A tapered, cylindrical flask (i.e., diameter varies with vertical position) cont

Question

A tapered, cylindrical flask (i.e., diameter varies with vertical position) contains a mixture of oil and water, constrained at the top by a spring?loaded stopper, as shown in the figure below. The diameter of the opening of the flask is 5 cm and the diameter at the bottom is 35 cm. The bottom of the stopper is in contact with the oil. The stopper has a spring constant of 0.5 kN/m and is compressed by 2 cm. The water depth is 12 cm and has a specific gravity of 1.0. The oil depth is 12 cm and has a specific gravity of 0.8. Atmospheric pressure may be assumed to be =101.325 kPa.

What is the absolute pressure at point

A tapered, cylindrical flask (i.e., diameter varies with vertical position) contains a mixture of oil and water, constrained at the top by a spring? loaded stopper, as shown in the figure below. The diameter of the opening of the flask is 5 cm and the diameter at the bottom is 35 cm. The bottom of the stopper is in contact with the oil. The stopper has a spring constant of 0.5 kN/m and is compressed by 2 cm. The water depth is 12 cm and has a specific gravity of 1.0. The oil depth is 12 cm and has a specific gravity of 0.8. Atmospheric pressure may be assumed to be =101.325 kPa. What is the absolute pressure at point "A" on the bottom of the flask in kPa? What is the absolute pressure at point "B" on the bottom of the flask in kPa? Is the flask system at equilibrium?

Explanation / Answer

1) Height of A from spring = 35 x 8 / 24 = 11.66 cm

Pressure at point A = Spring pressure + oil pressure + water pressure

spring pressure = F/ A

A = pi x D^2 / 4 = 1.96 x10^-3 m^2

F = k x X = 0.5 x 2 x 10^-2 = 0.01 KN

So Spring pressure = 0.01 / 96 x 10^-3 = 5.1021 Kpa

Oil pressure = sp. gravity of oil xwater densityxgx h

= 0.8 x 1000 x 9.81 x 12 x 10^-2 = 941.76 x 10^-3 Kpa

Water pressure = sp. gravity of water *water density x g x h

= 1 x 1000 x 9.81x 11.66 = 1144.5 x 10^-3 Kpa

So absolute pressure at A = atm press + pressure at A

= 101.325 + 5.0121 + 0.94176 + 1.1445 = 108.42 Kpa

2) Absolute pressure at b = atm press + oil press + water press

= 101.325 + 0.94176 + 1.1445 =103.411 KPa

3) Due to variable pressure acting forces the system is not in equilibrium.

so . NO.

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