OF Y YERR =PROB ERROR OF Y
26 YERR(N)=T90*SYBAR(N)
DO 28 IK = I»NML
SUYM(IK)=0.0
SSQYM(IK)=0.0
DO 27 JK = I ,NOBS
SSQYM (IK) =SSQYM (IKH-YM (IK,JK)**2.
27 SUYM(IK)=SUYMtIKHYM(IK,JKl
YA(IK)=SUYM(IK)/OBS
AMBRQt IK)=ABSFf (SSQYM(IK)-SUYM(IK )**2./OBS)/(OBS*(OBS-I.) ))
SYMRRl IK)=SQRTFtAMBRQl TK))
SUYM,SSQYM,YA,AMBRQ,SYMBR,YAERR SAME AS ABOVE BUT FOR MERCURY TUBES
28 YAERRt IK )=T90*5YMBR(IK)
DO 30 N=I ,NOBS
CON(N)=I.-QW(N )/QM(N )
SUCON=SUCON+CON(N )
CON=CONCENTRAT ION SUCON =SUM OF CONC. ACON =ABSOLUTE VALUE CONC.
ACON=ABSFtCON(N) >
30 SSQC =SSQC +AC ON**2
CONC=SUCON/OBS
PC ON=C ONC*100.
IF (PCON-I.0) 90,90,91
90 PCON=O.OO
91 c o n a r =a b s f (sucoN)
TESTA=(SSQC-CONAB**2/OBS)/(OBS*!OBS-I.))
VARNC =ABSFt TESTA)
SCBAR=SQRTF(VARNC)
SSQC=SUM OF ACON CONC=AVG CONCENTRATION SCBAR=STD DEVIATION OF CONG.
CERR=PROB ERROR OF CONC. QA=AVG OMlX QB=AVG QWATER
CERR=T90*SCBAR*100.
QA=SUQM/OBS
OB=SUQWZOSS
n r> n n
C
C
C
C
GO TO (100, HO, 120, 130), MB
MB=MERCURY LOOP CODE MB=I NO MERCURY LOOPS USED
MB =2 I MERCURY LOOP AND ALL TAPS
MB=3 2 MERCURY LOOPS AND ALL TAPS
MB=A 2 MERCURY LOOPS NO TAP NO.8 (GATE VALVE ONLY)
100 DO 101 1=1,NS
101 DPHDt I)=C*(YB(I)-YG(D)
DPHD=DIFFERENTIAL PRES HEAD REFERENCED TO TAP NO ONE
GO TO 129
H O DO 119 I= I ,NS
IF (I-NT A )111,112,113
FIRST MERCURY LOOP IS BETWEEN TAP NO. NTA AND TAP NO. NTA-I
111 DPHD(I)=C*(YD(I)-YG(I))
GO TO 119
112 DPHDt I)=C*(YBtA)-YSt I))+CC*(YA(2)-YA(I))
113 DPHD(I)=C*(YB(A)+YB(I)-YB(S)-YB(I>)+CC*(YA(2)-YA(I))
GO TO 119
119 CONTINUE
GO TO 129
120 DO 229 1=1,NS
IF (I-NTA)121,122,123
121 DPHD(I)=C*!YB(I)-YB(I))
GO TO 229
122 DPHD(I )=C*(YB (A)-YB(I) )+CC*(YA(2)-YA(I))
FIRST MERCURY LOOP IS BETWEEN TAP NO. NTA AND TAP NO. NTA-I AND THE
SECOND MERCURY LOOP IS BETWEEN TAP NO. NTB AND TAP NO. NTB-I
GO TO 229
123 IF (I-NTD)163,125,126
12 5 DPHD(I)=C*(YB (A)-YBt I) )+CC*(YA(A )+YA(2!-YA(3)-YA(I))
GO TC 229
126 D P H D (I)=C* (Y B (I)+YB(A )-Y B (6 )-Y B (I ))+CC* (YA (A )+Y A (2)- Y A ( S ) - Y A d ))
229 CONTINUE
GO TO 129
130 CONTINUE
DO 139 1= 1,NS
IF (I-NTA) 131,132,133
131 DPHDf I)=C*(YBtI)-YB(I))
GO TO 139
132 DPHDt I)=C*(YB(S)-YBtl) )+CC*(YA(2)-YA(I))
GO TO 139
133 IF (I-NTB) 134, 135,136
134 DPHDt I)=C* (Y B (5) + YB(7)-Y B (6)-Y B (I ) )+CC*(Y A (2)-Y A (I ) )
GO TO 139
135 DPHDt I)=O
GO TO 139
136 DPHDt I )=C* (YB (I )+YBt 7) +YBt 5 )- YB (9 )- YB (6 )- YB (I )>+CC* (YA (4.) + YA (2 )-YA
I (3) -Y A ( I ) )
139 CONTINUE
129 VU=(QA*576.)/(448.8*3.1416*D**2)
DENOM=VU**2/64•4
C VU=VEL OC IT Y IN FPS DENOM=VELOC ITY HEAD D IMPH=D IMENS IONLESS PRES HEAD
DO 141 1=1,NS
141 DIMPH(I)=DPHDt I)/DFNOM
PRINT 45
PRINT 41
PRINT 41
PRINT 46, RIDENT , NVEL ,CVAL , PCON
PRINT 41
PRINT 41
PRINT 47
PRINT 48
PRINT 49,(X(I),1=1,NS)
PRINT 41
PRINT 50
PRINT 51
PRINT 41
J=NTA+I
K=NTB+!
