pressure of a fluid. calculate the a.) absolute pressure b.) gauge pressure at an ocean depth of 1000m. Assume the density of a sea water is 1024 kg cubic meter and that the air above exerts a pressure of 101.3kPa
Absolute pressure is the pressure on a surface including atmospheric pressure.
Gauge pressure is the additional pressure acting on a surface over and above atmospheric pressure.
At the ocean depth of 1000 m, gauge pressure is the pressure exerted by the weight of water above the point under consideration.
At a depth of 1000m, and ignoring the variation of g over depth, we have
gauge pressure
=ρgh
=1024*9.81*1000 Pa
=10045 kPa
Absolute pressure is the gauge pressure plus the atmospheric pressure of 101.3 kPa, so
absolute pressure
= 10045+101.3
= 10147 kPa
To calculate the absolute pressure and gauge pressure at an ocean depth of 1000m, we need to consider the hydrostatic pressure formula.
1. Calculate the absolute pressure:
The absolute pressure of a fluid at a given depth is calculated by considering the weight of the fluid above it, as well as any additional atmospheric pressure. The formula to calculate absolute pressure is:
P_absolute = P_atm + ρgh
Where:
P_absolute is the absolute pressure,
P_atm is the atmospheric pressure,
ρ is the density of the fluid, and
g is the acceleration due to gravity,
h is the depth.
Given:
P_atm = 101.3 kPa (pressure exerted by the air),
ρ = 1024 kg/m³ (density of seawater),
h = 1000 m (ocean depth).
First, convert the atmospheric pressure to Pascals (Pa):
P_atm = 101.3 kPa = 101.3 × 10^3 Pa
Now, substitute the given values into the formula:
P_absolute = (101.3 × 10^3 Pa) + (1024 kg/m³ × 9.8 m/s² × 1000 m)
Simplify the equation:
P_absolute = 101,300 Pa + 9,996,800 Pa
P_absolute = 10,098,100 Pa
Therefore, the absolute pressure at an ocean depth of 1000m is 10,098,100 Pa (or 10.0981 MPa).
2. Calculate the gauge pressure:
Gauge pressure is the difference between the absolute pressure and atmospheric pressure. Therefore, to calculate the gauge pressure, subtract the atmospheric pressure from the absolute pressure:
P_gauge = P_absolute - P_atm
Substitute the values:
P_gauge = 10,098,100 Pa - 101,300 Pa
P_gauge = 9,996,800 Pa
Therefore, the gauge pressure at an ocean depth of 1000m is 9,996,800 Pa (or 9.9968 MPa).
To calculate the absolute pressure and gauge pressure at an ocean depth of 1000m, we need to consider the hydrostatic pressure equation.
a.) Absolute Pressure:
Absolute pressure is the total pressure acting on a fluid, including the atmospheric pressure. The formula to calculate the absolute pressure is:
P absolute = P atmospheric + P hydrostatic
Given:
P atmospheric = 101.3 kPa (pressure exerted by air)
Density of seawater = 1024 kg/m^3
Ocean depth (h) = 1000 m
To calculate the hydrostatic pressure, we can use the following formula:
P hydrostatic = ρgh
Where:
ρ = density of the fluid (seawater)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height or depth of the fluid (ocean depth)
Substituting the given values into the formula, we have:
P hydrostatic = (1024 kg/m^3) * (9.8 m/s^2) * (1000 m)
P hydrostatic = 10,073,600 N/m^2 (or Pascal)
Now, we can calculate the absolute pressure:
P absolute = P atmospheric + P hydrostatic
P absolute = 101.3 kPa + 10,073,600 N/m^2 (converted to kPa)
P absolute = 101.3 kPa + 10,073.6 kPa
P absolute = 10,174.9 kPa
b.) Gauge Pressure:
Gauge pressure is the difference between the absolute pressure and atmospheric pressure. It represents the pressure above atmospheric pressure. The formula to calculate the gauge pressure is:
P gauge = P absolute - P atmospheric
Substituting the given values, we have:
P gauge = 10,174.9 kPa - 101.3 kPa
P gauge = 10,073.6 kPa
Therefore, the absolute pressure at an ocean depth of 1000m is 10,174.9 kPa, while the gauge pressure at the same depth is 10,073.6 kPa.