# Formulas For Pipes & Cisterns

## Formulas For Pipe And Cistern

• Pipe : There are usually two kinds of Pipes
• Inlet : Inlet pipe is the pipe that fills the cistern or Tank.
• Outlet : Outlet Pipe is the pipe that empties the cistern or tank.

### Definition & Formula for  Pipes & Cisterns

•  A pipe is connected to a tank or cistern to fill or empty the tank or cistern
• Inlet: A pipe which is connected to fill a tank is known as an inlet.
• Outlet: A pipe which is connected to empty a tank is known as an outlet.
• In pipes and cisterns problems – we need to find out what portion of the tank each of the pipes fill or drain in unit time (say in a minute or hour or second) and then perform arithmetic operation on this value.

Formula

1. If pipe can fill a tank in x hours , then part filled in one hour = $\frac{1}{x}$

2. If pipe can empty a tank in y hours , then part emptied in one hour = $\frac{1}{y}$

3. If pipe A can fill a tank in x hours, Pipe B can empty the full tank in y hours (where y > x). Then, on opening both the pipes, the net part filled in one hour= $\frac{1}{x} – \frac{1}{y}$ OR $\frac{xy}{y-x}$ hours

4. If pipe A can fill a tank in x hours. Pipe B can empty the full tank in y hours (where x > y). Then, on opening both the pipes, the net part filled in one hour= $\frac{1}{y} – \frac{1}{x}$ OR $\frac{yx}{x-y}$ hours.

5. If pipe A can empty a tank in X hours. Pipe B can empty the same tank in Y hours. Then part of the tank emptied in one hour when both the pipes start working together = $\frac{1}{x} + \frac{1}{y}$