# River channel problem using Bernoulli and Continuity

1. Jan 27, 2008

### tere_lai

[SOLVED] River channel problem using Bernoulli and Continuity

1. The problem statement, all variables and given/known data

A river (100 m wide) flows through its rectangular channel at a depth of 2.560 m at a velocity of 2.050 m/s. What is the velocity of the discharge if the channel is narrowed to 90 m?

2. Relevant equations

Continuity equation: Q1 = 100m x 2.560 m x 2.050 m/s
Q2 = 90 m x H2 x V2

Bernoulli equation: V^2/2g + P/pg + z = constant

3. The attempt at a solution

I can't seem to set up the equations properly in order to find intercept. I'm sure that P1 (ie. pressure1) is zero, but P2 isn't. I actually tried solving the question with P2=0 but it's wrong.

A little help?

(you may have seen this in "Introductory Physics" but I don't know how to move/delete the previous thread, sorry)

Last edited: Jan 27, 2008
2. Jan 28, 2008

### Pyrrhus

Hey there, in open channel flow usually the version of Bernoulli equation used is:

$$y + \frac{v^2}{2g} + z = constant$$

In your case the z value probably can be ignored assuming the river doesn't have any vertical variations in its geometry. You could use this equation which is also known as the specific energy.

$$y + \frac{v^2}{2g} = constant$$

3. Jan 28, 2008

### tere_lai

The height of the water (z) is assumed to change due to the narrowing of the river channel. I think I know how to answer the question now...

4. Jan 28, 2008

### Pyrrhus

Great!, good luck, if you have more questions feel free to ask them.

5. Jan 28, 2008