A reservoir dam holds an 8 km2 lake behind it. Just behind the dam, the lake is 14.0m deep. What is the gauge pressure at the base of the dam (in Pascals)?
What is the absolute pressure at a point 2.5 m down from the surface? Assume the pressure at the surface is one atmosphere.
To find the gauge pressure at the base of the dam, we can use the equation for pressure at a given depth in a fluid:
P = ρgh
Where:
P = pressure (in Pascals)
ρ = density of the fluid (in kg/m^3)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = depth or height of the fluid column (in meters)
Given:
Density of water (ρ) ≈ 1000 kg/m^3
Depth of the lake behind the dam (h) = 14.0 m
Plugging in these values, we can calculate the gauge pressure at the base of the dam:
P = (1000 kg/m^3) * (9.8 m/s^2) * (14.0 m)
P ≈ 137,200 Pa
Therefore, the gauge pressure at the base of the dam is approximately 137,200 Pascals.
To find the absolute pressure at a point 2.5 m down from the surface, we need to consider both the gauge pressure and the atmospheric pressure. The atmospheric pressure is typically around 101,325 Pa.
So, the absolute pressure at a point 2.5 m down from the surface would be:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 137,200 Pa + 101,325 Pa
Absolute Pressure ≈ 238,525 Pa
Therefore, the absolute pressure at a point 2.5 m down from the surface is approximately 238,525 Pascals.
To calculate the gauge pressure at the base of the dam, we need to find the pressure exerted by the water column above it. We can use the formula for pressure in a fluid:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid (water),
g is the acceleration due to gravity, and
h is the height of the fluid column.
First, we need to convert the depth of the lake (14.0 m) to meters since the density of water is typically given in kilograms per cubic meter (kg/m^3). Next, we'll calculate the pressure at the base of the dam:
P = ρgh
Where:
ρ = density of water = 1000 kg/m^3 (approximately),
g = acceleration due to gravity = 9.8 m/s^2 (approximately), and
h = height of the fluid column = 14.0 m.
Substituting the values into the formula:
P = (1000 kg/m^3)(9.8 m/s^2)(14.0 m)
Calculating the product:
P = 137,200 N/m^2 (or Pascals)
Therefore, the gauge pressure at the base of the dam is 137,200 Pascals.
Now, let's calculate the absolute pressure at a point 2.5 m down from the surface. Absolute pressure includes atmospheric pressure, so we need to account for that as well.
The formula for absolute pressure is:
P_absolute = P_gauge + P_atmosphere
Where:
P_absolute is the absolute pressure,
P_gauge is the gauge pressure (calculated above), and
P_atmosphere is the atmospheric pressure.
Given that the pressure at the surface is one atmosphere, which is equivalent to 101,325 Pascals, we can calculate the absolute pressure at a point 2.5 m down from the surface:
P_absolute = P_gauge + P_atmosphere
Substituting the values into the formula:
P_absolute = 137,200 Pascals + 101,325 Pascals
Calculating the sum:
P_absolute = 238,525 Pascals
Therefore, the absolute pressure at a point 2.5 m down from the surface is 238,525 Pascals.
gauge pressure=g*1E3kg/m^3*14m
= 9.8*1E3*14 Pa=9.8*14kPa
absolute pressure, add 101kPa to the above to add in atmospheric pressure.