At the surface of a freshwater lake the pressure is 102 kPa.
(a) What is the pressure increase in going 34.7 m below the surface?
b) What is the approximate pressure decrease in going 33 m above the surface? Air at 20° C has density of 1.2 kg/m3.
To answer these questions, we need to use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at a certain depth. It depends on the density of the fluid and the height or depth of the point of interest.
(a) To find the pressure increase in going 34.7 m below the surface of the freshwater lake, we will use the equation:
ΔP = ρgh
Where:
ΔP is the pressure change,
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth or height.
1. We need to convert the depth from meters to kilograms per cubic meter since the density of the fluid is given in that unit. The equation is:
ΔP = (1.2 kg/m3) × (9.8 m/s2) × (34.7 m)
Calculating this equation, we find:
ΔP = 405.12 Pa
Therefore, the pressure increase when going 34.7 m below the surface is approximately 405.12 Pa.
(b) To find the approximate pressure decrease in going 33 m above the surface, we also use the equation:
ΔP = ρgh
Again:
ρ is the density of the fluid,
g is the acceleration due to gravity, and
h is the depth or height.
2. In this case, we need to find the pressure decrease, so we'll use a negative value for the height. The equation is:
ΔP = (1.2 kg/m3) × (9.8 m/s2) × (-33 m)
Calculating this equation, we find:
ΔP = -384.12 Pa
Therefore, the approximate pressure decrease when going 33 m above the surface is approximately -384.12 Pa.