ENGI 2103: Thermo-Fluid Engineering II
Winter 2021
Problem Set #1
[1] The Stokes-Oseen formula for drag force F on a sphere of diameter D in a fluid stream of low
velocity V, density ρ, and viscosity μ is shown below. Is this formula dimensionally homogenous?
F=3 π μ D V +
9π
ρ V 2 D2
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[2] The mean free path of a gas, l, is defined as the average distance traveled by molecules between
collisions. A proposed formula for estimating l of an ideal gas is:
l=1.26
(
μ
ρ √ RT
)
Is the constant (1.26) a pure constant? If not, what are its dimensions?
[3] An approximation for the boundary-layer shown in the figure below is:
u( y)≈U sin
( )
π y
, 0≤ y≥δ
2δ
where U is the stream velocity far from the wall and δ is the boundary layer
thickness. If the fluid is helium at 20°C and 1 atm, and if U = 10.8 m/s and
δ = 3 cm, use the formula to
(a) estimate the wall shear stress τw in Pa, and
(b) find the position in the boundary layer where τ is one-half of τw.
ENGI 2103: Thermo-Fluid Engineering II
Winter 2021
[4] A glass barometer consists of a glass bulb with a thin spout which
is open to the atmosphere. The barometer is partially filled with water
so that a volume of air is trapped in the bulb. As the exterior
atmospheric pressure changes with different weather patterns the level
of the water in the spout will change. In the glass barometer shown in
the figure, the water level is h=L/2 in the bulb and the spout when the
atmospheric pressure is 1 atm (dashed line). You may assume that the
air is dry air and acts as an ideal gas (i.e. assume no water evaporates).
a) What will happen to the water level in the spout during:
i) stormy weather,
ii) clear weather,
ii) explain in a short paragraph why this happens.
b) Derive an equation which estimates the atmospheric pressure based
on the height of the water in the spout above the base of the
barometer.
𝑃𝑎≈𝑓(ℎ)
c) If L=10cm, D=5cm, d=1cm, W=5cm and Tamb=20°C estimate the
full range of atmospheric pressures this device is capable of
measuring.
[5] Gate ABC is 1 m square and is hinged at B. It will open automatically
when the water level h becomes high enough. Determine the lowest
height for which the gate will open. Neglect atmospheric pressure. Is this
result independent of the liquid density?
h
ENGI 2103: Thermo-Fluid Engineering II
Selected Answers:
[1] Yes, it is dimensionally homogenous
[2] Yes, it is a pure constant
2δ
[3] (b) y=
3
[4] (c) The device can measure from 96.92 kPa to 105.08 kPa
[5] h>0.333m
Winter 2021