H16 Losses in Piping Systems
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2. 1.
© TecQuipment Limited
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2. 1.
© TecQuipment Limited
No part part of this publica publication tion may may be reprodu reproduced ced or transm transmitted itted in any form or by any means, electronic or mechanical, including photocopy photocopy,, recording recording or any informatio information n storage storage and retrieval retrieval system without the express permission of TecQuipment Limited. Exception to this restriction is given to bona fide customers in educational or training establishments in the normal pursuit of their teaching duties. Whilst all due care has been taken to ensure that the contents of this manual are accurate and up to date, errors or omissions may occur from time to time. If any errors are discovered in this manual please inform TecQuipment Ltd. so the problem may be rectified. A Packing Contents List is supplied with the equipment and it is recommended that the contents of the package(s) are carefully checked against the list to ensure that no items are missing, damaged or discarded with the packing materials. In the event that any items are missing or damaged, contact your local TecQuipment agent or TecQuipment directly as soon as possible.
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. 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, circuits , one painted dark blue, blue , one painted light blue, blue , each one containi containing a number of pipe system components . Bot Both circui circuits are supplied with water from the same hydraulic bench . The components in each of the circuits are as follows: follows: Dark Blue Circuit
Light Blue Circuit
3. 4.
1.
Gate Valve
2.
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° 90° Radius Bend
10.
50mm 90° Radius Bend
TECQUIPME NT H16 LOSSES IN PIPING S YSTEMS
Key to Apparatus Arrangement A
Straight Pipe 13.7mm Bore
B
90° Sharp Bend (Mitre)
C
Proprietar y 90° Elbow
D
Gate Valve
E
Sudden Enlargement - 13.7mrn/26.4mm
F
Sudden Contraction - 26.4mrn/13.7rnrn
G
Smooth 90° Bend 50mm Radius
H
Smooth 90° Bend 100mrn Radius
J
Smooth 90° Bend lS0mm Radius
K
Globe Valve
L
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.
SECTIO N 2.0 THEOR Y
Figure 2.1
Figure 2.2
Figure 2.3
For an incompressible fluid flowing through a pipe the following equations apply:
(Continuity)
Notation: Q Volumetric flow rate (m3/s) V Mean Velocity (m/s) 3 A Cross sectional area (m ) Z Height above datum (m)
(Bernoulli)
P Static pressure (N/m2) hL Head Loss (m) ρ
Density (kg/m3)
g Acceleration due to gravity (9.81m/s2)
2.1
Head Loss The head loss in a pi pe 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 diff er from that estimated fr om 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 ex pression:
where f is a dimensionless constant which is a f unction of the Reynolds number of the flow and the roughness of the internal sur f ace of the pipe. Head Loss due to Sudden Changes in Area of Flow Sudden Expansion: The head loss at a sudden ex pansion is given by the expression:
TECQUIPME NT H16 LOSSES IN PIPI NG SYSTEMS
Sudden Contraction: The head loss at a sudden contraction is given by the ex pression:
where K is a dimensionless coefficient which depends upon the area ratio as shown in Ta ble 2.1. This ta ble can be f ound 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 Coeff icient For Sudden Contractions
Head Loss Due To Bends The head loss due to a bend is given by the ex pression:
wher e K is a dimensionless coef ficient which depends upon the bend radius/ pipe radius r atio 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 ty pical loss coefficients.
Head Loss due to Valves The head loss due to a valve is given by the expr ession:
where the value of K depends upon the ty pe of valve and the degrees of opening. Ta ble 2.2 gives typical values of loss coef ficients 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. Pr inciples of Pr essure Loss Measurements
Figure 2.4 Pressurised Piezometer Tubes to Measure Pressur e Loss between Two Points at Dif f erent Elevations Considering Figure 2.4, apply Ber noulli's equation between points 1 and 2:
but:
(2-1)
therefore
(2-2)
Consider Piezometer tubes:
()
(2-3)
(2-4)
ρ
also
giving
()
(2-5)
Comparing Equations (2-2) and (2-5) gives
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:
= h ()
(2-7)
L
Consider the U-tube. Pressure in both limbs of the U-tube is equal at level 00. Therefore equating pressure at 00:
()
(2-8)
TECQUIPME NT H16 LOSSES I N PIPI NG SYSTEMS
Figure 2.5 U- Tube Containing Mercury used to measure Pressure Loss across Valves
giving
(2-9)
hence:
() (2-10)
Considering Equations (2-7) and (2-10) and taking the specific gravity of mercur y as 13.6: hL = 12.6x
(2-11)
TECQUIPMENT H16 LOSSES I N PIPI NG 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 val ve 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 t o 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 lock s 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 shou ld 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.
