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:
-
Multiply the density by the acceleration due to gravity: \[ 1000 \times 9.81 = 9810 , \text{kg/(m} \cdot \text{s}^2\text{)} \]
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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:
\[ \boxed{19620 , \text{Pa}} \text{ (Pascals)} \]
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