Pipes and Cisterns important facts and formulae

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

2. Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

3. If a pipe can fill a tank in x hours, then:

part filled in 1 hour = \begin{aligned}\frac{1}{x}\end{aligned}

4. If a pipe can empty a tank in y hours, then:

part emptied in 1 hour = \begin{aligned}\frac{1}{y}\end{aligned}

5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then

the net part filled in 1 hour = \begin{aligned}\frac{1}{x}-\frac{1}{y} \end{aligned}

6. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then

the net part emptied in 1 hour = \begin{aligned}\frac{1}{y}-\frac{1}{x} \end{aligned}