H16
Losses in Piping Systems
The equipment described in this manual is
manufactured and distributed by
TECQUIPMENT LIMITED
Suppliers of technological laboratory
equipment designed for teaching.
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2.
1.
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TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
SECTION 1.0
INTRODUCTION
One of the most common problems in fluid mechanics is the estimation of
pressure loss. This apparatus enables pressure loss measurements to be made on
several small bore pipe circuit components, typical of those found in central
heating installations. This apparatus is designed for use with the TecQuipment
Hydraulic Bench H1, although the equipment can equally well be supplied from
some other source if required. However, al1 future reference to the bench in this
manual refers directly to the TecQuipment bench.
1.1
Description of Apparatus
The apparatus, shown diagrammatically in Figure 1.1, consists of two separate
hydraulic circuits, one painted dark blue, one painted light blue, each one
containing a number of pipe system components. Both circuits are supplied with
water from the same hydraulic bench. The components in each of the circuits are
as follows:
Dark Blue Circuit
Light Blue Circuit
3.
4.
1.
2.
Gate Valve
Standard Elbow
3.
90° Mitre Bend
4.
Straight Pipe
5.
Globe Valve
6.
Sudden Expansion
7.
Sudden Contraction
8.
lS0mm 90° Radius Bend
9.
100mm 90° Radius Bend
10.
50mm 90° Radius Bend
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Key to Apparatus Arrangement
A
B
Straight Pipe 13.7mm Bore
90° Sharp Bend (Mitre)
C
Proprietary 90° Elbow
D
Gate Valve
E
F
G
Sudden Enlargement - 13.7mrn/26.4mm
Sudden Contraction - 26.4mrn/13.7rnrn
Smooth 90° Bend 50mm Radius
H
J
Smooth 90° Bend 100mrn Radius
Smooth 90° Bend lS0mm Radius
K
L
Globe Valve
Straight Pipe 26.4mm Bore
In all cases (except the gate and globe valves) the pressure change across each of
the components is measured by a pair of pressurized Piezometer tubes. In the case
of the valves pressure measurement is made by U-tubes containing mercury.
SECTION 2.0 THEORY
Figure 2.1
Figure 2.2
Figure 2.3
For an incompressible fluid flowing through a pipe the following equations apply:
𝑄 = 𝑉1 𝐴1 = 𝑉2 𝐴2 (Continuity)
𝑃
𝑉2
𝑃
𝑉2
1
2
𝑧1 + 𝜌𝑔1 + 2𝑔
= 𝑧2 + 𝜌𝑔2 + 2𝑔
+ ℎ𝐿1−2 (Bernoulli)
Notation:
Q Volumetric flow rate (m 3/s)
V Mean Velocity (m/s)
A Cross sectional area (m3)
Z Height above datum (m)
P Static pressure (N/m2)
hL Head Loss (m)
Density (kg/m3)
g Acceleration due to gravity (9.81m/s2)
ρ
2.1
Head Loss
The head loss in a pipe circuit falls into two categories:
(a)
That due to viscous resistance extending throughout the total
length of the circuit, and;
(b)
That due to localized effects such as valves, sudden changes in
area of flow, and bends.
The overall head loss is a combination of both these categories. Because of
mutual interference between neighboring components in a complex circuit the
total head loss may differ from that estimated from the losses due to the
individual components considered in isolation.
Head Loss in Straight Pipes
The head loss along a length, L, of straight pipe of constant diameter, d, is
given by the expression:
ℎ𝐿 =
4𝑓𝐿𝑉 2
2𝑔𝑑
where f is a dimensionless constant which is a function of the Reynolds
number of the flow and the roughness of the internal surface of the pipe.
