Refer to Image 6.1 to answer Questions 6.1 and 6.2.
Image 6.1
oil = 0.88 m
brine= 1.11 m
P oil= 790 kg/m^3
P brine= 1025 kg/m^3
Question 6.1
What is the gauge pressure at the bottom of the cylinder?
Question 6.2
Using the gauge pressure, calculate the force exerted at the bottom of cylinder tube whose radius is 90 cm.
Question 6.3
What is the absolute pressure at the bottom of the cylinder considering that the container is open on top?
To determine the gauge pressure at the bottom of the cylinder, we need to find the pressure difference between the oil and the brine.
Question 6.1: What is the gauge pressure at the bottom of the cylinder?
Answer: The gauge pressure can be calculated by subtracting the pressure of the brine from the pressure of the oil.
Gauge Pressure = P oil - P brine = 790 kg/m^3 - 1025 kg/m^3
= -235 kg/m^3 (Since the pressure of the brine is greater than the pressure of the oil, the gauge pressure is negative.)
Question 6.2: Using the gauge pressure, calculate the force exerted at the bottom of the cylinder tube whose radius is 90 cm.
Answer: The force exerted at the bottom of the cylinder can be calculated using the formula:
Force = Pressure * Area
= Gauge Pressure * Area
Since the radius is given in centimeters and the gauge pressure is given in kg/m^3, we need to convert the radius to meters.
Radius = 90 cm = 0.9 m
Area = π * r^2
= π * (0.9 m)^2
Now we can calculate the force using the gauge pressure and the calculated area.
Force = (-235 kg/m^3) * [π * (0.9 m)^2]
Note: The unit for force will be kg * m/s^2 or N.