Updated 11/26/08
Energy Losses in Bends
Introduction
Energy losses in pipe flows are the result of friction between the fluid and the pipe walls
and internal friction between fluid particles. Minor (secondary) head losses occur at any
location in a pipe system where streamlines are not straight, such as at pipe junctions,
bends, valves, contractions, expansions, and reservoir inlets and outlets. In this
experiment, you will measure minor head losses through a pipe section that has several
bends, transitions, and fittings as shown in Figure 1.
Figure 1. Schematic drawing of the energy-loss apparatus.
Objective
The objectives of this lab are to measure head losses through bends, transitions, and
fittings, and to use these measurements to estimate the loss coefficients for each transition
or fitting.
Theory
The energy balance between two points in a pipe can be described by the Bernoulli
equation, given by
p1
V2
p
V2
 z1  1  2  z2  2  hL ,

2g

2g
(1)
where pi is static pressure (in Pa) at point i,  is specific weight of the fluid (in N/m3), zi is
the elevation (in meters) of point i, Vi is the fluid velocity (in m/s) at point i, g is the
gravitational constant (in m/s2), and hL is head loss (in meters). The term pi/ is referred
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to as the static head; zi is the elevation head; and Vi/2g is the dynamic (or velocity) head.
The summation of the static head and the elevation head, pi/ + zi, is referred to as the
piezometric head. The piezometric head is what is measured with the piezometer
(manometer) board on the apparatus for this experiment.
Head loss, hL, includes the sum of pipe friction losses, hf, and all minor losses,
hL  h f 
h ,
i 1n
i
(3)
where hi is the minor head loss (in meters) for the ith component and n is the number of
components (fittings, bends, etc.). Pipe friction losses are expressed as the DarcyWeisbach equation given by
L V2
,
(2)
hf  f
D 2g
where f is a friction factor, L is the pipe length, and D is the pipe diameter. Pipe friction
losses are assumed to be negligible in this experiment.
Minor losses occur at any bend, transition, or fitting where the streamlines are not straight
and are proportional to the velocity head. For all components, head loss is given by
V2
,
hi  Ki
2g
(5)
where Ki is the loss coefficient (dimensionless) for the ith component and V is the fluid
velocity as it travels through the pipe component. For the expansion and contraction, the
V used in Equation (5) is the velocity of the fluid in the smaller-diameter pipe.
In this experiment, the loss coefficients for different pipe components will be
experimentally determined by calculating the minor head loss using Equation (1) and
utilizing Equation (5) to find the loss coefficient. In Exercise B a pressure difference
across a gate valve is measured from a pressure gauge in units of bars and must be
converted to an equivalent head loss using the following relationship
1 bar = 10.2 m water.
2
(6)
Updated 11/26/08
Equipment


