How Do You Calculate the Flow Rate from a Rectangular Opening in a Tank?

[burningnachos]

Homework Statement

A rectangular opening is cut into the side of a large open-topped water tank. The opening has width W and height H2 - H1, where H1 is the distance from the top of the tank to the top of the opening, and H2 is the distance from the top of the tank to the bottom of the opening. Determine the volume V of water that emerges from the opening per second.

You may assume that the surface area of the tank is extremely large compared to the area of the opening, but you should not assume that the water emerges from the opening with a single, uniform velocity.

Homework Equations

Bernoulli's equation

The Attempt at a Solution

So I first tried to get the velocity at H1 and H2 using Bernoulli's equation. Then I assume you have to integrate to account for the rate in between, but I'm having trouble setting up the integral. Help is appreciated, thanks.

 

[paisiello2]

Can you find the velocity at any arbitrary depth y?