Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
Page 1
Grading Sheet
~~~~~~~~~~~~~~
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 3
SIMPLE PIPE FLOW
Students’ Names / Section №
POINTS
PRESENTATION—Applicable to Both MS Word and Mathcad Sections
10
10
10
GENERAL APPEARANCE
ORGANIZATION
ENGLISH / GRAMMAR
ORDERED DATA, CALCULATIONS, & RESULTS—MATHCAD
VARIABLE DEFINITIONS AND RAW DATA
CALCULATIONS WITH DETAILED EXPLANATIONS
GRAPH OF MOODY DIAGRAM AND EXPERIMENTAL POINTS
10
10
25
TECHNICAL WRITTEN CONTENT
DISCUSSION OF RESULTS
CONCLUSIONS
ORIGINAL HAND-WRITTEN (NOT TYPED) DATASHEET
TOTAL
COMMENTS
d
GRADER—
10
10
5
100
SCORE
TOTAL
Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
MIME 3470—Thermal Science Laboratory
~~~~~~~~~~~~~~
Experiment №. 3
SIMPLE PIPE FLOW
~~~~~~~~~~~~~~
LAB PARTNERS: NAME
NAME
NAME
NAME
NAME
NAME
SECTION
№
EXPERIMENT TIME/DATE: TIME, DATE
The calibration curve of horif vs. Q for the sharp-edged, 5/8 orifice
is in English units (gph vs. inH20). Points from that curve were
roughly fitted with a curve. The data points and fitted curve are
shown in the Figure 1. The equation for the curve is
h(inH2O)= 3.2103Q +1.51104Q2+14109Q3 = f(Q); Q(gph) (3)
64
60
56
52
48
44
40
h
36
32
h fit( Q)
28
24
20
16
12
8
4
0
~~~~~~~~~~~~~~
OBJECTIVE—of this experiment is to observe the effects of pipe
friction for three different flow rates in pipes of three different inside
diameters. Calculations of pipe friction factor, f, and Reynolds number, Re, for the nine cases will be plotted on a Moody diagram, where
said Moody diagram was generated using a function from Lab 1.
INTRODUCTION—Fluids are usually transported through pipes
from one location to another by pumps. In order to size a pump for
a given application, it is necessary to predict the pressure drop
which results from friction in the pipe and fittings. The study of
pressure losses in pipe flow is the subject of this experiment.
EXPERIMENTAL APPARATUS—The pipe flow test rig is
shown in the Appendix. It contains a sump tank, used as a water
reservoir, from which a centrifugal pump discharges water to the
circuit. The circuit consists of three different diameter pipes made of
plastic tubing. The circuit contains valves for directing and
regulating the flow to make up various series and parallel piping
combinations. The circuit has a provision for measuring pressure
loss through the use of static pressure taps at useful locations which
are to be connected to manometer limbs (manometer not shown in
schematic). Finally, since the circuit also contains an orifice meter
which is used as a flow meter. The flow rate can be determined as a
function of measured pressure loss across the orifice meter.
PROCEDURE1—Pressure Drop Through a Single Pipe: For
three different flow rates measured in cubic meters of water per
second, measure the pressure losses in inches of water for flow
through individual pipes having inside diameters of 0.595, 0.804,
and 1.150 inches. From these data, calculate the Reynolds number,
Re, and pipe friction factor, f (aka Euler number). These
dimensionless values are defined as follows:
V D
Re =
(1)

 p 


g  h
  
f =
(2)

2 

 L   V   L   V 2 
 
 
 D   2   D   2 
where, V  velocity of flow, m/s
D  inside diameter of pipe, m
  kinematic viscosity, m2/s
p  friction pressure drop over length L, Pa = kg m1 s2
L  length of pipe generating pressure loss p, m
g  acceleration of gravity, m/ s2
h  manometer head due to friction pressure drop, m
  density of manometer fluid.
NOTE: Pressure drop, p = gh, data will be taken using a
manometer; i.e., a head difference,h in inH2O. However, the only
pressure units that Mathcad uses are inches of mercury, in_Hg, and
Pascals, Pa. So, being very careful of units, the student will have
to convert from inches of water to inches of mercury.
1
There are PowerPoint files for all labs which use LabVIEW.
Page 2
0
40 80 120 160 200 240 280 320 360 400 440 480 520 560 600
GPH  Q
Figure 1—Calibration curve for sharp edged orifice flow meter
The student asks: given a value of horif, isn’t computing Q going to
be difficult? The answer is: it’s not as difficult as one first thinks. For
a given value of horif, the desired value of Q occurs when horif –
f(Q) = 0. Mathcad has a function called root that finds the value that
satisfies this equation (i.e. the point where the function crosses the
abscissa and is zero).2 The only caveat occurs when there is more
than one root. Then the “search range” should straddle only one
root. (To know what search range to use, it is often convenient to
plot the function.) Mathcad’s help describes a call to root as:
root(f(var1, var2, ...),var1, [a, b]) Returns the value of var1
lying between a and b at which the function f is equal to zero.
The followingi example
should help: j  i
 1  3
CA LCULA TIONS:
Calculate v olumetric flow rate for all 9 cases --use a root crossing
function. First define calibration curv e function.:
3
4
2
9
3
fEng ( Q)  3.2  10
 Q  1.51  10
 Q  14  10
Q
Example: If for Pipe 2 & Run 2
see
plot
at
below.
h orif
 14.5
22
100
75
fEng ( Q)
50
fEng ( Q)  h orif
25
22
0
0
25
50
0 100 200 300 400 500 600
Q
NOTE: No units have been applied to h.orif as it has English units
of "H2O and w e do not w ant Mathcad to conv ert it to SI.
There is only 1 zero crossing ov er the entire range. This is true for all
data v alues of h.orif. Use "root" to compute flow rate in GPH.
Q
22
 root h orif

A s a check , note that
Q
22
22
 fEng ( Q)  Q  0  600 
 315.909

fEng Q

22
  14.5
NOW, apply units to Q of gal/hr and let Mathcad conv ert to SI:
QSI
22
 Q
22

gal
hr
QSI
22
 3.322  10
4
3 -1
m s
For the results, plot the followings:
• The laminar friction factor curve (from Lab 1),
• The turbulent friction factor curve (also from Lab 1) for relative
roughness values of 0.05 and 0.000001 (smooth pipe), and
• The nine points computed from the data.
2
There is also a handout on root finders.
Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
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ORDERED DATA, CALCULATIONS, AND RESULTS (Use sufficient comments so I can follow your work—I’m not a mind reader!)
MATHCAD OBJECT--DOUBLE CLICK TO OPEN
Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
DISCUSSION OF RESULTS Do not reiterate objective, theory,
or procedure!—these have already been supplied. The student
may discuss anything pertaining to problems in performing the
lab and, of course, the results. However, grading is based on
answers to the following questions:
1. In general, how do calculated values of friction factor compare
with the Moody diagram?
Answer here
2. Why do the discrepancies noted in Item 1 exist?
Answer here
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CONCLUSIONS (Based on Objective, Results, and Discussion)
Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
Page 5
APPENDIX - Data Sheet for Simple Pipe Flow
Time/Date:
__________________________________
Lab Partners:
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
Distance between pipe pressure taps, L: ________________
Temperature of water:
________________
0.595 I.D.
Run
1
2
3
d
d
0.804 I.D.
1.150 I.D.
horifice
hfriction
horifice
hfriction
horifice
hfriction
inH2O
inH2O
inH2O
inH2O
inH2O
inH2O
Last Rev.: 17 MAY 08
Simple Pipe Flow : MIME 3470
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