Armfield Hydraulics Bench with Energy Losses apparatus
Stop Watch
The Energy Losses apparatus is a pipe with several pipe fittings. Piezometers (a type of
manometer) are connected to the pipe upstream and downstream of each fitting to
measure the pressure in the pipe at those locations.
Technical Data
The following dimensions from the equipment are used in the appropriate calculations.
Internal diameter of main pipe:
Internal diameter of enlargement outlet and contraction inlet:
0.0196 m
0.0240 m
Procedure
Exercise A
1. Setup the Energy Losses in Bends (ELB) accessory on a hydraulic bench with its base
level. This is necessary for accurate height measurements from the manometers.
2. Connect the quick disconnect of the ELB Accessory to the bench flow supply in the
basin of the hydraulics bench and run the outlet extension tube into the volumetric
tank. Make sure both ends are secure to prevent water from spraying everywhere. If
you can see the ball bearings on the quick disconnect of the hydraulics bench, the
inlet tube is not secure.
3. On the hydraulics bench, completely close (i.e. turn all the way clockwise) the valve
for the pump, and then open the valve about one turn. (If the valve is fully open when
you turn on the pump, the water exits too quickly through the exit tube and sprays
water all over the lab). Do NOT turn on the pump yet!
4. On the head loss apparatus, completely open (i.e. turn all the way counter clockwise)
the gate valve fitting, located just below the pressure gauge, and the flow-control
valve, located on exit of the module.
5. Check that the pressure taps from either side of the mitre bend are not clamped by the
white clamps.
6. Attach a piece of plastic tubing to the air-bleed valve (Figure 1). Point the air-bleed
tube into the hydraulics bench.
7. Turn on the hydraulics bench pump.
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8. Slowly open the air-bleed screw completely to purge the manometer board of all air
bubbles.
a. Be sure the air-bleed tube is pointing into the reservoir.
b. Slowly close the flow-control valve (not all the way!) on the exit of the
head loss apparatus to force the water out the air-bleed tube until the
manometer board readings are be completely full of water (no air
bubbles).
9. Close the air-bleed screw.
10. Remove the air-bleed tube and attach the bicycle pump to the air-bleed valve.
11. Close the flow-control valve, located on exit of the module.
12. Quickly, open the air-bleed screw and pressurize the manometer board by forcefully
pumping air until the water levels are near 320 mm.
13. Immediately close the air-bleed screw and remove the bicycle pump. Be sure the
water levels are still near 320 mm.
14. Slowly open the flow-control valve on the head loss apparatus to select a flow rate of
approximately 18-20 L/min. . The maximum flow rate that can be obtained while
keeping all manometer levels at a recordable level is 20 liters per minute.
a. The flow-control valve and the pump valve of the hydraulic bench may be
adjusted, but do not use the gate valve.
b. Make sure that the difference between the first and second manometer
readings is at least 8mm so that the pressure difference is significantly higher
than the measurement error. Be sure to maintain this difference at lower flow
rates where the two measurements start to converge.
c. Monitor the manometer board to make sure the sixth manometer reading does
not exceeding the manometer range and the twelfth reading does not drop too
low as to be off the manometer board. These are the limiting cases for
measurement range. The air-bleed screw may need to be opened to
add/release air from the manometer board to get just the right reference
pressure in order to maximize your measurement range for the various flow
rates.
15. Record the flow rate using the following proceedure.
a. Close the dump valve via the dump valve handle on the Hydraulics Bench.
The fluid will start to rise in the volume measuring tank. Wait for the water
level to reach zero on the upper scale of the side tube scale (near the pump
ON/OFF switch) before starting your measurement.
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b. Using the side tube scale and a stopwatch, measure the volume change as a
function of time (at least 30 seconds to obtain an accurate flow rate
measurement).
c. Once you have obtained your timed volume collection – reopen the dump
valve to drain the tank.
16. Record the level of water in each of the manometers using the included table. Also,
record to what location each manometer reading corresponds.
17. Repeat Steps 14-16 for four additional flow rates (total of five) that span the range
from approximately 10-20 L/min.
18. Continue directly to Exercise B.
Exercise B
19. Clamp the tubes running from the pressure taps on either side of the mitre bend with
the white, hose clamps in order to prevent air from getting into the system.
20. Close the gate valve completely.
21. Fully open the flow-control valve and the pump valve of the hydraulic bench.
22. Open the gate valve by approximately 50% of one turn (after taking up any backlash
in the valve—watch the pressure gauge for a change).
23. For each of five flow rates, measure the pressure drop across the valve using the
pressure gauge that is mounted above the valve.
a. Adjust the flow rate by use of the flow-control valve at the exit of the
accessory. Do not adjust the gate valve.
b. Determine the flow rate as in the previous exercise.
24. Repeat Steps 20-23 for the gate valve open approximately 70% and 85% of one turn.
Shut Down
25. Unclamp the white, hose clamps from the hoses of the mitre bend.
26. Open the gate valve completely.
27. Fully open the flow-control valve at the exit of the accessory.
28. Turn off the pump of the hydraulics bench.
29. Completely close the pump valve of the hydraulics bench.
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Calculations and Results
Fill in Tables 3 – 5 with calculated results. Assume that the pipe friction losses between
the upstream and downstream manometer ports are negligible, so the total head loss is
due to minor head losses. Remember the piezometric head is what is measured with the
piezometer (manometer) board on the experimental apparatus.
Questions
1. For Exercise A, prepare plots that show the effect of dynamic head on minor head
loss and the effect of flow rate on loss coefficients. Use error bars to depict
measurement uncertainty.
2. For Exercise B, prepare plots that show the effect of dynamic head on equivalent
head loss (Equation (1) is not used) and the effect of flow rate on loss coefficients.
Use error bars to depict measurement uncertainty.
3. Comment on and explain the relationships evident in the plots of Questions 1 and 2.
Include a comparison of the loss coefficients and geometry for the four types of
bends.
a. Is it justifiable to treat the loss coefficient as constant for a given fitting?
Explain.
b. How does the loss coefficient for the gate valve vary with the extent of the
opening of the valve? Explain.
4. Compare the experimental loss-coefficient values for different fittings to those found
in a fluid mechanics text book (or another source). Be sure to cite the source of the
published values.
5. Does the static pressure increase or decrease for the enlargement and contraction?
Explain the increase or decrease in static pressure.
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Raw-Data Tables
Q
(L/min)
Enlargement
1
2
(mm)
(mm)
Table 1. Raw Data for All Fittings Except Gate Valve
Piezometer Readings
Contraction
Long Bend
Short Bend
3
4
5
6
7
8
(mm)
(mm)
(mm)
(mm)
(mm)
(mm)
Q
(L/min)
Table 2. Raw Data for Gate Valve
Valve-Gauge Readings
Valve Position
Red
Black
(% of 1 turn)
(downstream)
(upstream)
(bar)
(bar)
7
Elbow
9
(mm)
10
(mm)
Mitre Bend
11
12
(mm)
(mm)
Updated 11/26/08
Result Tables
Q
(L/min)
Q
(L/min)
Table 3. Minor Head Losses of All Fittings Except Gate Valve
Minor Head Losses
Enlarge.
Contract.
Long Bend
Short Bend
Elbow
Mitre Bend
(m)
(m)
(m)
(m)
(m)
(m)
Table 4. Loss Coefficients for All Fittings Except Gate Valve
Loss Coefficients
Enlarge.
Contract.
Long Bend
Short Bend
Elbow
Mitre Bend
(m)
(m)
(m)
(m)
(m)
(m)
Table 5. Equivalent Minor Head Loss and Loss Coefficient for Gate Valve
Q
(L/min)
Minor Head
Loss of Valve
(m)
8
Loss
Coefficient