Inlet and Outlet Pipes with Filling and Emptying Methods
Inlet and Outlet Pipes problems deal with pipes that fill or empty a tank at fixed rates. The main method is to express each pipe’s work as a fraction of the tank per unit time, take inlet rates as positive and outlet rates as negative, and calculate the net rate to find the required time.
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What Are Inlet and Outlet Pipes?
If a pipe fills a tank in a hours, its rate is 1/a tank per hour. If another pipe empties the tank in b hours, its rate is -1/b tank per hour. For pipes working together, net rate = sum of inlet rates − sum of outlet rates, and time = required work ÷ net rate.
Inlet and Outlet Pipes Video Lessons
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Pipes Inlet and Outlet Together
Understand how to solve time and work problems involving inlet and outlet pipes running simultaneously, including their combined rates and net effect on filling or emptying a tank.
Inlet and Outlet Pipes Formula & Tricks
Important Formulas
If an inlet fills the complete tank in a hours, it fills 1/a of the tank in one hour.
If an outlet empties the complete tank in b hours, its rate is negative because it removes water.
Add all filling rates and subtract all emptying or leakage rates.
For a completely empty tank, required work is 1 tank. Therefore, time = 1 ÷ net rate.
If the tank capacity is represented by a common multiple, each pipe’s hourly work can be calculated directly.
Quick Tricks
Take the tank capacity as the LCM of the individual filling or emptying times. This converts fractional rates into whole units per hour.
A leak or outlet reduces the amount of water. Subtract its rate instead of adding it.
A positive net rate fills the tank, a negative net rate empties it, and a zero net rate keeps the water level unchanged.
Inlet and Outlet Pipes Concepts
Finding the Rate of a Single Pipe
For an inlet, write the rate as +1/T. For an outlet or leak, write it as −1/T. The unit of rate is tank per hour, or litres per hour if the tank capacity is known.
Two or More Inlet Pipes Working Together
If pipes fill a tank in a, b and c hours, combined rate = 1/a + 1/b + 1/c. The filling time is the reciprocal of this combined rate.
Inlet and Outlet Pipes Working Together
For inlet times a and b and outlet time c, net rate = 1/a + 1/b − 1/c. If the net rate is positive, filling time for an empty tank is 1/net rate.
Alternate Operation of Pipes
If one pipe works for x hours at rate r₁ and another works for y hours at rate r₂, total work is xr₁ + yr₂. For repeated cycles, find the work done in one complete cycle and divide the remaining work by the applicable rate.
Inlet and Outlet Pipes Data Table
Use the structured data below while following the explanation and examples.
Signs of Pipe Rates
The sign of a pipe rate shows whether the pipe adds or removes water.
| Pipe type | Rate expression | Effect on tank |
|---|---|---|
| Inlet filling in a hours | +1/a tank per hour | Increases water |
| Outlet emptying in b hours | −1/b tank per hour | Decreases water |
| Closed pipe | 0 | No change |
| Several pipes together | Sum of signed rates | Determines net change |
Note: Use the signed rates before calculating the time.
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Inlet and Outlet Pipes Revision Points
Use signed work rates to solve filling, emptying and leakage problems.
- An inlet filling a tank in T hours has rate +1/T tank per hour.
- An outlet or leak emptying a tank in T hours has rate −1/T tank per hour.
- Net rate = total inlet rate − total outlet rate.
- For an empty tank, filling time = 1 ÷ net rate when the net rate is positive.
- If net rate is zero, the water level remains constant.
- For pipes operating at different times, calculate work separately for each interval and add the work done.
Inlet and Outlet Pipes FAQs
What is the inlet and outlet pipes formula?
Net rate = sum of inlet rates − sum of outlet rates. If an inlet fills in a hours and an outlet empties in b hours, net rate = 1/a − 1/b.
An inlet fills a tank in 10 hours and an outlet empties it in 15 hours. How long will the tank take to fill?
Net rate = 1/10 − 1/15 = 1/30 tank per hour. Therefore, the tank fills in 30 hours.
What happens when the inlet and outlet rates are equal?
The net rate is zero, so the water level remains unchanged while both pipes operate together. For example, 1/8 − 1/8 = 0.
How do you solve a pipe and leak problem?
Treat the leak as an outlet with a negative rate. For a pipe filling in 5 hours and a leak emptying in 20 hours, net rate = 1/5 − 1/20 = 3/20, so filling time is 20/3 hours, or 6 hours 40 minutes.
How is tank capacity used in inlet and outlet problems?
Choose a convenient capacity, usually the LCM of the given times. If a 12-hour pipe and an 18-hour pipe work on a 36-unit tank, their rates are 3 units/hour and 2 units/hour.
What does a negative net rate mean?
A negative net rate means the outlet pipes remove water faster than the inlet pipes add it. The tank is emptying rather than filling.