Head Loss due to Sudden Changes in Area of Flow
Sudden Expansion: The head loss at a sudden expansion is given by the
expression:
ℎ𝐿 =
(𝑉1 −𝑉2 )2
2𝑔
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Sudden Contraction: The head loss at a sudden contraction is given by the
expression:
𝐾𝑉22
ℎ𝐿 =
2𝑔
where K is a dimensionless coefficient which depends upon the area ratio
as shown in Table 2.1. This table can be found in most good textbooks on
fluid mechanics.
A2/A1
0
0.1
0.2
0.3
0.4
0.6
0.8
1.0
K
0.50
0.46
0.41
0.36
0.30
0.18
0.06
0
Table 2.1 Loss Coefficient For Sudden Contractions
Head Loss Due To Bends
The head loss due to a bend is given by the expression:
ℎ𝐿 =
𝐾𝐵 𝑉 2
2𝑔
where K is a dimensionless coefficient which depends upon the bend
radius/pipe radius ratio and the angle of the bend.
Note:
The loss given by this expression is not the total loss caused by the bend
but the excess loss above that which would be caused by a straight pipe
equal in length to the length of the pipe axis.
See Figure 4.5, which shows a graph of typical loss coefficients.
Head Loss due to Valves
The head loss due to a valve is given by the expression:
ℎ𝐵 +
𝐾𝑉 2
2𝑔
where the value of K depends upon the type of valve and the degrees of
opening.
Table 2.2 gives typical values of loss coefficients for gate and globe valves.
Globe Valve, Fully Open
10.0
Gate Valve, Fully Open
0.2
Gate Valve, Half Open
5.6
Table 2.2
2.2. Principles of Pressure Loss Measurements
Figure 2.4 Pressurised Piezometer Tubes to Measure Pressure Loss
between Two Points at Different Elevations
Considering Figure 2.4, apply Bernoulli's equation between points 1 and 2:
𝑃1 𝑉12 𝑃2 𝑉22
𝑧+
+
=
+
+ ℎ𝐿
𝜌𝑔 2𝑔 𝜌𝑔 2𝑔
but:
𝑉1 = 𝑉2
(2-1)
therefore
ℎ𝐿 = 𝑧 +
(𝑃1 −𝑃2 )
𝜌𝑔
(2-2)
Consider Piezometer tubes:
P = P1 + ρg[z − (x + y)]
(2-3)
𝑃 = 𝑃2 − 𝜌𝑔𝑦
(2-4)
also
giving
𝑥 =𝑧+
(𝑃1 −𝑃2 )
𝜌𝑔
(2-5)
Comparing Equations (2-2) and (2-5) gives
ℎ𝐿 = 𝑥
2.2.1
(2-6)
Principle of Pressure Loss Measurement
Considering Figure 2.5, since points 1 and 2 have the same elevation and pipe
diameter:
𝑃1 −𝑃2
𝜌(𝐻2 𝑂) 𝑔
= hL
(2-7)
Consider the U-tube. Pressure in both limbs of the U-tube is equal at level 00.
Therefore equating pressure at 00:
𝑃2 − 𝜌𝐻2𝑂 𝑔(𝑥 + 𝑦) + 𝜌𝐻2𝑂 𝑔𝑥 = 𝑃1 − 𝜌𝐻2𝑂 𝑔1 𝑦1
(2-8)
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Figure 2.5 U- Tube Containing Mercury used to measure Pressure Loss
across Valves
giving 𝑃1 − 𝑃2 = 𝑥𝑔(𝜌𝐻𝑔 − 𝜌𝐻2 𝑂)
(2-9)
hence:
𝑃1 − 𝑃2
= 𝑥(𝑠 − 1)
𝜌𝐻2 𝑂 𝑔
(2-10)
Considering Equations (2-7) and (2-10) and taking the specific gravity of
mercury as 13.6:
hL = 12.6x
(2-11)
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
SECTION 3.0
(1)
INSTRUCTIONS FOR USE
Connect the hydraulic bench supply to the inlet of the apparatus and
direct the outlet hose into the hydraulic bench weighing tank.
