Fluid Mechanics question

shroomz

shroomz

shroomz

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Hey all, kinda stuck on this question, think there isn't enough data to complete:

A bridge crosses an 8m wide river. Upstream of the bridge the water depth is 1.6m. The distance between the piers is 6.5m. The river depth between the bridge piers is 1.45m. (a)Calculate the mean velocities upstream of the bridge and between the piers. Assumptions: river bed is horizontal, river banks are parallel, ideal flow.
(b) calculate the volumetric flowrate of water under the bridge.

Using the extended form of Bernoulli's equation I can reduce it to be a function of velocity upstream and velocity downstream, but no further. It seems to me like the flowrate upstream is required to solve this?

Any people clued up on Fluid Mechanics that can see a way of solving it without the flowrate?

Cheers
 
It would seem to me (someone with no education in this topic at all) that all you can do is provide the function, perhaps that is the "correct answer" ?
 
There's not enough information. You need to know more about the flow rate, velocity field, or forces acting on the fluid.

Given the information you've specified, the fluid could very well just be perfectly static in the river.
 
I've solved it although I'm not sure if it was the right way: I used the height difference to work out a pressure difference between the 2, I then substituted it into the Bernoulli equation to get

u2^2 - u1^2 = 2.94 m^2/s^2

I then took the cross sectional flow area on both sides and since u1A1=u2A2 when rho1=rho2

12.63u1=9.425u2

This gives 2 equations in 2 unknowns. I solved them simultaneously to get the right answer... I should probably have seen that straight away, being a Chem Eng student and all but oh well. Thanks for trying anyway guys xD

@Inquisitor, the height difference before and under the bridge creates a pressure difference and this is the driving force behind the flow
 
Brings back memorys.

Wait till you get to heterogeneous reactor design ;) or some of the more funky control stuff.
Dear god I hated that maths.
 
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