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.

1 answer

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:

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