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
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.
To calculate the force exerted at the bottom of the cylindrical tube, we need to determine the pressure at the bottom of the tube using the gauge pressure.
Step 1: Convert the gauge pressure to absolute pressure:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Step 2: Calculate the force exerted at the bottom of the tube using the formula:
Force = Pressure x Area
Given:
Gauge Pressure of Oil (Poil) = 0.88 m
Gauge Pressure of Brine (Pbrine) = 1.11 m
Radius of the tube (r) = 90 cm = 0.9 m
Step 1: Convert the gauge pressure to absolute pressure:
To convert the gauge pressures to absolute pressures, we need to add the atmospheric pressure, which is typically 1 atm or 101,325 Pascals.
Absolute Pressure of Oil (Poil) = 0.88 m + 101,325 Pa = 101,325.88 Pa
Absolute Pressure of Brine (Pbrine) = 1.11 m + 101,325 Pa = 101,326.11 Pa
Step 2: Calculate the force exerted at the bottom of the tube using the formula:
Force = Pressure x Area
Area (A) = π * r^2
Area of the tube (A) = π * (0.9 m)^2 = 2.54 m^2
Force exerted by the Oil = Poil * A
Force exerted by the Brine = Pbrine * A
Now we can substitute the values to calculate the forces.
Force exerted by the Oil = 101,325.88 Pa * 2.54 m^2 = 257,419.39 N (approximately)
Force exerted by the Brine = 101,326.11 Pa * 2.54 m^2 = 257,436.05 N (approximately)
Therefore, the force exerted at the bottom of the cylindrical tube is approximately 257,419.39 N for the oil and 257,436.05 N for the brine.