Final answer:
The gauge pressure at the bottom of a 13.9 ft deep freshwater swimming pool is calculated using the equation P = ρgh and is found to be approximately 6.03 psi.
Step-by-step explanation:
The gauge pressure at the bottom of a freshwater swimming pool is determined by the depth of the water above it. The gauge pressure is the pressure exerted by the water alone, not including atmospheric pressure. To calculate the gauge pressure in psi (pounds per square inch), we can use the formula P = ρgh, where ρ is the density of water (1000 kg/m³, which is approximately 62.43 lb/ft³), g is the acceleration due to gravity (9.81 m/s³ or 32.2 ft/s³), and h is the depth of the water in meters or feet. Converting the depth from feet to meters, we have 13.9 ft × 0.3048 m/ft, and then calculate the pressure in pascals (Pa) or newtons per square meter (N/m²). Finally, we convert from Pa to psi (1 psi = 6894.76 Pa).
Using these conversions, we can calculate the gauge pressure at a depth of 13.9 ft in a swimming pool as follows:
- Convert the depth to meters: 13.9 ft × 0.3048 m/ft = 4.23732 m.
- Calculate the pressure in pascals: P = ρgh = 1000 kg/m³ × 9.81 m/s³ × 4.23732 m = 41562.37 Pa.
- Convert the pressure to psi: 41562.37 Pa × (1 psi / 6894.76 Pa) = 6.03 psi (rounded to two decimal places).
Therefore, the gauge pressure at the bottom of a freshwater swimming pool that is 13.9 ft deep is approximately 6.03 psi.