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River channel problem using Bernoulli and Continuity 
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#1
Jan2708, 11:31 PM

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) 


#2
Jan2808, 12:26 PM

HW Helper
P: 2,277

Hey there, in open channel flow usually the version of Bernoulli equation used is:
[tex] y + \frac{v^2}{2g} + z = constant [/tex] 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. [tex] y + \frac{v^2}{2g} = constant [/tex] 


#3
Jan2808, 03:35 PM

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...



#4
Jan2808, 06:02 PM

HW Helper
P: 2,277

River channel problem using Bernoulli and Continuity
Great!, good luck, if you have more questions feel free to ask them.



#5
Jan2808, 06:09 PM

P: 4

thanks for your help!



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