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Answer :
Final answer:
The pressure difference between the top and bottom of a 5-m deep pool, with a liquid density of 1,139 kg/m³, is approximately 8.11 lb/in², calculated using the formula for pressure in a fluid at depth and converting the result from Pascals to pounds per square inch.
Explanation:
To calculate the pressure difference between the top and bottom of a pool with a depth of 5 meters, containing a liquid with density of 1,139 kg/m³, and converting the result into lb/in², we use the formula for pressure in a fluid at depth, which is P = hρg. Here, h represents the depth of the fluid, ρ indicates the fluid's density, and g is the acceleration due to gravity.
Assuming the standard value of gravity (g) to be approximately 9.8 m/s², we calculate the pressure difference and then convert the units from Pascals (Pa) to pounds per square inch (lb/in²) using the conversion factor 1 Pa = 1.45037738e-4 lb/in².
Firstly, the pressure difference (in Pascals) due to the liquid's weight can be calculated as follows: Pressure difference = hρg = 5m * 1,139 kg/m³ * 9.8 m/s² = 55,917.4 Pa. To convert this into lb/in², we multiply by the conversion factor: 55,917.4 Pa * 1.45037738e-4 lb/in²/Pa = 8.11 lb/in².
Therefore, the pressure difference between the top and bottom of the pool is approximately 8.11 lb/in².
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