Calculating Hole Size for Desired Flow Rate in Tank/Reservoir

[qazwsxedc]

Specifically, I have a certain flow rate in (volume/sec) and I know the pressure of the resevoir at a certain point. If there is a hole in the tank/resevoir at that point, how big should it be to achieve the given certain flow rate?

 

[xts]

If you may ignore friction, the easiest approach is to use energy conservation. Kinetic energy of liquid flowing out must be equal to work done by pressure pushing this volume out:

P - pressure, s - area of the hole, v - velocity $\rho$ - density of the liquid
$$Psv = \rho sv\frac{v^2}{2}$$
thus
$$P = \frac{\rho v^2}{2}$$

 

[granpa]

pressure = potential energy