Hydraulics 1 Laboratory: Momentum and Energy
(2010)
In this experiment you will use water flumes to investigate open channel flows, employing the concepts
of momentum and energy are introduced in the lectures. During the experiments you should
concentrate on recording accurate measurements of the flow. At the end of the laboratory analysis
there are some further problems to complete later. Some of the analysis and the further problems will
need to be completed on extra sheets of paper and stapled to the back of this booklet.
Flume
Two slightly different flumes will be used. One is a closed circuit and the flow rate is measured using
a flow meter while to measure the flow in the other flume you need to divert the flow into a measuring
tank for a measured period of time and record the change in level.
Flume width
Flume E, flow rate calculation
Factor_____________m3/in
w = ____________ m
Reading before___________
Volume_____________m3
Reading after____________
Time________________s
Difference______________
Flow rate____________m3 s-1
Flume K, flow rate calculation
Flow rate___________litres/min
Flow rate_____________ m3 s-1
Hydraulic Jump
Measure the height of the water surface and the tank bottom and find the difference to calculate the
water depth upstream and downstream of the hydraulic jump. You should use the point gauge (with
the vernier scale) to measure these depths.
h2
h1
Upstream
Downstream
Water surface
Tank bottom
Water depth
h1
h2
1
Sluice
At the start of the flume the water is forced under a sluice gate. The sluice gate has some small holes
connected to manometer tubes which allow us to measure the pressure. There are two sets of tubes:
those on one side measure the pressure towards the top of the sluice gate while those on the other side
measure the pressure near the bottom of the sluice gate where the flow becomes shallower and faster.
For this experiment just use the set of seven tubes near the bottom of the gate (fast, shallow flow). All
the heights here can just be measured using a ruler.
(seven tubes in all)
h0
L = water level in manometer tube
(relative to tank bottom)
h
Fluid depth upstream of sluice:
h0 = _____________________
For each of the seven tube positions, measure the height of the bottom of the sluice from the tank
bottom and also measure the height of the water in the tube (again relative to the tank bottom). It may
be hard to measure the water level in the manometer tubes for the last two or three but at least make an
estimate of the maximum value the level could be.
Position
1
h
L
2
3
4
5
6
7
[End of experimental measurements section]
2
Analysis of laboratory experiments
Hydraulic Jump
u1
u2
h1
h2
Copy the water depths from your experiments (page 1) and calculate the relative size of the jump.
h1 =
h2 =
r = h2/h1 =
Using this value of r, calculate the theoretical estimate of the flow speed u1 (see notes).
[space for working]
Theoretical estimate for u1 (based on r):
Now use your measurements of flow rate, channel width and fluid depths to calculate the actual
velocities and Froude numbers.
Values based on measurements:
u1 =
u2 =
u1
Fr1 = √gh =
1
u2
Fr2 = √gh =
2
Compare the observed velocity with the theoretical prediction.
Using the measured depths and the velocities found from the flow rate measurements (not the
theoretical estimate), calculate the head loss and thus the power loss at the jump.
Head loss
Power loss
3
Sluice gate
(a) Bernoulli
z
L
(L - h)
streamline
h
Following a streamline just below the gate, the height of the streamline above the bottom of the tank is
z = h, while the pressure (relative to atmospheric pressure) is p = ρg(L - h), as (L - h) is the height of
the water in the manometer tube. For the seven tubes copy the values of h and L from your results
(page 2) and complete the rest of the table (including filling in the missing units).
z=h
L
p
ρg
= (L - h)
units
position
1
m
u
Q
= wh
dynamic
head
piezometric
head
u2
2g
p
+z
ρg
total head
m
2
3
4
5
6
7
Plot a graph showing dynamic head, piezometric head and total head as functions of position (attach
the graph to the end of this booklet).
Compare your results with the result you would expect from Bernoulli's equation:
4
(b) Force on sluice gate (control volume)
h0
F = horizontal force by water on gate
P0
u0
h1
u1
P1
For the control volume sketched above, what is the total (horizontal) hydrostatic pressure force P
(remember to include the channel width w)?
Calculate the rate of change of momentum of the fluid passing through the control volume,
(ρQu1 - ρQu0).
The total horizontal force (ignoring friction) on the water in the control volume is P - F (since the force
by the gate on the water is -F). Thus calculate the force on the sluice gate, F.
5
Further Problems
Attach the answers to the back of the booklet, along with any other extra sheets and graphs used for the
experiment sections.
1) Air is flowing through a tapering pipe that connects a larger diameter pipe to a smaller diameter
pipe. The upstream pipe has diameter 0.35 m while the downstream pipe has diameter 0.20 m. These
two sections are connected by a simple contraction where the diameter changes linearly from 0.35 m to
0.20 m over a distance of 0.5 m.
x
0.35 m
0.20 m
0.5 m
(a) If the flow rate along the pipe is 0.06 m3 s-1, find an expression for the speed of the flow as a
function of the distance from the start of the contraction, x.
(b) Find an expression for the acceleration of the air as a function of distance along the contraction.
(c) If there is no energy loss in the contraction, find the pressure difference between the ends of the
contraction (take the density of air to be 1.20 kg m-3).
2) Air is flowing through a horizontal venturimeter, with a contraction from a diameter of 100 mm to a
diameter of 40 mm (take the density of air to be 1.20 kg m-3). A water manometer connected between
the inlet and the contraction as shown gives a difference in level of 8.5 cm. If the discharge coefficient
for the venturimeter is Cd = 0.95, what is the air flow rate?
3) There is a flow of water of 0.012 m3 s-1, through a 60° (horizontal) bend with a contraction from
diameter 85 mm to 50 mm and into the atmosphere. What is the horizontal force required to hold the
nozzle in place? (Assume no energy loss in the bend/contraction.)
Atmosphere
Plan
60°
6