If you dive to 50 m below the surface of a lake,
a) what is the pressure due to the water alone?
b)What is the total or absolute pressure at that depth?
a) (water density)*g*(depth)
Your answer should be in N/m^2, equal to about 5 atmospheres)
b) [(water density)*g*(depth)] + atmospheric pressure
(1 atm more than part (a) )
To determine the pressure at a given depth underwater, you can use the principles of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at rest and is determined by the height and density of the fluid above a certain point.
a) The pressure due to the water alone, known as the gauge pressure, can be calculated using the equation:
P = ρgh
Where:
P is the pressure in Pascals (Pa)
ρ (rho) is the density of the fluid (water in this case) in kilograms per cubic meter (kg/m³)
g is the acceleration due to gravity, approximately 9.8 m/s²
h is the height or depth below the surface in meters (m)
For this question, let's assume the density of water is approximately 1000 kg/m³.
Using the equation, the pressure due to the water alone (gauge pressure) at a depth of 50 meters would be calculated as:
P = (1000 kg/m³) * (9.8 m/s²) * (50 m) = 490,000 Pa = 490 kPa
Therefore, the pressure due to the water alone at a depth of 50 meters is 490 kPa.
b) To calculate the total or absolute pressure at a given depth, we need to consider the atmospheric pressure as well. The total pressure includes both the pressure due to the water and the atmospheric pressure.
Atmospheric pressure can vary depending on factors such as weather and altitude. Let's assume the atmospheric pressure is approximately 101.3 kPa, which corresponds to standard atmospheric pressure at sea level.
To calculate the total or absolute pressure, we need to add the atmospheric pressure to the gauge pressure calculated in part a).
Total Pressure = Gauge Pressure + Atmospheric Pressure
Total Pressure = 490 kPa + 101.3 kPa = 591.3 kPa
Therefore, the total or absolute pressure at a depth of 50 meters is approximately 591.3 kPa.