GQA=QA/448.8
GO TO (70,75,75,80), MB
C PRINTING SEQUENCE— MB SAME AS ABOVE
70 DO 72 L=I,NOBS
PRINT 40,L,QM(L) ,QW(L) ,CON(L) ,(Y (I,L )* I= 1,NS 5
72 PRINT 41
,
co
f
PRINT
PR INT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
73 PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PR INT
PRINT
GO TO
75 DO 77
PRINT
77 PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PR INT
PRINT
PRINT
GO TO
41
52 , NOBS
41
53, QA,QB,CONC »(YB(I),I = I,NS)
45
46» RIDENT, NVEL ,CVAL , PCON
41
41
54
55 ,CERR ,(YERR(I),1= 1,NS)
41
41
57
56
58» (DPHD( I),1= 1,NS)
41
59
58, (DIMPHt I),1= 1,NS)
41
41
41
41
95
L= I,NOBS
40 ,L »QM (L )»QVI(L ),CON (L) »(Y( I,L )»1 = 1, NS )»(YM (I
41
41
52 , NOBS
41
53, QA ,QB,CONC,(YB( I),I= I,NS),(YA(I) ,I= I♦NML)
45
46» RIDENT, NVEL ,CVAL , PCON
41
41
54
55, CERR,(YERRI I),I= I ,NS),(YAERRI I),1 = 1,NML)
73
I
CD
I
80 DO 82 L=IiNOBS
PRINT 60»L >QM( L) ♦QW(L) ,CONIL )»(Y( I»1) »I= I >J) »( Y( I »L )»I=K»NS) ,(Y M U
I,L),I=I,NML)
82 PRINT 41
PRINT 41
PRINT 52, NOBS
PRINT 41
PRINT 61 , QA ,08 ,CONC ,IYB (I),I= I ,J ),IYB (I) ,I=!<,NS ),IYA II ),I= I ,NML )
PRINT 45
PRINT 46, RIDENT,NVEL,CVAL,PCON
PRINT 41
PRINT 41
PRINT 54
PRINT 62,CERR,(YERR( I) ,I= I ,J ),IYERRt I),I=K,NS) ,(YAERRt I),I= I,NML)
PRINT 41
PRINT 41
PRINT 57
PRINT 56
PRINT 63, (DPHDt I),I= I ,J),(DPHDt I),I=K,NS)
PRINT 41
PRINT 59
PRINT 63, (DIMPHt I), I= I,J},!DIMPHt I) ,I=K ,NS)
PRINT 41
PRINT 41
PRINT 41
PRINT 41
95 TS=NTU
NA=KUI
NO=KUF
NB=I
145 SXY=OeO
SSX=OeO
ScIY= O eO
SX=0.0
SY=OeO
DO '146 I=NA ,NO
SX = SXtXt I)
I
Ol
cc
I
C
C
C
C
SY =SY+DIMPH(I!
SSY=SSYX DIMPHt I )5**2
SSX=SSX-H X( I55**2
146 SXY=SXY-K X (I5*D IMPHt I55
THIS SECTION COMPUTES SUMS FOR USE IN THE REGRESSION CALCS
SYS=SY**2
SXS=SX**2 •
AX=SXZTS
AY=SYZTS
BINB)=(SXY-(SX*SY)ZTS>Z(SSX-(SXSZTS55
A(NB)=AYHAX*BtNB 55
EVAR(NB) = !SSY-(SYSZTS)-I ((TS*SXY)-(SX*SY)5Z( (TS*SSX)-SXS 555Z (TS-2.
