Calculating Hydraulic Jump with Unknown Cross Sectional Area: Help Needed

In summary, the conversation is about solving for h2 in the equation V1(b1h1) = V1(b2h2). The person is having trouble determining the base measurement of the cross section of the water as it was not given in the problem. The solution manual assumed that the base is the same for both streams, but the person disagrees as the smaller stream would have a smaller base. They ask for a diagram to help with the problem.
  • #1
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Homework Statement
A hydraulic jump (see Video V10.11) is in place downstream
from a spillway as indicated in Fig. P5.10. Upstream of
the jump, the depth of the stream is 0.6 ft and the average stream
velocity is 18 ft/s. Just downstream of the jump, the average stream
velocity is 3.4 ft/s. Calculate the depth of the stream, h, just downstream
of the jump.
Relevant Equations
Q1=Q2 or V1A1=V2A2 where A is the cross sectional area of the water.
I have 90% of this done. When i looked in my manual i noticed an odd jump they made and i don't get why. that is where i need the help

V1(b1h1) = V1(b2h2)

Im solving for h2.

What i can't figure out is what to use for the base measurement of the cross section of the water. i have no idea how wide the reservoir channel is. It never gave me that number and we can't just "assume" that the base is the same in the smaller stream than it is in the larger stream. But the solution manual made that assumption so that the bases cancel out. I disagree with that. Since the stream IS SMALLER, therefore it has a smaller base than the larger stream at the bottom... Canceling out the bases can't work.

thanks for the help:)
 
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  • #2
Could you post a diagram?
 

FAQ: Calculating Hydraulic Jump with Unknown Cross Sectional Area: Help Needed

What is a hydraulic jump?

A hydraulic jump is a phenomenon that occurs when a fast-moving fluid abruptly slows down and transforms into a turbulent flow. It is commonly seen in open-channel flows, such as rivers and spillways, and is characterized by a sudden rise in water surface elevation.

What causes a hydraulic jump?

A hydraulic jump is caused by a sudden change in flow conditions, such as a decrease in flow velocity or an increase in flow depth. This change in flow causes a buildup of pressure, leading to the formation of the jump.

What are the applications of hydraulic jumps?

Hydraulic jumps have various applications in engineering, such as energy dissipation in dams and spillways, mixing and aeration in wastewater treatment, and controlling flow in irrigation systems. They are also used in recreational activities like whitewater rafting and kayaking.

How is the size of a hydraulic jump determined?

The size of a hydraulic jump is determined by the Froude number, which is the ratio of the flow velocity to the square root of the product of gravity and flow depth. A higher Froude number indicates a larger hydraulic jump.

How can hydraulic jumps be controlled?

Hydraulic jumps can be controlled by altering the flow conditions, such as using different channel geometries, adding baffle blocks or roughness elements, or changing the flow rate. These methods can help reduce the energy dissipation and minimize the size of the jump.

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