Hydraulic Jump
Objectives
In this laboratory you will investigate an open-channel flow (flow down a channel with a free
surface, e.g., not confined by a rigid surface as would be the case in pipe flow) using conservation
equations (mass, linear momentum and energy). You will be introduced to the hydraulic
phenomenon known as the hydraulic jump (see Figure 1-1) – the sudden transition from a higher
energy state to a lower energy state while conserving momentum (analogous to a shock wave in
compressible gas flows). This is your chance to get a tangible sense of these conservation
equations and concepts such as the energy grade line and hydraulic grade line. You will also get a
chance to think about the energy equation and when the assumptions of the Bernoulli equation are
Figure 1-1.
Constant-head flume with supercritical flow exiting the sluice gate at the left-hand side
of picture, a hydraulic jump at the beginning of the test section, and subcritical going over the weir at the
outlet.
1
valid and when they are violated .
Theory
Flow through a sluice gate can be reasonably modeled using the Bernoulli equation. The
potential energy of the water behind the sluice gate is converted into kinetic energy as the water
passes under the gate. Thus the velocity of the water can be calculated directly from the height of
the water behind the sluice gate. Hydraulic jumps occur in open channel flow when the flow
transitions from supercritical to subcritical flow. A description of the phenomena can be found in
Munson, et al. page 653. The upstream (y1) and downstream (y2) depths are related by equation
1.2.

y2 1
 1  1  8Fr12
y1 2

1.2
where the upstream Froude number (Fr1) is defined as
1
Adapted from Lab #3 Conservation Equations and the Hydraulic Jump, CEE 331 Fall 2001,
Professor Cowen, Cornell University)
Fr1 
V1
1.3
gy1
The velocity in the channel can be determined by applying the Bernoulli equation in the region
where velocity is increasing between the reservoir and immediately
downstream of the sluice gate. The velocity can also be measured
with a stagnation tube connected to a pressure sensor. The
Pressure sensor
stagnation tube will be filled with water prior to connecting to the
pressure sensor and the pressure sensor output will be zeroed with
the stagnation tube held vertically (in the same orientation used for
Stagnation tube
taking measurements.) Thus the pressure sensor will measure the
pressure at point 3 (Figure 1-2). From the Bernoulli equation
1
across streamlines we can obtain the following relationship.
p1

Since
p1

 z1 
p2

 z2
1.5
2
3
z
=0 we have
p2

 z1  z2
1.6
Figure 1-2.
Stagnation tube and
pressure sensor used to measure
velocity in open channel flow.
From the Bernoulli equation along streamlines we have
p2

 z2 
V2
V22 p3
  z3  3
2g 
2g
1.7
V32
where
will be measured using a pressure transducer. Since
is zero and z2  z3 we can

2g
p3
obtain
p3

 z1  z3 
V22
2g
1.8
Thus the stagnation pressure head includes both the static head based on the submergence of the
stagnation tube tip as well as the velocity head.
Experimental Methods
A small flume will be set up with a stable hydraulic jump. Your goal is to measure the flume
dimensions and fluid velocity upstream and downstream from the hydraulic jump.
Make the following measurements Height of water in the reservoir (cm)
using the bottom of the channel as your Stagnation pressure head at the
elevation datum. In addition to these opening of the sluice gate (cm)
measurements you should play with the Stagnation pressure head just upstream
stagnation tube and the hydraulic jump of the hydraulic jump (cm)
so you can answer the questions for the
Depth of submergence of the
lab report.
stagnation
tube
for
previous
measurement (cm)
Questions
Depth of water just upstream of the
Before doing lab:
hydraulic jump (cm)
Depth of water downstream of the
1) Roughly plot the EGL to see what hydraulic jump (cm)
kind of energy changes you expect to
happen.
2) Think about a way to calculate the fluid velocity right outside the sluice gate without having
to use a Pitot or stagnation tube. Also, since we won’t be taking measurements in the region
after the hydraulic jump, figure out a way to find the velocity there.
After the lab:
1) Calculate the velocities and Froude numbers in the super and sub critical regions.
2) Create a more exact EGL plot using your test data. Was it similar to what you expected? If
not, what are the reasons for this?
3) Why was the weir important in generating the hydraulic jump?
4) Explain which equations you can or can’t use to analyze the different sections of the set-up.
Why?
5) Describe the properties of the sub and super critical regions. If you had no instruments, what
could you do to differentiate between sub and super critical flows.
6) What happens if you measure the stagnation pressure at the very bottom of the
channel? Explain based on the properties of real fluids.