I5
COET(NB)=SQRTFt ((TS*SXY)-(SX*SY) )**2Z( ((TS*SSX)-SXS5*( (TS*SSY)-SYS
I 55 5
IF ICOFTtNB5-1 .05 600,500,500
500 COFT(NB 5=1 .000000
600 CONTINUE
NB = I FOR UPSTR SECTION NB =2 FOR DNSTR SECTION B = REGRESSION LINE
SLOPE A=Y-TNTERCEPT EVAR=EST OF VARIANCE ABOUT REGRESSION
COFT=CORRELATION COEFFICIENT
IF(NB-I) 147,147,148
147 TS=NTD
NB =2
NA=KDI
NO=KDF
GO TO 145
148 DO 149 NI = I ,2
149 HL (N I5=A(N I5+ (XVAL*B(NI?)
HLCOFT =HLf 2)-HL(I)
H L O S S = ( H L C O F T )*DENOM
C HLOSS=HEAD LOSS OCURRING AT THE VALVE
C HLCOFT=THE HEAD LOSS OOEFFIOIENT=DIFFERENCE BETWEEN UPSTR AND DNSTR
C REGRESSION LINES AT THE VALVE WHERE X=XVAL
PRINT 150
150 FORMAT(5X,55HREGRESSION INFO
UPSTREAM
DOWNSTRE
IAM )
co
f
C
C
C
C
C
C
C
PRINT 41
PRINT 151,(0(1),I=I,2)
151 FORMAT(5X,5HSLOPE,23X,F9.6,8X,F9.6)
PRINT 152,(Al I),1= 1,2)
152 FORMAT(5X,9HINTERCEPT,19X,F9.6,8X,F9.6)
PRINT 153,(EVAR( I),1= 1,2)
153 FORMAT(5 X,20HESTIMATE OF VARIANCE,7X,F10.6,7X,F10.6)
PRINT 154,(COFTt II,1=1,2)
154 FORMAT(5X ,23HCORRELAT ION COEFFIC IENT,5X,F9.6,8X,F9.6)
PRINT 41
PRINT 180, VU
180 FORMAT(5X,17HAVG TRUE VELOCITY,F8.3,IX,IOHFT PER SEC)
PRINT 181, QA
181 FORMAT(5X,17HAVG MIX FLOW RATE,F8.3,IX,11 HGAL PER MIN)
PRINT 182, GOA
182 FORMAT(5X,I7HAVG MIX FLOW RATE,F8.4,IX ,I3HCU FT PER SEC )
PRINT 41
PRINT 155,HLCOFT, HLOSS
155 FORMAT(5X,3 5HHFADLOSS COEFFICIENT OF THIS RUN IS ,IX ,F9.6,5X ,I2HHEA
ID LOSS IS,1X,F9.6,5H FEET)
PUNCH 178,PCON,QA,HLCOFT
I78 FORMAT(5X,19HCHIP CONCENTRATION ,F6.2,18H PERCENT
QMIX=,F5.0,1
I6H HEADLOSS COEF ,F8.4)
PUNCH 179, (DIMPHIN),N=I,NS)
179 FORMAT(5X ,2 IMD IMENLESS PRES HEADS ,9F6.2/(5X,9F6.2) )
IF(NC-I) 22,163,163
NC=O READS MORE DATA AT DIFF CONCENTRATION FOR SAME VALVE CLOSURE
163 IF(KVO-NVO) 21, 171, 171
KVO LESS THAN NVO READS MORE DATA FOR DIFF VALVE CLOSURE
171 IF(NVEL-NFV) 20,37,37
NVEL LESS THAN NFV READS MO°E DATA AT DIFF NOMINAL VELOCITY
EACH NOMINAL VELOC DATA SET INCLUDES DATA SETS FOR DIFFERENT VALVE
CLOSURES EACH OF WHICH INCLUDE DATA SETS FOR DIFFERENT CONCENTRATIONS
DATA INPUT IS IN ORDER OF LOWEST NOMINAL VELOC TO HIGHEST, ZERO PER
CENT VALVE CLOSURE TO MAX CLOSURE, ZERO CONC TO MAX CONC.