(2)
Close the globe valve, open the gate valve and admit water to the Dark
Blue circuit by starting the pump and opening the outlet valve on
hydraulic bench.
(3)
Allow water to flow for two or three minutes.
(4)
Close the gate valve and manipulate all of the trapped air into the air
space in piezometer tubes. Check that the piezometer tubes all indicate
zero pressure difference.
(5)
Open the gate valve and by manipulating the bleed screws on the Utube fill both-limbs with water ensuring no air remains.
(6)
Close the gate valve, open the globe valve and repeat the above
procedure for the Light Blue circuit.
The apparatus is now set up for measurement to be made on the components
in either circuit.
The-datum position of the piezometer can be adjusted to any desired position
either by pumping air into the manifold with the bicycle pump supplied, or by
gently allowing air to escape through the manifold valve. Ensure that there are
no water locks in these manifolds as these will tend to suppress the head of
water recorded and so provide incorrect readings.
3.1
Filling the Mercury Manometer
Important:
Mercury and its vapors are poisonous and should be treated with great
care. Any local regulations regarding the handling and use of mercury
should be strictly adhered to.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Due to regulations concerning the transport of mercury, TecQuipment Ltd. are
unable to supply this item. To fill the mercury manometer, it is recommended
that a suitable syringe and catheter tube are used (not supplied) and the
mercury acquired locally.
If you are wearing any items of gold or silver, remove them.
Remove the manometer from the H16 before filling with mercury. The object
is to fill the dead-ended limb with a continuous column of mercury and then
invert the column so that a vacuum is formed in the closed end of the tube.
Hold the manometer upside down and support it firmly. Thread a suitable
catheter tube into the manometer tube, ensuring the catheter tube end touches
the sealed end of the glass column. Fill a syringe with 10ml of mercury and
connect to the catheter tube. Slowly fill the glass column using the syringe,
and as the mercury fills the column, withdraw the tube ensuring there are no
air bubbles left. Fill up to the bend and return the manometer to its normal
position. The optimum level for the mercury is 400mm from the bottom of the
U-Tube.
When the manometer has the correct amount of mercury in it, a small quantity
of water should be poured into the reservoir to cover the mercury and so
prevent vapors from escaping into the air.
3.2
Experimental Procedure
The following procedure- assumes that pressure loss measurements are to be
made on all the circuit components.
Fully open the water control valve on the hydraulic bench. With the globe valve
closed, fully open the gate valve to obtain maximum flow through the Dark Blue
circuit. Record the readings on the piezometer tubes and the U- tube. Collect a
sufficient quantity of water in the weighting tank to ensure that the weighing takes
place over a minimum period of 60 seconds.
Repeat the above procedure for a total of ten different flow rates, obtained by
closing the gate valve, equally spaced over the full flow range.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
With simple mercury in glass thermometer record the water temperature in the
sump tank of the bench each time a reading is taken.
Close the gate valve, open the globe and repeat the experimental procedure for the
Light Blue circuit.
Before switching off the pump, close both the globe valve and the gate valve. This
procedure prevents air gaining access to the system and so saves time in
subsequent setting up.
.-
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
SECTION 4.0
4.1
TYPICAL SET OF RESULTS AND CALCULATIONS
Results
Basic
Data
Bend Radii
= 13.7mrn
Pipe Diameter (internal)
Pipe Diameter [between sudden expansion
(internal) and contraction]
Pipe Material
Distance between pressure tappings for straight
= 26.4mrn
pipe and bend experiments
= 0.914m
90° Elbow (mitre)
90° Proprietary elbow
=0
= 12.7mm
90° Smooth bend
= 50mm
90° Smooth bend
= 100mm
= 150mm
90° smooth bend
4.1.1 Identification of Manometer Tubes and Components
Manometer Tube
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Unit
Proprietary Elbow Bend
Straight Pipe
Mitre bend
Expansion
Contraction
150mm bend
100mm bend
50mm bend
Copper Tube
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
4.2
Straight Pipe Loss
The object of this experiment is to obtain the following relationships:
(a)
(b)
Head loss as a function of volume flow rate;
Friction Factor as a function of Reynolds Number.
