To calculate the force exerted at the bottom of the cylinder tube, we need to first convert the gauge pressure to absolute pressure.
Given:
Radius of the cylinder tube, r = 90 cm = 0.9 m
Gauge pressure of oil, P_oil = 0.88 m
Density of oil, ρ_oil = 790 kg/m^3
Gauge pressure of brine, P_brine = 1.11 m
Density of brine, ρ_brine = 1,025 kg/m^3
To calculate the force, we'll use the formula for pressure, force, and area:
Pressure = Force / Area
The area of the bottom of the cylinder tube is given by:
Area = π * r^2
Let's start by calculating the force exerted by the oil:
Absolute pressure of oil = Gauge pressure of oil + Atmospheric pressure
P_oil_absolute = P_oil + P_atm
Assuming atmospheric pressure is negligible, we'll consider P_atm = 0.
P_oil_absolute = 0.88 m
The force exerted by the oil at the bottom of the cylinder tube is given by:
Force_oil = Pressure_oil * Area
Area_oil = π * (0.9 m)^2
Area_oil = 2.54 m^2 (approx.)
Force_oil = P_oil_absolute * Area_oil
Force_oil = (0.88 m) * (2.54 m^2)
Force_oil = 2.2332 N
Next, let's calculate the force exerted by the brine:
Absolute pressure of brine = Gauge pressure of brine + Atmospheric pressure
P_brine_absolute = P_brine + P_atm
P_brine_absolute = 1.11 m
The force exerted by the brine at the bottom of the cylinder tube is given by:
Force_brine = Pressure_brine * Area
Area_brine = π * (0.9 m)^2
Area_brine = 2.54 m^2 (approx.)
Force_brine = P_brine_absolute * Area_brine
Force_brine = (1.11 m) * (2.54 m^2)
Force_brine = 2.8154 N
Therefore, the force exerted at the bottom of the cylinder tube by the oil is approximately 2.2332 N and by the brine is approximately 2.8154 N.
Using the gauge pressure, calculate the force exerted at the bottom of cylinder tube whose radius is 90 cm
Oil = 0.88m
Poil = 790kg
Brine = 1.11m
Pbrine = 1,025 kg
1 answer
1 answer