bernoulli's eqn

[frazil]

I actually got to use some of my schoolin' on the job. Here's the problem: There's an aquifer running underneath a dam. The pressure head of the aquifer goes to 15 ft above the water surface behind the dam. They want to release water from the aquifer into the pool to relieve some of the pressure.

The question is what is the velocity out of the pipe at different lengths (h)?

 

[Guest]

Frazil --

I put together something very simple based on your general problem setup. I also included some assumptions and things to consider as you are putting this problem together.

I uploaded my typed out soluton below - if you have additional constraints/assumptions or questions post a follow-up Q.

JR

 

[frazil]

I knew you'd be the first to take up the challenge JR!! :multiplespotting:

I forgot to mention, you can assume the velocity in the aquifer is 0 because it's so slow compared to that coming out of the pipe.

Another hint: you need to use bernoulli's equation on the aquifer and the point right at the mouth of the pipe (not the entire waterbody) and solve for the velocity at the mouth as a function of h

 

[Guest]

Well, if the velocity head in the aquifer is also neglible, you are simply looking at the force (momentum) of the two water masses.

Assuming that the masses are equal in density, one could claim the 'simple' solution is the difference in head between the aquifer and the surface water body: V(h) = SQRT(2g(h+15)).

That makes a lot of gross assumptions though, that may not be valid for one reason or another. I will have to stump along on this one later - busy Friday + weekend for me :multiplespotting:

JR