The hydrostatic equation holds not just for air, but for other fluids such as water (air, though it is a gas, is often referred to as a 'fluid') as well. In the case of water the equation becomes even easier, as water (as opposed to air) can be treated as incompressible, meaning the density is constant. Use a value of 1000 kilogram per cubic metre as density.
Using this information, compute the local pressure (in [Pa]) at 2.5 metres depth in a swimming pool situated at 2400 metres altitude in the mountains. Assume a standard atmosphere.
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To compute the local pressure at a given depth in a swimming pool, we can use the hydrostatic equation:
Pressure = Pressure at the surface + (density of fluid) * (acceleration due to gravity) * (depth)
In this case, the swimming pool is located at an altitude of 2400 meters, so we need to account for the difference in atmospheric pressure at this altitude compared to sea level. We will assume a standard atmosphere, which means the pressure at sea level is 101325 Pascals (Pa).
Step 1: Calculate the pressure at the surface.
At 2400 meters altitude, we need to determine the difference in atmospheric pressure compared to sea level. For every 8.5 meters increase in altitude (approximately), the atmospheric pressure decreases by about 1000 Pascals.
Difference in altitude = 2400 meters
Difference in altitude (in units of 8.5 meters) = 2400 / 8.5
Number of "units" = 282.35 (approximately)
Pressure at the surface = 101325 - (282.35 * 1000)
Pressure at the surface = 72850 Pa
Step 2: Calculate the pressure at 2.5 meters depth.
We are given the density of water as 1000 kilograms per cubic meter and the acceleration due to gravity is approximately 9.8 meters per second squared.
Pressure at 2.5 meters depth = Pressure at the surface + (density of water) * (acceleration due to gravity) * (depth)
Pressure at 2.5 meters depth = 72850 + (1000 * 9.8 * 2.5)
Pressure at 2.5 meters depth = 72850 + 24500
Pressure at 2.5 meters depth = 97350 Pa
Therefore, the local pressure at a depth of 2.5 meters in the swimming pool situated at 2400 meters altitude is 97350 Pascals (Pa).