TECQUIPME NT H16 LOSSES IN PIPI NG SYSTEMS
With simple mercur y in glass thermometer record the water temperatur e in the sump tank of the bench each time a reading is taken .
Close the gate valve, open the globe and repeat the ex perimental procedur e for the
Light Blue
circuit.
Before switching off the pump, close both the globe val ve 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 = 13.7mrn
Pipe Diameter (internal)
Basic Data
Pipe Diameter [between sudden expansion (internal) and contraction]
= 26.4mrn
Pipe Material
Copper Tube
Distance between pressure tappings for straight
Bend Radii
pipe and bend ex periments
= 0.914m
90° Elbow (mitre)
=0
90° Proprietar y elbow
= 12.7mm
90° Smooth bend
= 50mm
90° Smooth bend
= 100mm
90° smooth bend
= 150mm
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
tikungan standar pipa lurus tikungan siku tajam
Expansion
ekspansi
Contraction
kontraksi
150mm bend
tikungan 150mm
100mm bend
tikungan 100mm
50mm bend
tikungan 50mm
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
4.2
Straight Pipe Loss
The object of this experiment is to obtain the following relationships: (a)
Head loss as a function of volume flow rate;
(b)
Friction Factor as a function of Reynolds Number.
Test
Time To
Piezometer Tube Readings (cm)
U-Tube
Number
Collect 18 kg
Water
(cm) Hg
Water (s)
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
146.2
52.6
44.4
54.4
37.7
78.4
66.1
47.3
10.3
10
229.8
52.9
49.1
45.0
41.5
77.4
72.0
50.3
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
Gate-Valve
TECQUIPME NT H16 LOSSES I N PIPI N G SYSTEMS
Volume flow rate (Q)
Area of flow (A)
Mean Velocity (V)
Reynolds Number (Re)
For water at 23°C Therefore Re
Friction Factor (f)
⁄
⁄
Figure 4.1 shows the head loss - volume flow rate relationship plotted as a graph of log hL against log Q. n
The graph shows that the relationship is of the form h L α Q with n = 1.73
TECQUIPME NT H16 LOSSES I N PIPI NG SYSTEMS
This value is close to the normally accepted r ange of 1.75 to 2.00 for turbulent flow. The lower value n is found as in this appar atus, in comparatively smooth pipes at com par atively low Reynolds Number . Figure 4.2 shows the Fr iction Factor - Reynolds Number relationship plotted as a graph of fr iction factor against Reynolds Number . The
graph
also
shows
for
compar ison
the
relationshi p
circulated
f ro m
Blasius's equation for hydraulically smooth pi pes. Blasius's equation:
f
In the range 10 4 < Re < 105 ⁄
As would be ex pected the gra ph shows that the friction factor for the copper pipe in the appar atus is greater than that pr edicted for a smooth pipe at the same R eynolds Number .
Figur e 4.1 Head Loss - Volume Flow R ate
5.