Test
Time To
Piezometer Tube Readings (cm)
U-Tube
Number
Collect 18 kg
Water
(s)
Water
(cm) Hg
1
2
3
4
5
6
1
63.0
51.0
14.0
49.5
16.3
86.9
29.2
29.4
28.6*
2
65.4
52.5
18.2
50.3
19.5
87.5
33.2
31.9
25.9
3
69.4
51.9
21.6
49.7
21.6
86.5
37.3
33.8
24.0
4
73.9
52.2
25.1
49.2
24.0
85.5
41.7
35.8
22.0
5
79.9
53.1
29.4
48.6
27.0
84.2
47.1
38.1
19.5
6
88.8
53.4
33.4
48.0
29.7
83.0
52.1
40.5
17.0
7
99.8
53.2
36.5
46.6
31.7
81.6
56.8
42.7
14.8
8
111.0
52.6
39.2
46.1
33.7
80.0
59.8
44.0
13.5
9
10
146.2
229.8
52.6
52.9
44.4
49.1
54.4
45.0
37.7
41.5
78.4
77.4
66.1
72.0
47.3
50.3
10.3
7.3
* Fully Open
Water Temperature 23°C
Table 4.1 Experimental Results for Dark Blue Circuit
Specimen Calculation
From Table 4.1, test number 1
Mass flow rate
Head loss
18
= 63
= 0.286 𝑘𝑔/𝑠
= 0.332 𝑚 𝑤𝑎𝑡𝑒𝑟
Gate-Valve
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
=
Volume flow rate (Q)
=
𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑅𝑎𝑡𝑒
𝐷𝑒𝑛𝑠𝑖𝑡𝑦
0.286
103
= 286 × 10−6 𝑚3 ⁄𝑠
𝜋
= 4 × 13.72
Area of flow (A)
= 147.3𝑚𝑚2
𝑄
=𝐴
Mean Velocity (V)
=
286 × 10−6
147.310−6
= 1.94𝑚/𝑠
𝑑
Reynolds Number (Re)
=𝑉×𝑣
For water at 23°C
= 9.40 × 10−7 𝑚2 ⁄𝑠
Therefore Re
=
1.94 × 13.7 × 10−3
9.40×10−7
= 2.83 × 104
Friction Factor (f)
=
=
ℎ𝐿 × 2𝑔𝑑
4𝐿𝑉 2
0.332 × 2 × 9.81 × 13.7 × 10−3
4 × 914 𝑥 10−3 × 1.942
= 0.0065
Figure 4.1 shows the head loss - volume flow rate relationship plotted as a
graph of log hL against log Q.
The graph shows that the relationship is of the form h L α Qn with n = 1.73
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
This value is close to the normally accepted range of 1.75 to 2.00 for turbulent
flow. The lower value n is found as in this apparatus, in comparatively
smooth pipes at comparatively low Reynolds Number.
Figure 4.2 shows the Friction Factor - Reynolds Number relationship plotted
as a graph of friction factor against Reynolds Number.
The graph also shows for comparison the relationship circulated from
Blasius's equation for hydraulically smooth pipes.
Blasius's equation:
f=
0.0785
𝑅𝑒 1⁄4
In the range 104 < Re < 105
As would be expected the graph shows that the friction factor for the copper
pipe in the apparatus is greater than that predicted for a smooth pipe at the
same Reynolds Number.
