CIVL151 Fluid Mechanics
Laboratory Experiment 1: Hydraulic Jump
1. Definition
Hydraulic jump is a phenomenon that a rapidly flowing stream suddenly becomes a
slowly flowing stream with a larger cross-sectional area. In other words, there is a
depth increase for a hydraulic jump to exist by definition.
2. Objective
1) A prediction of whether or not a hydraulic jump can occur; and
2) To find the depths and velocity at the upstream and at the downstream; and
3) To calculate the energy loss through the hydraulic jump.
3. Theory
There are two equations to describe the hydraulic jump. One is the conservation of
mass and the other is the conservation of linear momentum.
-
Conservation of mass
It is because the flow rate is constant in section 1 and 2. Therefore,
Q1  Q2
V1 A1  V2 A2
( width b same)
V1 h1  V2 h2
Figure 1: A hydraulic jump in a channel flow.
-
Conservation of linear momentum
Newton’s second law states that the net force acting on a body in any fixed direction
is equal to the rate of increase of momentum of the body in that direction.
 Fx  F1  F2  g
h12
h2
 g 2  Q (v 2  v1 )
2
2

h2 1 
8v 2
  1  1  1
h1 2 
gh1

Note : Q is flow rate per unit width.
Here, we define Fr 
-
v1
gh1
and Fr is called the Froude Number.
Type
Will hydraulic jump
occur?
h2 > h1
Super-critical flow
Yes/No
Fr =1
h2 = h1
Critical flow
Yes/No
Fr < 1
h2 < h1
Sub-critical flow
Yes/No
Froude No.
Depth
Fr > 1
Energy dissipation
The energy will be loss in the hydraulic jump and the energy loss is
hL 
(h2  h1 ) 3
4h1 h2
(You should approve this equation by yourself and show it in the report!)
(All dimensions are in SI units.)
4.
1.
2.
3.
4.
5.
6.
Experimental Procedure
Adjust the channel to horizontal position and start the pump.
Wait until water level rises in the tank to the highest level mark of the tank
(several cm from the top). Allow a short interval of time between each
adjustment of the pump to allow the water level to stabilize. Otherwise the water
tank may be overtopped.
Then a supercritical flow can be seen throughout the entire length of the channel.
Let it run for a few more minutes to ensure stability.
Then place a straight edged ruler on the outside walls of the channels to measure
the heights h, h1 and h2 and take the readings of v and v2 from the computers.
Slowly reduce the pump to adjust the level of water to certain levels, which are
marked in the water tank.
By using different water levels by adjusting the pump to adjust the water to a
lower level mark, repeat step 4 to 5 for at least 6 times.
5.
1.
2.
3.
Result and calculation
Please derive theory from 1st principle.
Please calculate and plot relevant graphs to show your results.
Discuss assumptions of the theory and possible experimental errors.
(Please refer to your lecture notes, textbook or other related materials)
6.
1.
2.
3.
4.
Deadline for report submission
Each group of students MUST submit one report to pigeon hole outside TA
office (Rm2126) 2 weeks after the date of experiment.
The report should be typed and well-written. Poorly-written report will be
returned for resubmission.
Copying is not allowed and reference must be clearly stated at the end of report.
ZERO marks WILL be given if cases of plagiarism are found.
Experiment Record (Hydraulic Jump)
Group No.:
Date:
Experimental Data:
No.
Flow
rate
h
v1
h1
v2
1
2
3
4
5
6
7
Note:
1. Please hand in this record sheet to me after the experiment
h2
Does
hydraulic
jump
occur?
Experiment Record (Hydraulic Jump)
Group No.:
Date:
Experimental Data:
No.
Flow
rate
h
v1
h1
v2
h2
Does
hydraulic
jump
occur?
1
2
3
4
5
6
7
Note:
1. Acceleration due to gravity: g =9.8ms-2
2. Please hand in your experiment report with this experiment record sheet
together
3. Any comments or questions, please email to cechi@ust.hk