37 CALL EXIT
END
,
co
Tj
APPENDIX E
SUMMARY OF COMPUTED RESULTS
TABLE IV
Plug Valve Test, July 1968
Valve
V
4 fps
C
KL
V
6 fps
C
KL
V
8 fps
C
KL
V
10 fps
C
KL
3.950 0.00
4.4% 3.927 8.12
4.005 20.21
.009 6.009 0.00
.024 5.987 10.04
.194 6.022 20.40
.192 7.989 0.00
.175 7.989 9.69
.2 68 7.974 19.51
.052
.067
.094
9.968 0.00
9.927 9.41
9.932 19.71
.222
.229
.224
3.939 0.00
25.0% 4.02 6 9.74
3.945 19.14
.226 5.969 0.00
1.002 5.932 9.34
3.380 5.908 18.71
.655 7.924 0.00
.673 7.958 9.66
.763 7.932 19.74
.736 10.008 0.00
.730 10.034 9.20
.837 9.929 19.62
.562
.559
.590
4.008 0.00 5.982 6.013 0.00
50.0% 3.937 8.34 7.501 6. 047 10.98
3.927 18.75 13.462 5.890 18.33
6.700 7.948 0.00
7.442 8.034 10.44
8.856 7.937 19.40
6.003
75.0%
6 fps
70.0%
8 fps
Repeat
3.906 8.30
25.0% Closed
6.564 9.932 0.00 6.464
7. 158 10.005 10.06 6.970
8.293 9.990 20.18 7.932
0.00 38.458 7.953
0.00 29.261
7.916
9.74 27.028
Repeat
Repeat
10.72 7.124
6.
130
8.023
.036 6.023 10.55
50.0% Closed
50.0% Closed
TABLE
Summary
Valve
V
4 fps
C
KL
of Computed Results
V
6 fps
C
V
- Ball
KL
V
Valve Test,
8 fps
C
KL
July
1968
V
10 fps
C
KL
3.965 0.00 -.007 6.013 0.00
0.0% 3.987 10. 16 -.009 6.035 11.05
3.926 19.30 .021 5.987 19.94
-.125 7.991 0.00
.052 7.969 9.90
.027 8.044 20.26
.015 10.048 0.00
.015 10.000 10.06
.003 9.939 19.77
.02 6
.108
.052
3.919 0.00 .705 6.052 0.00
2 5.0% 4.005 11.22 .963 6.065 10.98
3.906 18.34 1.196 6.000 19.65
.586 7.929 0.00
.790 7.979 9.86
.897 7.93 7 19.43
.838 10.039 0.00
.815 10.055 9.52
.901 9.966 19.70
.820
.847
.952
3.940 0.00 6.397 6.02 6 0.00
50.0% 3.940 9.09 7.287 6. 000 10.46
3.929 18.83 9.176 5.963 20.07
6.458 7.927 0.00
7.140 8.005 10.42
7.930 7.914 19.19
6.374 9.942 0.00 6.508
6. 757 9.955 9.56 6.936
7.366 10.029 20.57 7.863
7.961 0.00 22.029
7.984 10.08 23.167
8.008 20.31 24.353
67.5%
5.984
5.969
75.0%
Repeat
4.017 20. 61
0.0% Closed
0.00 50.826
9.94 49.767
Repeat
.050 6.034 10.61
25.0% Closed
Repeat
.814 7.953 0.00 6.111
50.0% Closed
TABLE VI
Summary
Valve
V
4 fps
C
KL
of Computed Results
V
6 fps
C
KL
- Pinch
V
Valve
8 fps
C
T e s t , July
KL
V
1968
10 fps
C
KL
3.908 0.00
28.5% 3.930 8.85
3.961 15.62
.104 6.039 0.00
.323 5.974 10.07
.5 62 5.908 19.76
.140 7.882 0.00
.144 7.948 9.92
.263 7.935 19.33
.109 10.061 0.00
.115 9.996 9.59
.154 9.913 19.56
.064
.079
.105
3.963 0.00
40.0% 3.895 8.24
3.950 19.75
.169 5.969 0.00
.558 5.987 9.99
.874 6.013 20.26
.2 62 7.950
.354 7.966
.5 78 7.919
.409 10.018 0.00
.429 10.016 10.07
.506 9.937 19.97
.305
.3 68
.447
0.00
9.85
9.94
3.992 0.00 .521 5.979 0.00 .755 7.940 0.00 .859 9.940 0.00 .845
50.0% 3.971 9.54 .754 5.987 10.39 .899 7.914 9.74 .937 10.084 10.60 .917
3.971 19.67 ].5 62 6.031 20.72 L.205 7.961 19.51 1.117 9.911 19.62 I.028
60.0%
70.0%
5.987 0.00 I.484 7.979 0.00 1.894
5.958 9.48 1.737 7.974 10.03 2.055
5.953 20.02 2.323 7.966 19.92 2.296
7.997 0.00 3.631
8.000 10.52 4.264
Repeat
Repeat
Repeat
3.940 19.03 .514 5.953 9.66 .554 7.901 0.00 .820
28.5% Closed
40.0% Closed
50.0% Closed
TABLE VII
Summary
of Computed Results
Valve
% Clos ure % of Stem
Travel
0.0%
14.2%
38.9%
68.4%
V
6 fps
C
- Gate
KL
V
Valve
Test,
8 fps
C
September