Figure 4.1 Head Loss - Volume Flow Rate
5.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Figure 4:2 Friction Factor - Reynolds Number
4.3
Sudden Expansion
The object of this experiment is to compare the measured head rise across a
sudden expansion with the rise calculated on the assumption of:
(a)
(b)
No head loss;
Head loss given by the expression:
ℎ𝐿 =
(𝑉1 − 𝑉2 )2
2𝑔
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Test
Time To
Piezometer Tube Readings (cm)
V-Tube
Number
Collect 18 kg
Water
(s)
Water
(cm) Hg
7
8
9
10
11
11
73.2
38.7
43.5
42.5
12.1
38.3
37.4
20.2
12
76.8
39.2
43.5
42.5
22.1
38.5
38.5
19.0
13
82.6
39.1
43.0
42.2
24.5
38.3
40.2
17.4
14
15
16
95.4
102.6
130.8
39.4
39.7
40.0
42.0
42.2
41.5
41.5
41.7
41.1
28.5
30.2
33.8
38.3
38.0
37.3
43.0
44.0
46.5
14.7
13.6
11.7
17
144.6
40.4
41.5
41.2
35.2
37.5
47.5
10.1
18
176.9
40.7
41.4
41.2
37.0
37.3
49.1
8.6
19
20
220.8
277.8
41.0
41.2
41.5
41.6
41.4
41.6
38.6
39.6
37.4
37.5
50.2
51.4
7.5
6.5
Globe Valve
Table 4.2(a) Experimental Results For Light Blue Circuit
Test
Time To
Piezometer Tube Readings (cm)
V-Tube
Number
Collect 18 kg
Water
(s)
Water
(cm) Hg
12
13
14
15
16
Globe Valve
11
73.2
12.1
35.0
7.2
32.1
3.8
37.4
20.2
12
76.8
14.1
34.9
9.7
32.5
6.0
38.5
19.0
13
82.6
17.0
34.9
12.6
31.6
8.6
40.2
17.4
14
15
16
95.4
102.6
130.8
22.0
23.6
28.0
34.5
34.2
33.4
17.6
19.4
23.7
31.5
43.0
44.0
46.5
14.7
30.7
29.6
13.7
15.2
19.5
13.6
11.7
17
144.6
29.7
33.4
25.5
29.8
21.4
47.5
10.1
18
176.9
31.9
33.2
27.7
29.4
23.5
49.1
8.6
19
20
220.8
227.8
33.6
35.0
33.3
33.4
39.4
30.9
29.5
29.5
25.4
26.8
50.2
51.4
7.5
6.5
Table 4.2(b) Experimental Results For Light Blue Circuit (continued)
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Specimen Calculation
From Table 4.2 test number 11.
Measured head rise = 48mm
(a)
Assuming no head loss
(𝑉12 − 𝑉22 )
ℎ2 − ℎ1 =
2𝑔
(Bernoulli)
Since
𝐴1 𝑉1 = 𝐴2 𝑉2
ℎ2 − ℎ1 =
(Continuity)
1 − (𝐴1 ⁄𝐴2 )2
]
2𝑔
𝑉12 [
1 − (𝑑1 /𝑑2 )4
= 𝑉12 [
]
2𝑔
From the table,
𝑉1 =
=
𝑄
𝐴1
18
73.2 × 103 × 147.3 × 10−6
= 1.67m/s
therefore
h2 - h1
= 1.672 [
1−(13.7/26.4)4
2 ×9.81
= 0.132m
]
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Therefore head rise across the sudden expansion assuming no head
loss is 132mm water.
(b)
Assuming
ℎ𝐿 =
2
ℎ2 − ℎ1 =
(𝑉1 − 𝑉2 )2
2𝑔
2
(𝑉1 − 𝑉2 )
2𝑔 − ℎ𝐿
(Bernoulli)
(𝑉21 − 𝑉22 ) (𝑉1 − 𝑉2 )2
=
−
2𝑔
2𝑔
On rearranging and inserting values of d. = 13.7mm and d2 = 26.4mm,
this reduces to
0.396𝑉21
ℎ2 − ℎ1 =
2𝑔
which when
V1 = 1.67m/ s
gives
ℎ2 − ℎ1 = 0.0562𝑚
Therefore head rise across the sudden expansion assuming the simple
expression for head loss is 56mm water.
