Pipes & Cisterns
Pipes and Cisterns is a mathematical concept used to calculate how much time it takes to fill or empty a container. This topic is almost exactly like the 'Time and Work' chapter. In these problems, the 'work' is the job of filling or emptying a tank. A tank is often called a cistern in exam questions. There are two main types of pipes involved. An 'Inlet' pipe is used to fill the tank. Since it adds water, we treat its work as positive (+). An 'Outlet' pipe is used to drain or empty the tank.
Concepts (3)
If a pipe fills a tank in 'x' hours, the part filled in 1 hour is 1/x. Similarly, if an outlet empties it in 'y' hours, the part emptied in 1 hour is 1/y. When both are open, the net work in one hour is (1/x - 1/y).
If a pipe fills a tank in 'x' hours, the part filled in 1 hour is 1/x. Similarly, if an outlet empties it in 'y' hours, the part emptied in 1 hour is 1/y. When both are open, the net work in one hour is (1/x - 1/y). Example: If Pipe A fills in 10 hours and Pipe B empties in 20 hours, net work in 1 hour is 1/10 - 1/20 = 1/20.
Assume the tank capacity is the LCM of the times taken by different pipes. Divide this capacity by individual times to find 'units per hour' (efficiency). Example: Pipe A fills in 10 hours, Pipe B in 15 hours. LCM of 10 and 15 is 30.
Assume the tank capacity is the LCM of the times taken by different pipes. Divide this capacity by individual times to find 'units per hour' (efficiency). Example: Pipe A fills in 10 hours, Pipe B in 15 hours. LCM of 10 and 15 is 30. So, Tank = 30 units. Pipe A = 3 units/hour. Pipe B = 2 units/hour. Together = 5 units/hour. Time = 30/5 = 6 hours.
Sometimes pipes are closed before the tank is full. Calculate the work done while all pipes were open first. Then, calculate the remaining work for the remaining pipes.
Sometimes pipes are closed before the tank is full. Calculate the work done while all pipes were open first. Then, calculate the remaining work for the remaining pipes. Example: If 3 pipes work for 2 hours and then one closes, find out how many units they filled in those 2 hours and subtract from the total capacity.
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