Pipe and Cistern

Pipe and Cistern

In problems related to pipes and cistern usually consist a cistern or tank to which one or more pipes are connected to fill or empty it.

Basic fundamental of concerned chapter is similar to time and work the only difference lies in the fact that here work can positive (filling the tank) as well as negative (emptying the tank) whereas in time and work, the work done is always positive.

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

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

• If a pipe fills a tank in x h, then the part of tank filled in \[1\,h=\frac{1}{x}.\]

• If a pipe fills \[\frac{1}{x}\]part of the tank in 1 h, then the time taken by pipe to fill the full tank = x h.

Quicker One

Ø  If a pipe fills a tank is x h and another pipe can fill the same tank in y h, then time taken to fill the tank when both pipes are opened together\[=\frac{xy}{x+y}h.\]

Ø  If a pipe fills a tank in x h and another pipe can empty it in y h. Then, time taken to till the tank by both pipes working together \[=\frac{xy}{y-x}h\](when y>x)\[=\frac{xy}{x-y}h\] (when x > y).

Ø  If three pipes can fill a tank separately in x, y and z h, then time taken to fill the tank by working together\[=\frac{xyz}{xy+yz+zx}h.\]

Ø  Two pipes A and 6 can fill a tank in x and y h, respectively. If both the pipes are opened simultaneously, then the time after which pipe B should be closed, so that the tank is full in\[T\,h.\,T\,h=\left[ y\left( 1-\frac{t}{x} \right) \right]h.\]

Ø  Two pipes A and B together fill a tank in time t. If time taken by A alone is more than t by x and time taken by 8 alone is more than t by y, then\[t=\sqrt{xy}.\]