Pipes and Cistern Formulae

In this class, We discuss Pipes and Cistern Formulae.

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

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

1) If a pipe can fill a tank in x hours, the part filled in one hour is 1/x.

Similar to A can do a work in n days. Then A’s one-day work is 1/n.

2) If a pipe can empty a full tank in y hours, then part emptied in one hour is 1/y.

3) If a pipe can fill a tank in x hours and another pipe can empty a full tank in y hours, where (y> x). Then on opening both the pipes, the net part filled in one hour = (1/x – 1/y).

The below diagram shows the graphical intuition of the formula.

y > x means emptying takes more time when compared to filling the tank.

Important: Inflow is much when compared to outflow. So we can fill the tank.

Example:

x = 10 l/h

y = 5 l/h

net filled in one hour = 10 – 5 = 5 l/h.

4) If a pipe can fill a tank in x hours and another pipe can empty a full tank in y hours, where (x> y). Then on opening both the pipes, the net part emptied in one hour = (1/y – 1/x).