Figure 4.3 shows the full set of results for this experiment plotted as a graph
of measured head rise against calculated head rise.
Comparison with the dashed line on the graph shows clearly that the head
rise across the sudden expansion is given more accurately by the assumption of a
simple head loss expansion than by the assumption of no head loss.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Figure 4.3 Head Rise Across a Sudden Enlargement
4.4
Sudden Contraction
The object of this experiment is to compare the measured fall in head across a
sudden contraction, with the fall calculated in the assumption of:
(a)
(b)
No head loss;
Head loss given by the expression
𝐾 𝑉2
ℎ𝐿 =
2𝑔
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Specimen Calculation
From Table 4.2, test number 11.
Measured head fall = 221mm water
(a)
Assuming no head loss
Combining Bernoulli's equation and the continuity equation gives:
ℎ2 − ℎ1 = 𝑉22 [
1 − (𝑑1 /𝑑2 )4
]
2𝑔
= 0.927
𝑉22
2𝑔
Which when V2 = 1.67m/s gives
ℎ2 − ℎ1 = 0.132𝑚
Therefore head fall across the sudden contraction assuming no head
loss is 132mm water.
(b)
Assuming
𝐾 𝑉22
ℎ𝐿 =
2𝑔
ℎ2 − ℎ1 = 𝑉22 [
=
1 − (𝑑1 /𝑑2 )4
]
2𝑔 + ℎ𝐿
1 − (𝑑1 /𝑑2 )4
𝑉22
[
2𝑔 +
𝐾𝑉22
2𝑔 ]
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
𝐴
From Table 1, when 𝐴2 = 0.27
1
K = 0.376
giving
ℎ2 − ℎ1 = 0.927
= 1.303
𝑉22
𝑉22
+ 0.376
2𝑔
2𝑔
𝑉22
2𝑔
Which when V2 = 1.67m/s gives
h1 – h_2 = 0.185m
Therefore head fall across the sudden contraction assuming loss
coefficient of 0.376 is 18.5cm water.
Figure 4.4 shows the full set of results for this experiment plotted as a graph
of measured head fall against calculated head fall.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Calculated decrease in head (cm of water)
Figure 4.4 Head Decrease across a Sudden Contraction
The graph shows that the actual fall in head is greater than predicted by the
accepted value of loss coefficient for this particular area ratio. The actual
value of loss coefficient can be obtained as follows:
Let hm = measured fall in head and K' = actual loss coefficient
then
ℎ𝑚 = 0.927
𝑉 2 𝐾′𝑉 2
+
2𝑔
2𝑔
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
hence
𝐾′ =
ℎ×2×𝑔
𝑉22
− 0.927
which when
v2 = 1.67 m/s gives K' = 0.63
Bends
4.5
The aim here is to measure the loss coefficient for five bends. There is some
confusion over terminology, which should be noted; there are the total bend
losses (KL hL) and those due solely to bend geometry, ignoring frictional
losses (KB, hB).
2𝑔
𝐾𝐵 = 𝑉 2
(Total measured head loss - straight line loss)
i.e.
i
.
e
.
𝐾=
2𝑔
𝑉2
(Head gradient for bend - k x head gradient for straight pipe)
Where k = 1 for KB
𝐾 =1−
For either,
ℎ=𝐾
2𝑃𝑖
2𝐿
𝑉2
2𝑔
Plotted on Figure 4.5 are experimental results for K B and KL for the 5 types of
bends and also some tabulated data for KL. The last was obtained from
'Handbook of Fluid Mechanics' by VL Streeter. It should be noted though,
that these results are by no means universally accepted and other sources
give different values. Further, the experiment assumes that the head loss is
6.
independent of Reynolds Number and this is not exactly correct.
Figure 4.5 Graph of Loss Coefficient
Is
the
form
of
Kg
what
you
would
expect?