KL
V
1965
LO fp s
C
KL
0.0%
5.908 0.00
5.908 4.87
5.935 11.01
5.945 15.56
5.935 20. 70
0.013
0.015
0.017
0.018
0.032
7.869 0.00
7.848 4.73
7.895 10.59
7.843 15.00
7.869 20.27
.016
.017
.017
.023
.028
9.856 0.00
9.804 4.80
9.856 10.08
9.878 15.31
9.856 19.89
0.014
0.027
0.023
0.023
0.025
25.0%
5.882 0.00
5.942 5.40
5.935 10.57
5.961 15.79
5.963 20.21
0.2 62
0.278
0.298
0.316
0.363
7.869 0.00
7.869 5.32
7.895 10.60
7.817 14.38
7.885 19.76
.267
.269
.284
.301
.316
9.882 0.00
9.935 5.79
9.827 9.81
9.856 15.12
9.882 20. 11
0.193
0.277
0.254
0.281
0.336
50.0%
5.908 0.00
5.908 4.87
5.911 10.21
5.935 15.42
5.935 20. 70
1.531
1.674
I .722
2.273
2.720
7.838 0.00
7.874 5.38
7.843 9.67
7.922 15.84
7.840 19.64
1.841
1.920
2. 101
2.359
2.407
9.830 0.00
9.840 4.89
9.804 9.60
9.908 15.57
9.864 19.96
1.980
I .939
2.210
2.356
2.500
75.0%
5.908 0.00 18.008 7.843 0.00 18.117 9.830
5.908 4.87 20.898 7.874 5.04 19.207 9.830
5.924 10.28 23.380 7.848 9.73 20.986
7.854 14.78 18.030
7.872 20.29 20.816
0.00 14.993
5.59 16.336
L I T E R A T U R E CITED
1.
Charley, Robert W., The Effect of Chip-Shaped Solids on
Energy Losses in Axi-Symmetric Pi pe ~Expans ions , UnpufP""
lished Master’s Thesis, Department of Civil Engineering
and Engineering Mechanics, Montana State University,
Bozeman, Montana, June, 1965.
2.
Flow of Fluids through Valve Fittings and Pipe, Technical
Paper No. 410, Crane Company, Chicago, Illinois , 1957.
3.
Hi no, Mikio, "Turbulent Flow with Suspended Particles,"
Journal of the Hydraulics Division, ASCE Proceedings,
V0I. 89, No. 4, July, 1963, pp. 161-185.
4.
Hunt, William A., An Economic Analysis of Transporting
Low Value Forest Products Continuously in Hydraulic Pipe
Lines , Unpublished Final Report, Department of Civil
Engineering and Engineering Mechanics, Montana State
University, Bozeman, Montana, March, 1965.
5.
Liptak, Bela G., "Control Valves for Slurry and Viscous
Service," Chemical Engineering, April 13, 1964,
pp. 185-192.
6.
Miller, Irwin and Freund, John E., Probability and
Statistics for Engineers, Prentice Hall, Inc., Englewood
Cliffs, New Jersey, 1965.
7.
Pao, Richard F., Fluid Mechanics, John Wiley and Sons,
Inc., New York and London, 1965.
8.
Rouse, Hunter, Engineering Hydraulics, Proceedings of
the Fourth Hydraulics Conference, Iowa Institute of
Hydraulic Research, John Wiley and Sons, Inc., New York,
1950.
9.
Soo, Shao L., Fluid Dynamics of Multiphase Systems,
Blaisdell Publishing Co., Waltham, Massachusetts, 1967.
10.
Steele, Robert G. D. and Torrie, James H., Principles
and Procedures of Statistics, McGraw-Hill Book Co., Inc.,
New York, i960.
11.
Streeter, Victor L., Fluid Mechanics, McGraw-Hill Book
Co., Inc., New York, 1966.
12.
Zandi, Iraj and Govatos, George, "Heterogeneous Flow of
Solids in Pipe Lines," Journal of the Hydraulics Division,
ASCE Proceedings, Vol. 93, No. 3, May, 1967, pp. 145-159.
MONTANA STATE UNIVERSITY LIBRARIES
762 100 4578
'
J631
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Johnson, David Allan
The effects of chip­
shaped solids on valve
head loss characteristii :s
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