# [SOLVED] River channel problem using Bernoulli and Continuity

by tere_lai
Tags: bernoulli, channel, continuity, river, solved
 P: 4 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)
 HW Helper P: 2,280 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. $$y + \frac{v^2}{2g} = constant$$
 P: 4 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...
HW Helper
P: 2,280

## [SOLVED] River channel problem using Bernoulli and Continuity

Great!, good luck, if you have more questions feel free to ask them.
 P: 4 thanks for your help!

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