Using the gauge pressure, calculate the force exerted at the bottom of cylinder tube whose
radius is 90 cm.
oil= 0.88m
brine= 1.11m
p oil= 790 kg/m^3
p brine= 1025 kg/m^3
To calculate the force exerted at the bottom of the cylinder tube, we need to calculate the pressure at the bottom first using the gauge pressure.
The gauge pressure is given as 0.88m for oil and 1.11m for brine.
First, let's calculate the pressure due to oil:
ρ_oil = 790 kg/m^3
gauge pressure (P_oil) = 0.88 m
To calculate the absolute pressure (P_abs) at the bottom of the cylinder, we need to add the atmospheric pressure (P_atm). Let's assume the atmospheric pressure is 1 atm.
P_abs = P_atm + P_oil
Now, let's calculate the force exerted by the oil at the bottom of the cylinder:
The area of the bottom of the cylinder (A) can be calculated using the radius (r) of the cylinder tube:
r = 90 cm = 0.9 m
A = π * r^2
The force (F) is calculated using the formula:
F = P_abs * A
Now, let's substitute the values and calculate the force exerted by the oil at the bottom of the cylinder:
A = π * (0.9)^2
F_oil = (P_atm + P_oil) * A
Next, let's calculate the force exerted by the brine:
ρ_brine = 1025 kg/m^3
gauge pressure (P_brine) = 1.11 m
P_abs = P_atm + P_brine
F_brine = (P_atm + P_brine) * A
Now, we have calculated the forces exerted by both the oil and brine at the bottom of the cylinder.