Question

A swimming pool measures 8 m by 15 m and has a uniform depth of 2 m. What is the water pressure on the bottom of the swimming pool? The density of water is 1000 kg/m3.

Answer 1

To calculate the water pressure at the bottom of the swimming pool, we can use the formula for hydrostatic pressure:

\[
P = \rho g h
\]

where:
- \( P \) is the pressure,
- \( \rho \) is the density of the fluid (water in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height of the fluid column (which in this case is the depth of the swimming pool).

Given:
- The density of water \( \rho = 1000 \, \text{kg/m}^3 \)
- The depth of the swimming pool \( h = 2 \, \text{m} \)

Now we can plug in the values:

\[
P = 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 2 \, \text{m}
\]

Calculating it step-by-step:

1. Multiply the density by the acceleration due to gravity:
\[
1000 \times 9.81 = 9810 \, \text{kg/(m} \cdot \text{s}^2\text{)}
\]

2. Multiply the result by the height:
\[
P = 9810 \times 2 = 19620 \, \text{Pa}
\]

Therefore, the water pressure at the bottom of the swimming pool is:

\[
\boxed{19620 \, \text{Pa}} \text{ (Pascals)}
\]