How Long Will It Take to Empty a Rectangular Tank?

Capacity calculations for tanks are crucial in many industries, such as plumbing, engineering, and environmental management. A common scenario involves determining how long it will take to drain water from a rectangular tank to its brim. This article will walk you through the necessary steps and provide you with a clear understanding of the process.

Volume of the Rectangular Tank

Consider a rectangular tank measuring 40 cm by 50 cm by 60 cm. Theoretically, if this tank is filled to its brim with water and then drained at a rate of 15 liters per minute, how long would it take to empty the tank?

Step 1: Calculate the Volume of the Tank

The volume V of a rectangular tank can be calculated using the formula:

V Length times; Width times; Height

Given the dimensions:

Calculating the volume:

V 40 cm times; 50 cm times; 60 cm 120,000 cm3

Step 2: Convert the Volume into Liters

To convert cubic centimeters to liters, we use the conversion factor: 1 liter 1000 cm3.

Volume in liters 120,000 cm3 / 1000 cm3/liter 120 liters

Step 3: Calculate the Time to Drain the Tank

The water is being drained at a rate of 15 liters per minute. To determine the time it will take to drain the entire volume of the tank:

t Volume / Rate 120 liters / 15 liters/minute 8 minutes

Therefore, it will take 8 minutes to empty the tank.

Further Calculations

Alternately, you can convert the volume from cubic centimeters to cubic meters before performing the calculation. The volume in cubic meters:

V 120,000 cm3 0.12 m3

Given the rate is in liters per minute, we can convert the rate to cubic meters per minute:

15 liters/minute 0.015 m3/minute

t 0.12 m3 / 0.015 m3/minute 8 minutes

Conclusion

Based on the steps outlined, it will take 8 minutes to drain the tank. This method is useful in a variety of practical situations, such as designing drainage systems or managing water reservoirs.

For a comprehensive set of calculations, you can follow the formula:

t Volume of Tank}{Time Rate of Emptying the Tank}

t 40cmtimes;50cmtimes;60cm}{15000cm^{3}min^{-1}}

t 8 minutes