## Friday, June 7, 2019

### The weight of liquids in a pool or acquarium

Below are some questions about the weight of water and other liquids.  These problems require knowledge about units of volumes, conversion between the metric system and the English system, volume of objects, and density.

Enjoy !!!!

Question:  What is the weight of water in a full 10-gallon aquarium?

Answer:  One gallon has 3,785.41 milliliters or 3.78541 liters.   One milliliter of water weights one gram.  Alternatively one liter of water weighs one kilogram.  Therefore there are 3.78541 kilograms in a one gallon of water.

There are 10 gallons so there are 37.8541 kilograms in a 10 gallon tank.

Let’s convert to pounds.

1 kilogram is equal to 2.20462 pounds  Therefore 37.8541 kilograms is equal to 83.4 (2.20462 x 37.8541) pounds.

Ten gallons of water weighs 37.8541 kilograms or 83.4 pounds.

Question:  A swimming pool full of water is 25 meters long, 25 meters wide and 7 meters deep.   How much does the water in the pool weigh?

The  volume of the pool is 4,375  (m3). 1 cubic meter is equal to 1000 liters; consequently, there are 4,375,000 liters of water in the pool.   Since one liter of water weighs one kilogram the water in the pool weighs 4,375,000 kilograms.

Convert to pounds by multiplying by 2.20462 so there are 9,645,212.5 pounds of water in the pool.  This is 4,823 tons.

Question:  The pool is full of oil.  What is the weight of the oil in the pool?

Answer:   Oil is lighter than water.  (Oil floats on water after an oil spill.)  The exact answer depends on the type of oil because different oils have different densities.  The density of most oil is near 0.9 so an answer of 4340 tons is reasonable.

Question:  The pool is full of mercury.   What is the weight of the mercury in the pool?  The density of mercury is 13.6 gm/ml  compared to 1 gm/ml for water.   The mercury in the pool should weigh around 59,033 tons.