a) What is the gauge pressure of water at a depth of 38.7 m?
kPa
b) What is the actual pressure of water at this depth?
kPa
what formulas do i use and how do i do this?
a) gauge pressure = (water density, kg/m^3)x(depth, meters)x(acceleration of gravity, m/s^2)
The answer will be in Pascals
b) add atmospheric pressure to the gauge pressure
To calculate the gauge pressure of water at a certain depth, you can use the equation:
P = ρgh
Where:
P is the pressure,
ρ is the density of water,
g is the acceleration due to gravity, and
h is the height or depth.
a) To find the gauge pressure of water at a depth of 38.7 m, you need to know the density of water. The density of water is approximately 1000 kg/m³.
Using the formula mentioned earlier:
P = ρgh
P = (1000 kg/m³)(9.8 m/s²)(38.7 m)
P ≈ 381,660 Pa
To convert the pressure from Pascal (Pa) to kilopascal (kPa), you divide the pressure by 1000:
P ≈ 381,660 / 1000 ≈ 381.66 kPa.
Therefore, the gauge pressure of water at a depth of 38.7 m is approximately 381.66 kPa.
b) To find the actual pressure of water at this depth, you need to consider the atmospheric pressure at the surface. Atmospheric pressure typically ranges from 90 to 110 kPa, so for this calculation, we'll use 100 kPa as an approximation.
To calculate the actual pressure, you add the gauge pressure to the atmospheric pressure:
Actual pressure = gauge pressure + atmospheric pressure
Actual pressure = 381.66 kPa + 100 kPa
Actual pressure ≈ 481.66 kPa
Therefore, the actual pressure of water at a depth of 38.7 m is approximately 481.66 kPa.