Question

Rain is falling at the rate of 8.0 cm/h and accumulates in a pan.

If the raindrops hit at 5.0 m/s , estimate the force on the bottom of a 0.50 m2 pan due to the impacting rain which does not rebound. Water has a mass of 1.0×103kg per m3.

Answer 1

Given,

The rate of rainfall, R = 8 cm/h = 0.08 m/h

The velocity of rainfall, v = 5 m/s

The area of a bottom of the pan, A = 0.50 m²

The volume of the rain collected in a second, V = A * R / 3600

V = (0.50 * 0.08) / 3600

= 11.1 * 10^-6 m³

The mass of the rain collected in a second, M = Volume * density

M = 11.1 * 10^-6 * 1 * 10³

= 11.1 * 10^-3 Kg

The force on the bottom is, F = M * V / t

Here, t = 1 sec

=> F = 11.1 * 10^-3 * 5 / 1

= 55.5 * 10^-3

= 0.0555 N

Therefore, the force at the bottom is 0.555 N