TECQUIPME NT H16 LOSSES I N PIPI NG SYSTEMS
Figure 4:2 Friction Factor - Reynolds Number
4.3
Sudden Expansion
naik coy tinggi tekannya
The object of this ex periment is to compare the measured head rise across a sudden expansion with the rise calculated on the assumption of: (a)
No head loss;
(b)
Head loss given by the expression:
( ) dipakai dua asumsi (a) dan (b) yang kemudian akan dibandingkan
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Test
Time To
Piezometer Tube Readings (cm)
V-Tube
Number
Collect 18 kg
Water
(cm) Hg
expansion
Water (s)
7
8
9
10
11
Globe Valve
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
95.4
39.4
42.0
41.5
28.5
38.3
43.0
14.7
15
102.6
39.7
42.2
41.7
30.2
38.0
44.0
13.6
16
130.8
40.0
41.5
41.1
33.8
37.3
46.5
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
220.8
41.0
41.5
41.4
38.6
37.4
50.2
7.5
20
277.8
41.2
41.6
41.6
39.6
37.5
51.4
6.5
Table 4.2(a) Experimental Results For Light Blue Circuit
Test
Time To
Piezometer Tube Readings (cm)
V-Tube
Number
Collect 18 kg
Water
(cm) Hg
Water (s)
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
95.4
22.0
34.5
17.6
31.5
13.7
43.0
14.7
15
102.6
23.6
34.2
19.4
30.7
15.2
44.0
13.6
16
130.8
28.0
33.4
23.7
29.6
19.5
46.5
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
220.8
33.6
33.3
39.4
29.5
25.4
50.2
7.5
20
227.8
35.0
33.4
30.9
29.5
26.8
51.4
6.5
Table 4.2(b) Experimental Results For Light Blue Circuit (continued)
(delta h = 17,2)
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Specimen Calculation From Table 4.2 test number 11. Measured head rise = 48mm
(a)
(43,5 - 38,7 = 4,8 cm)
Assuming no head loss hL = 0
) ( (Bernoulli) Since
( ⁄ ) ( )
(Continuity)
From the table,
= 1.67m/s therefore
h2 - h1
() = [ ] = 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 <> 0
( )
(Bernoulli)
) (
On rearranging and inserting values of d. = 13.7mm and d2 = 26.4mm, this reduces to Dalam menyusun kembali dan memasukkan nilai d = 13,7 mm dan d2 = 26,4 mm akan mengurangi:
which when V1 = 1.67m/ s
gives
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. garis putus-putus
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. (hL <> 0) lebih akurat daripada (hL = 0)
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
garis A lebih dekat dengan garis putus-putus, berarti garis A lebih akurat
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 assumpt ion of: (a)
No head loss;
(b)
Head loss given by the expression
TECQUIPME NT H16 LOSSES I N PIPI NG 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:
() Which when V2 = 1.67m/s gives
Therefore head fall across the sudden contraction assuming no head loss is 132mm water.
(b)
Assuming
) (
() [ ]
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
Fr om Table 1, when
K = 0.376
giving
Which when V2 = 1.67m/s gives h1 – h _2 = 0.185m Therefore head fall across the sudden contraction assuming loss coef ficient of 0.376 is 18.5cm water.
Figure 4.4 shows the full set of results for this exper iment plotted as a graph of measur ed head fall against calculated head f all.
TECQUIPME NT H16 LOSSES I N PIPI NG SYSTEMS
Calculated decrease in head (cm of water)
Figure 4.4 Head Decrease across a Sudden Contraction
The gra ph shows that the actual fall in head is gr eater than pr edicted by the acce pted value of loss coefficient for this particular area ratio. The actual value of loss coef f icient can be obtained as follows: Let hm = measur ed fall in head and K' = actual loss coefficient then
TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS
hence
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 (K L hL) and those due solely to bend geometry, ignoring frictional losses (K B, hB).
Koefisien kehilangan tinggi tekan total - KL Koefisien kehilangan tinggi tekan oleh geometri pipa - KB
(Total measured head loss - straight line loss)
i.e. i . e .
(Head gradient for bend - k x head gradient for straight pipe)
Where k = 1 for K B
For either,
Plotted on Figure 4.5 are experimental results for K B and K L for the 5 types of bends and
also some tabulated data
for K L. 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
ex pect?
Does
putting
have any eff ect? Which do you consider more useful to measure , K L or K B?
vanes
in
an
elbow
4.6
The
Valves
object
of
this
experiment
is
to
de termine
the
relationship
coefficient and volume flow rate for a globe type valve and a gate type valve .
Specimen Calculation
Globe Valve
From Table 4.2, test number 11 .
Volume flow rate U-tube reading Therefore hL
Giving K
=
(valve fully open)
mercury
=
= Velocity (V)
=
water
=
=
= 15.3
Figure 4.6 shows the full set of resul ts for both valves in the form of a graph of loss coefficient against percentage volume flow.
between
loss
TECQUIPME NT H16 LOSSES IN PIPING SYSTE MS
Percentage Flow Rate
Figure 4.6 Loss Coefficients for Globe and Gate Valves
7.
8.
TECQUIPMENT H16 LOSSES I N PIPI NG SYSTEMS
Normal
manufacturing
tolerances
assume
greater
importance
when
the
physical scale is small. This effect ma y 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 ma ximum accuracy of pressure reading. Concerning again all published inf ormation 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
ex per iments,
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 ver y briefly above are off ered as a guide to ex plain discrepancies between ex perimental 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 equi pment. In conclusion the general trends and magnitudes obtained gi ve a valuable indication of pressure loss fr om the various components in the pipe system. The student is ther ef ore given a realistic appreciation of relating ex per imental to theoretical or published inf or mation.
