AE 340 Homework set #1
Due Feb. 8, 22
1. A linearly varying pressure [P(x) = Pmax* x /L] is acting on a plate. Calculate the total
force (resultant) and how far it acts from the origin? Later we shall call this the center of
pressure.
Solution
2. A flat plate floating on a 0.05 cm thick water film is pulled by the force F. Calculate F
for an area of 1 m2 and for U=1m/sec [note that for water = 0.001 kg/(m sec) ].
Solution
3a. A thin oil film is covering the surface of an inclined plane, as shown. Develop an
expression for the terminal velocity of a block of weight W, sliding down the slope.
Assume that the oil film thickness and viscosity are known, as well as the incline angle
and the contact surface area.
Solution
F = mgsin q
U
S
h
mgsin q × h
U=
m×S
3b. Calculate the terminal velocity of a 0.2m wide, 0.3m long and 5kg block sliding down
an incline of 30 deg, as shown in the figure. Assume the oil film thickness is 1 mm and
the oil viscosity, (from Table 1.1) is 0.29 N s/m2.
Solution
5 × 9.8 × sin 30 × 0.001
u=
= 1.4m / s
0.29 × 0.2 × 0.3
F = tS= m
4. Two circular tubes are inserted vertically into a large container filled with liquid that
has a surface tension of  = 0.07 N/m, and contact angle of 
the liquid is 960 kg/m3 the diameter of the first tube is 1.5 mm, and the diameter of the
second tube is 2.5 mm. a) calculate how high will the liquid columns rise in each tube. b)
Is this in conflict with Pascal’s law? Explain.
Solution