Pipes and Cisterns-Outlet

Pipe and cisterns are concepts of time and work in mathematics. Time to do work is equal to the time of filling cisterns. This report discussed the concepts of pipes and cisterns and the factors of pipe and cisterns outlets. In addition, it also provides some examples of pipes and cisterns for a better understanding of the topic. 

Concepts of pipes and cisterns

Pipes and cisterns concepts are somewhat similar concepts to that of time and work. In this type of mathematical question, it has been asked what the time is taken to fill the tank or to empty a tank. There are two major terms in this type of mathematical problem such as inlet and outlet. Inlet pipe is used to fill the tank with water and it is a positive type of work. On the other hand, the outlet pipe is used to empty the tank and it shows the negative type of work done. Therefore, to solve the questions of pipe and cisterns an individual should understand both the term important formula of pipes and cisterns 

There are a few important formulas of time and cisterns, which can be used by an individual to solve the problems of the present topics. 

• If x hours are required to fill a tank, then the part of the tank filled in one hour is equal to 1/x
• If y hours are required to empty the tank, then the part of the tank empty in one hour is equal to 1/y
• If the pipes fill in X hour and can empty in y hours then the time required to fill the tank is one hour when both the pipes are opened at the same time = xy/x+y, where x is greater than y. And when y is greater than x then the formula will be xy/ y-x
• Net work done = some of the work done by inlets – some of the work done by outlet 
• One inlet can fill a tank in x hours and another inlet can fill the same tank in y hours, when both the inlets are opened the time taken to fill the whole tank is = xy/x+y

Factors of pipe and cisterns outlets

There are various factors of pipes and cisterns outlets that can increase or decrease within required time used by the pipes to fill or empty the tank. The volume of the tank and the radius of the inlets and outlets pipes are coherently generated to bring out the actual figure. In addition, time is also a very big factor in this type of mathematical problem. There are certain conditions also such as in order to fill the tank with both inlet and outlet pipes the inlets pipes must have greater than outlet pipes. 

Examples of pipes and cisterns

Example 1

Three pipes X, Y, and Z take 6 hours to fill a tank. When all of them worked together for 2 hours and then Z was closed and X and Y filled the remaining tank in 7 hours. How many hours would Z take to fill the tank alone?

Part of the tank which is filled in 2 hours =2/6 = ⅓ 

Therefore, the part of a tank remaining to be filled = 1- ⅓ = ⅔ 

Work done by X and Y together in 7 hours is = ⅔ 

Thus, work done by X and Y together in 1 hour is = ⅔ /7 = 2/21

Thus, work done by Z in one hour is = X+Y+Z’s one hour work – X+Y’s one hour work 

= ⅙ – 2/21 = 1/14 

Therefore, Z would take 14 hours to fill the tank alone. 

Conclusion 

The present report has discussed the pipes and cisterns outlet concepts and different components of need to know in order to solve this type of mathematical problem. It also provided some formulas in order to solve the pipe and cisterns problems. In addition, some examples of the pipe and cisterns are also shown in the present report.