Question

assume that a raindrop's volume is 1 cubic centimeter. in centimeters, what would be the depth of water in a pan whose square base measured 1 meter by 1 meter after 1 hour of rain falls at a rate of 2 raindrops per second on a 10 centimeter by 10 centimeter region?

Answer 1

The volume of a fluid that flows past a point per unit time through an area is known as the flow rate, Q

The depth of water in the pan after one hour is 0.72 meters

Reason:

The given parameters are;

The volume occupied by one rain drop = 1 cm³

The area of the square base of the pan = 1 meter by 1 meter

Duration of the rain, t = 1 hour

Rate at which rain falls  = 2 raindrops per second

Region where the rain falls = 10 cm by 10 cm

Depth of water in the pan after 1 hour = Required

Solution:

The number of seconds in 1 hour = 3,600 seconds

Number of raindrops in a 10 cm by 10 cm region, n, is given as follows;

n = 10 drops × 10 drops = 100 drops

Number of raindrops in 1 hour = 2 × 100 drops/s × 3,600 s = 720,000 drops

Volume of water in the rain, V = 720,000 drops × 1 cm³/drop = 720,000 cm³

Area of the pan = 1 m × 1 m = 100 cm × 100 cm = 10,000 cm²

Cross sectional area of the pan = 10,000 cm²

• $Depth \ of \ water \ in \ the \ pan = \dfrac{Volume \ of \ rain \ water}{Cross \ sectional \ area \ of \ pan}$

$Depth \ of \ water \ in \ the \ pan = \dfrac{720,000 \ cm^3}{10,000 \ cm^2} = 72 \ cm$

Therefore;

• The depth of water in the pan after one hour, d = 72 cm = 0.72 m

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