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.

Question

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.

I don't understand what formula to use for this question. :/

Answer 1

It should be the Bernoulli one, but something that I still not getting.

Answer 2

To answer this question, you can use the hydrostatic equation, which states that the pressure at a certain depth in a fluid is equal to the atmospheric pressure plus the product of the fluid's density, the acceleration due to gravity, and the depth. In this case, the fluid is water and the density is given as 1000 kilograms per cubic metre.

The equation can be written as follows:
P = Patm + (ρ * g * h)

Where:
P - Local pressure at a certain depth
Patm - Atmospheric pressure
ρ - Density of the fluid (in this case, water)
g - Acceleration due to gravity
h - Depth

Since you are given that the swimming pool is situated at 2400 meters altitude in the mountains, you need to consider the atmospheric pressure at that location. The standard atmosphere pressure at sea level is approximately 101325 Pascals (Pa), but it decreases with increasing altitude. You can use a barometric formula to estimate the atmospheric pressure at 2400 meters altitude.

To calculate the local pressure at 2.5 meters depth, you will need to compute the atmospheric pressure at 2400 meters altitude and then use the hydrostatic equation.

Here are the steps to find the local pressure at 2.5 meters depth in the swimming pool:

Step 1: Calculate atmospheric pressure at 2400 meters altitude.
Use a barometric formula or altitude-based atmospheric pressure calculator to find the approximate atmospheric pressure at 2400 meters altitude. Let's assume it is 80% of the sea-level value, which is approximately 81060 Pa.

Step 2: Apply the hydrostatic equation.
Use the hydrostatic equation to calculate the local pressure at 2.5 meters depth using the density of water (1000 kg/m³), the acceleration due to gravity (9.8 m/s²), and the depth (2.5 meters).
P = Patm + (ρ * g * h)
P = 81060 Pa + (1000 kg/m³ * 9.8 m/s² * 2.5 m)
P = 81060 Pa + 24500 Pa
P = 105560 Pa

Therefore, the local pressure at 2.5 meters depth in the swimming pool situated at 2400 meters altitude in the mountains is approximately 105,560 Pascals (Pa).