# How do you relate the flow velocity through a pipe with the pressure of the resvoir?

1. Sep 12, 2011

### 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?

2. Sep 12, 2011

### xts

Re: How do you relate the flow velocity through a pipe with the pressure of the resvo

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
$$P = \frac{\rho v^2}{2}$$

3. Sep 13, 2011

### granpa

Re: How do you relate the flow velocity through a pipe with the pressure of the resvo

pressure = potential energy