Year 12s: what will be the first way you research your future options? >>

Fluid mechanics

Fluid mechanics problem :frown:

1) why is there a "1/2" in the solution? - (see denominator)
2) why is the force calculated with the area being 2piRH?

Thanks :smile:

Is it because the 1/2 makes it so you're using the radii rather than the diameters?

Reply 2

Stonebridge

Original post by LK2611

Fluid mechanics problem :frown:

1) why is there a "1/2" in the solution? - (see denominator)
2) why is the force calculated with the area being 2piRH?

Thanks :smile:

1) because the thickness of the oil film is not 50 - 49.5 it's half of that.
2) that is the formula for the surface area of a cylinder of end radius R and length H. The circumference 2pi.R times the length H

Reply 3

LK2611

Thanks for posting.

1) Stupid question, but why is it half?
2) Wouldn't they use the area of the circle, which is where the force is being applied?

Reply 4

lerjj

1) The oil is on both sides of the plunger. Basically you have two overlaps which equal 0.5 when added together.
Not sure about 2)

Reply 5

Stonebridge

Original post by LK2611

Thanks for posting.

1) Stupid question, but why is it half?
2) Wouldn't they use the area of the circle, which is where the force is being applied?

1) 50 and 49.5 are the outer and inner diameters. The thickness of the oil film is the difference between the outer and inner radius. Radius is half the diameter.
2) The surface area of the plunger in contact with the inner surface is a cylinder. The force is due to the viscosity of the oil film on the outside cylindrical surface of the plunger in contact with the inside surface of the channel.