Does
putting
have any effect? Which do you consider more useful to measure, KL or KB?
vanes
in
an
elbow
4.6
The
Valves
object
of
this
experiment
is
to
determine
the
relationship
coefficient and volume flow rate for a globe type valve and a gate type valve.
Specimen Calculation
2
𝐾𝑉
ℎ𝐿 =
2𝑔
Globe Valve
From Table 4.2, test number 11.
Volume flow rate = 246 × 10−6 𝑚3 /𝑠 (valve fully open)
U-tube reading
= 172𝑚𝑚 mercury
= 172 × 12.6
Therefore hL
= 2.17𝑚 water
= 1.67 𝑚/𝑠
Velocity (V)
Giving K
=
2.17×2×9.81
1.672
= 15.3
Figure 4.6 shows the full set of results for both valves in the form of a graph of loss
coefficient against percentage volume flow.
between
loss
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Percentage Flow Rate
Figure 4.6 Loss Coefficients for Globe and Gate Valves
7.
8.
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Normal
manufacturing
tolerances
assume
greater
importance
when
the
physical scale is small. This effect may be particularly noticeable in relation
to the internal finish of the tube near the pressure tappings. The utmost care
is taken during manufacturing to ensure a smooth uninterrupted. Bore of the
tube in the region of each pressure tapping, to obtain maximum accuracy of
pressure reading.
Concerning again all published information relating to pipe systems, the
Reynolds Numbers are large, in the region of 1 x 105 and above. The
maximum Reynolds Number obtained in these experiments, using the
hydraulic bench, HI, is 3 x 104 although this has not adversely affected the
results. However, as previously stated in the introduction to this manual, an
alternative source of supply (provided by the customer) could be used if
desired, to increase the flow rate. In this case an alternative flow meter would
also be necessary.
The three factors discussed very briefly above are offered as a guide to
explain discrepancies between experimental and published results, since in
most cases all three are involved, although much more personal investigation
is required by the student to obtain maximum value from using this
equipment.
In conclusion the general trends and magnitudes obtained give a valuable
indication of pressure loss from the various components in the pipe system.
The student is therefore given a realistic appreciation of relating experimental
to theoretical or published information.
SECTION
5.0
GENERAL
REVIEWS
OF
THE
EQUIPMENT
AND
RESULTS
An attempt has been made in this apparatus to combine a large number of pipe components
into a manageable and compact pipe system and so provide the student user with the
maximum scope for investigation. This is made possible by using small bore pipe tubing.
However, in practice, so many restrictions, bends and the like may never be encountered in
such short pipe lengths. The normally accepted design criteria of placing the downstream
pressure tapping 30-50 pipe diameters away from the obstruction i.e. the 90° bends, has been
adhered to. This ensures that this tapping is well away from any disturbances due to the
obstruction and in a region where there is normal steady flow conditions. Also sufficient pipe
length has been left between each component in the circuit; to obviate any adverse influence
neighboring components may tend to have on each other.
Any discrepancies between actual experimental and theoretical or published
results may be attributed to three main factors:
(a)
(b)
Relatively small physical scale of the pipe work;
Relatively small pressure differences in some cases;
(c)
Low Reynolds Numbers.
The relatively small pressure differences, although easily readable, are encountered on the
smooth 90° bends and sudden expansion. The results on these components should therefore be
taken with most care to obtain maximum accuracy from the equipment. The results obtained
however, are quite realistic as can be seen from their comparison with published data, as
shown in Figure 4.5. Although there is wide divergence even amongst published data, refer to
page 472 of “Engineering Fluid Mechanics”, it is interesting to note that all curves seem to
𝑟
show a minimum value of the loss coefficient 'K' where the ratio"𝑑 " is between 2 and 4. It is
important to realize and remember throughout the review of the results that all published data
have been obtained using much larger bore tubing (76mm and above) and considering each
component in isolation and not in a compound circuit.
. by Charles Jaeger and published by Blackie and Son Lt