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HW1
1- Crude oil having a viscosity of 9.52 x 10-4 lb.s/ft2 is contained between parallel
plates. The bottom plate is fixed and upper plate moves when a force P is
applied. If the distance between the two plates is 0.1 inch, what value of P is
required to translate the plate with a velocity of 3 ft/s? The effective area of the
upper plate is 200 inch2.
2- A 10-kg block slides down a smooth inclined surface as shown in the figure.
Determine the terminal velocity of the block if the 0.1-mm gap between the
block and the surface contains SAE 30 oil at 60oF. Assume the velocity
distribution in the gap is linear, and the area of the block in contact with the oil
is 0.2 m2.
3- A piston having a diameter of 5.48 in. and a length of 9.50 in. slides downward
with velocity V through a vertical pipe. The downward motion is resisted by an
oil film between the piston and pipe wall. The film thickness is 0.002 in., and
the cylinder weighs 0.5 lb. Estimate V if the oil viscosity is 0.016 lb.s/ft2.
Assume the velocity distribution in the gap is linear.
4- A thin layer of glycerin flows down an inclined, wide plate with the velocity
distribution shown in the figure. For h = 0.3 in. and   20 o , determine the
surface velocity, U. Note that for equilibrium, the component of weight acting
parallel to the plate surface must be balanced by the shearing force developed
along the plate surface. In your analysis assume a unit plate width.
5- A layer of water flows down an inclined fixed surface with the velocity profile
shown in the figure. Determine the magnitude and direction of the shearing
stress that the water exerts on the fixed surface for U = 3 m/s and h = 0.10 m.
6- A Newtonian fluid having a specific gravity of 0.92 and a kinematic viscosity of
4 x 10-4 m2/s flows past a fixed surface. The velocity profile near the surface is
shown in the figure. Determine the the magnitude and direction of the shearing
stress developed on the plate. Express your answer in terms of U and  , with U
and  expressed in units of meters per second and meters respectively.