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Sagot :
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
- [tex]Depth \ of \ water \ in \ the \ pan = \dfrac{Volume \ of \ rain \ water}{Cross \ sectional \ area \ of \ pan}[/tex]
[tex]Depth \ of \ water \ in \ the \ pan = \dfrac{720,000 \ cm^3}{10,000 \ cm^2} = 72 \ cm[/tex]
Therefore;
- The depth of water in the pan after one hour, d = 72 cm = 0.72 m
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