Question

Find the pressure exerted by a waterbed with dimensions of 2 m x 2 m which is 30 cm thick. (hint: 1000 kg/m3 density of water)

Answer 1

Complete question:

Find the pressure exerted by a waterbed with dimensions of 2 m x 2 m which is 30 cm thick. (hint: use 1000 kg/m³ as density of water)

Answer:

The pressure exerted by the waterbed is 2940 N/m²

Explanation:

Given;

Length of waterbed, L = 2 m

Width of waterbed, W = 2 m

Height of waterbed, H = 30 cm = 0.3 m

density of water, ρ = 1000 kg/m³

Hydrostatic pressure derivation:

$Pressure = \frac{Force}{Area} = \frac{mg}{L*W} =\frac{(\rho V)g}{L*W}= \frac{(V) \rho g}{L*W} =\frac{(L*W*H)\rho g}{L*W} = \rho gH$

The hydrostatic pressure exerted by the waterbed is directly proportional to the height of the waterbed. Thus, the hydrostatic pressure increases with increase in height of the waterbed.

Hydrostatic Pressure exerted by the waterbed:

P = ρgH

P = 1000 x 9.8 x 0.3

P = 2940 N/m²

Therefore, the pressure exerted by the waterbed is 2940 N/m²