Download Midterm #1 - Problems Solutions

Problem 1. (35 pts.) A Newtonian fluid having a specific gravity
of 0.92 and a kinematic viscosity of 4x10-4 m2/s flows past a fixed
surface. Due to the no-slip condition, the velocity at the fixed surface is
zero, and the velocity profile near the surface is shown in the figure
below. Determine the magnitude and direction of the shearing stress
developed on the plate. Express your answer in terms of U and δ, with U
and δ expressed in units of meters per second and meters, respectively.
Problem 2. (30 Pts.) A piston having a cross-sectional area of 3 ft2
and negligible weight is located in a cylinder containing oil (SG = 0.9) as
shown. The cylinder is connected to a pressurized tank containing water
and oil. A force, P, holds the piston in place. (a) Determine the required
value of the force, P. (b) Determine the pressure head, expressed in feet of
water, acting on the tank bottom.
Problem 3. ( 35 pts.) The rigid gate, OAB, is hinged at O and rests against
a rigid support at B. What minimum horizontal force, P, is required to hold the
gate closed if its width is 3 m? Neglect the weight of the gate and friction in the
hinge. The back of the gate is exposed to the atmosphere.
Extra credit
Q1. (3 pts.) If V is a velocity, l a length, W a weight, and μ a fluid property having dimensions of FL-2T, determine the
dimensions of: (a) Vl2μ/W, (b) Wμl.
a)
b)
Q2. (3 pts.) A person weighs 165 lb at the earth’s surface. (a) Determine the person’s mass in slugs and kilograms. (b) What is
this person’s mass on the moon in kilograms?
a)
b)
Q3. (4 pts.) A hydrometer is used to measure the specific gravity of liquids. For a certain liquid a hydrometer reading
indicates a specific gravity of 1.15. What is the liquid’s density and specific weight in SI units?