Answer:
Pgage at A = 101.30354 kPa
Pgage at B = 101.29646 kPa.
Step-by-step explanation:
To calculate the gauge pressures in chambers A and B, we need to use the formula:
Pressure = Force / Area
where force is the net force acting on the piston and area is the cross-sectional area of the piston.
First, let's calculate the net force acting on the piston. We know that the weight of the piston is 25 N, which is acting downwards. We also know that the piston is in equilibrium, so the net force acting on it is zero. Therefore, there must be an upward force acting on the piston that is equal in magnitude to the weight of the piston. This upward force is the pressure difference between the two chambers pushing up on the piston.
The area of the piston is given by:
Area = pi * (diameter/2)^2
= pi * (30 cm / 2)^2
= 706.9 cm^2
Now we can calculate the pressure difference between the two chambers:
Pressure difference = Force / Area
= 25 N / 706.9 cm^2
= 0.0354 N/cm^2
Since the fluid in both chambers is at the same level, the pressure in chamber A is equal to the atmospheric pressure plus the pressure difference, and the pressure in chamber B is equal to the atmospheric pressure minus the pressure difference. Assuming the atmospheric pressure is 101.3 kPa, we can calculate the gauge pressures in chambers A and B as follows:
Pressure in A = Atmospheric pressure + Pressure difference
= 101.3 kPa + 0.0354 N/cm^2
= 101.3 kPa + 0.00354 kPa
= 101.30354 kPa
Pressure in B = Atmospheric pressure - Pressure difference
= 101.3 kPa - 0.0354 N/cm^2
= 101.3 kPa - 0.00354 kPa
= 101.29646 kPa
Therefore, the gauge pressure in chamber A is 101.30354 kPa and the gauge pressure in chamber B is 101.29646 kPa.