Lab #3
Hydraulic Jump

Theory
A hydraulic jump occurs when a confined liquid flowing at a high velocity is exposed to a sudden reduction in pressure (often atmospheric conditions) as it exits the confinement.  In theory, the flow must be in the supercritical range where the Froude number (N_F) describes critical flow:
 

(1)

where:

u	is the fluid velocity (m/s)
g	is the acceleration of gravity (m/s2)
y	is the depth of the fluid stream (m)

If N_F = 1, the flow is considered critical
If N_F < 1, the flow is considered subcritical
If N_F > 1, the flow is considered supercritical

Consider the following steady but non-uniform flow in a rectangular channel of width w:

If we start with the continuity equation:
 

(2)

Rearranging and simplifying:
 

(3)

Recall that the hydrostatic forces exerted at the cross sections 1 and 2 is:
 

(4)

and
 

(5)

For moving fluids, force is also described in terms of momentum:
 

(6)

Substituting equations 3 and 4 into 5 and expanding the mass flow rate:
 

(7)

Since 
 

(8)

Since r = g/g and substituting for V₂ from equation 2, equation 7 can be manipulated into:
 

(9)

Since  is the Froude number squared:
 

(10)

Solving the quadratic:
 

(11)

The downstream depth is therefore predicted in terms of the upstream depth and the Froude number.

The energy loss through the turbulent transition in velocity is given by:
 

(12)

 

Equipment Pump Plexiglas trough and end weir Piping and valves Stopwatch Bucket

Procedure Measure y1 and the trough width. Create a hydraulic jump in the trough by turning the pump on and adjusting the flow control valve.  The position of the jump along the length of the trough (L) should remain constant over the entire experiment and is controlled by the weir at the end of the trough.

3. Measure y₂ and calculate u₁ from the flow rate and the cross sectional area.
4. Repeat steps 2 and 3 at a different flow rate by re-adjusting the flow control valve.  Repeat the procedure until the data for a total of five flow rates have been recorded.

1. Calculate the Froude number at each flow rate.
2. Calculate the ratio y₂/y₁ at each flow rate.
3. Plot y₂/y₁ vs N_F on linear graph paper.  Calculate and report the slope and the intercept of the resultant line.
4. Calculate the energy loss for each flow rate and comment.

(13)

Theoretically, a plot of y₂/y₁ vs N_F would yield a slope of  with an intercept of -1/2.  How does this compare to your plotted results?  Comment on any differences.

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