# Pipes and Cisterns

**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.

**Cisterns :**They are large tanks that store rainwater collected from impervious surfaces for domestic uses or for consumption.

### Definition of 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.

### Formulas for Pipes and Cisterns

- If x hours are required to fill up a tank, then part filled in 1 hr =1/x
- If y hours are required to empty the tank, then part emptied in 1 hour = 1/y
- If a pipe can fill a tank in x hours and can empty the same tank in y hours. When both the pipes are opened at the same time, then the net part of the tank filled in 1 hr = {(xy) / (y-x)}, provided y>x
- If a pipe can fill a tank in x hours and can empty the same tank in y hours. When both the pipes are opened at the same time, then the net part of the tank filled in 1 hr = {(xy) / (x-y)}, provided x>y
- Net work done = (Sum of work done by Inlets) – (Sum of work done by Outlets)
- One inlet can fill the tank in x hr and the other inlet can fill the same tank in y hrs, if both the inlets are opened at the same time, the time taken to fill the whole tank = {(xy) / (y+x)}
- If two pipes take x and y hours respectively to fill a tank of water and a third pipe is opened which takes z hours to empty the tank, then the time taken to fill the tank = {1 / (1/x)+(1/y)+(1/z)} and the net part of the tank filled in 1 hr = (1/x)+(1/y)-(1/z)

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