Hydraulic Jump is: Rather abrupt change from supercritical to subcritical flow

Location of Jump: Where the balance between upstream and downstream flow depths matches the ratio between y₁ and y₂.
Note y₁ (supercritical) changes more than y₂ (subcritical)

Common Position of Hydraulic Jump

Basic Equations

Cannot use energy equation because of unknown energy loss in jump, so use momentum equation
F_r = γA₁z₁ - γA₂z₂ + W sin θ - F_e
ρQ₂V₂ - ρQ₁V₁ = γA₁z₁ - γA₂z₂ + W sin θ - F_e


For horizontal channel of our flume, sin θ = 0. Also, F_e is the force on the outside of the channel and γ is ρg, so we only use
Q₂V₂ - Q₁V₁ = gA₁z₁ - gA₂z₂

From this we can get:


Equations Commonly Used
From Prior Equations:


Since y₂ is the subcritical flow and more easily measured, we can use the latter form to give the value of y₁ that we expect to have. [Note: We must have F_r1 > 1 and F_r2 < 1]

Given y₁ and y₂ (and the flow rate) we compute the energy loss


No theory to determine the length of the hydraulic jump, L.

Experimental data plotted into a common graphical form by the US Bureau of Reclamation

An approximate equation in literature gives
L/y₁ = 220 tanh((F_r1-1)/22) or
L/y₂ = 220 (y₁/y₂) (tanh(F_r1-1)/22)

Hydraulic Jump Experimental Procedures

Objectives:
Y₂/Y₁ (sequent depth/initial depth) vs. F₁ (Froude number @ initial depth)

∆ E/Y₁ (energy loss/initial depth) vs. F₁

L/Y₂ (length of hydraulic jump/subcritical depth) vs. F ₁

Water surface profiles of the hydraulic jump by point gage and manometer board readings.

Shape of water surface approaching the drop-off from the rectangular channel


Apparatus:
One-half meter glass-walled flume with sluice gates

Point gage(s) and manometer board with piezometer taps

Procedure:

Set up experiment
Close the drain valve on the head tank.
Take the zero datum readings for point gages and manometers.
Open the surge tank valve and turn on the large pump.


Conjugate depth and length measurements.

Water surface levels at the initial and sequent depths by point gage readings
Length of the jump within the flow reach (turbulent air bubbles)
Record the flow rate
Check Froude number F₁

Repeat at different Froude numbers of about 2-9 by adjusting either the flow rate or the sluice gate opening

Open the head tank drain valve and shut off the flow

Hydraulic Jump Experimental Results

Format: Memo Report

Data, Calculations, and Results:
Attach your data sheet and a sketch of the experimental set-up

Plot Y₂/Y₁ vs. F₁ (Froude number at initial depth) for both experimental and theoretical curves

Plot ∆ h/Y₁ vs. F₁ for both experimental and theoretical curves

Plot L/Y₂ (hydraulic jump length/sequent depth) vs. F₁


Plot the water surface profile for the section approaching the drop-off at the end of the channel.

Hydraulic Jump Equations

Merging these two equations gives


If y₁ is much less than y_o, it can be dropped, or estimated, giving F_r1 as a function of y_o & Q




Hydraulic Jump In Our Flume

The channel before the sluice gate is 3 ft high, so y_o is 3 ft or less
g is 32.2 ft/S² and b is 1.64 ft


THUS



     (I converted Q from cfs to gpm for our lab)

 

     With the flume full before the sluice gate




Q (gpm)	Froude # F1	Depth, y1	Froude # F1
(y1 = 3  ft)		(at Q = 600 gpm)
100	7.9	0.063	9.1
150	6.9	0.067	8.4
200	6.2	0.071	7.5
300	5.5	0.077	6.7
400	5.0	0.089	5.5
600	4.3	0.106	4.1




Key equations for data in this experiment are the following