Themes > Science > Physics > Mechanics > Fluid Mechanics > Past Examination Solutions > June 1996 > Question 7
7)
A plunger of diameter 0.1 m and length 0.15 m has five small holes of diameter 2 mm drilled through it in the direction of its length. The plunger fits closely inside a cylinder containing oil, such that no oil passes between the plunger and the cylinder. Calculate the force which must be applied to the plunger, in a downward vertical direction, to make the plunger fall with a speed of 0.0005 m/s. Assume that the upwards flow through the small holes is laminar and that the coefficient of viscosity of the oil is 0.2 kg/ms.
(20 marks)
Velocity, u = 0.0005 m/s
viscosity m = 0.2 kg m-1 s-1
length = 0.15m
hole diameter, d = 2mm = 0.002m
Plunger diameter D = 0.1m
The Hagen-Poiseuille equation for head loss during laminar flow in a pipe is:
Pressure difference between top and bottom of each hole is:
So we need a pressure of 120 N/m2 at the bottom of the cylinder.
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