# Bernoulli equation in leaked pipe

I'm currently trying to figure out how to apply Bernoulli equation into a leaked pipe, especially to find the change of pressure before and after a leak appeared. From what I found know, Bernoulli equation states that total head $H$ in

$$H=z+\frac{p}{\rho g}+\frac{v^2}{2g}$$

is constant throughout the flow of pipe (with assumption of steady, incompressible, and inviscid flow). But most example (in textbooks and various sites) only show application in single flow pipe, branched pipes, or reservoir-to-reservoir use cases.

How do I apply Bernoulli equation in leaked pipe situation? And how does the pressure (in the pipe, upstream the leak) change after the leak appeared?

## 1 Answer

Assuming you know the leak rate, you can approximate the flow rate increases by the leak rate, which is though not exact. Knowing the pipe cross section area and fluid density, you can estimate the velocity change. Then you can apply Bernoulli equation to calculate the pressure drop.

• So, if I try to apply it to the equation, will it looks like this? $H pipe = H leak$ – Muhamad Iqbal Sep 4 '16 at 3:57
• it will be $H_{pipe upstream}=H_{pipe downstream}+H_{leak}$ – user115350 Sep 6 '16 at 18:33
• if there's head loss included, could it be turned into $H_upstream = H_(downstream) + H_(leak) + h_f$ ? – Muhamad Iqbal Sep 6 '16 at 23:07
• If friction is considered, yes it should be included. – user115350 Sep 7 '16 at 0:53
• a bit question to clarify : why is it turned into $H_{upstream} = H_{downstream} + H_{leak}$? Is it because law of continuity? – Muhamad Iqbal Sep 7 '16 at 13:19