AER202S
FLUID MECHANICS
Quiz 4
6 April 2006
Closed Book, no aid sheets
Non-programmable calculators allowed
Instructor: J. W. Davis
Family Name:
Given Name:
s o \C C ~ C P A
Student #:
U s e l l data:
pair= 1.23 kg/m3
Pwater= 1000 kg/m3
pait= 1.8 x 1 OmsNslm2
pwater
= 1.1 x 1 OJ ~ s l m ~
Page 1 of 7
1)
Indicate whether the statement is True or False.
(10 marks)
A Pitot tube works on the principle of converting kinetic energy to potential
energy.
The divergence of the velocity vector is the rate of outflow of volume per unit
mass.
In the drag coefficient plot for flow past a sphere, the sudden drop in drag at
high Reynolds number is because the boundary layer suddenly becomes
turbulent.
In the Navier-Stokes equations, there are just three principle types of terms:
inertial, viscous and gravitational.
Control volumes must always be fixed in space.
The Froude number is important in determining the drag on ships because it
represents the ration of viscous to gravitational forces.
Helmholtz's theorem statesthat inviscid twodimensional flows are irrotational.
The flow velocity is always subsonic following a normal shock wave.
A boundary layer is aregion in which neither viscous nor inertial terms may be
neglected.
Stokes' law of drag (F,
= 3npU,D)
Page 2 of 7
is valid at low Reynolds number.
A cylinder is held in a two-dimensional duct of constant width Wand height D. As a result,
the downstream velocity distribution becomes as shown below. The density p i s constant and
the flow is steady. Find U, in terms of U, and find the force exerted by the fluid on the cylinder
in terms of p, U,, Wand D. Neglect fictional effects and assume that p, = p,. Does your
answer seem reasonable?
(10 marks)
ik
4~
d ; * C ~ b
4 S b - Page 3 of 7
For one dimensional unsteady compressible flow in a cylinder having velocity and density
fields of the form v(r,t) = u(x, t)i and p(x, t) respectively, show fiom first principles that the
equation governing conservation of mass takes the form:
A
-
(10 marks)
Page 4 of 7
The Bernoulli equation for steady, inviscid, compressible, adiabatic flow along a streamline
takes the form:
For an ideal gas, p = pRT, show that, when gravity is not important,
where p, is the pressure corresponding to q = 0, the stagnation pressure, and M is the Mach
Number.
Hint: for an ideal gas: e = CvT, C,
= Rl(y-1), p = C,pY.
(10 marks)
Page 5 of 7
A closed channel of width His connected to a contraction which reduces the width to HI3 as
depicted in the diagram. The incompressiblefluid approachingthe oncdistribution v(r, t) = u(y)k, where u increases linearly fiom U' at y = 0 to U, at y = H. By
assuming that the flow is frictionless and steady and that, downstream of the contraction the
streamlines are parallel to 4, find the pressure decrease p, - p, through the contraction.
(10 marks)
Page 6 of 7
6)
A golf ball manufacturer wants to study the effects of dimple size on the distance a golf ball
travels. A model ball five times the size of a regular golf ball is installed in a wind tunnel.
What parameters must be controlled to model the golf ball performance? What should be the
speed of the wind tunnel to simulate a golf ball speed of 60 d s ? To aid in visualization of the
flow, measurements of the model are to be made in a water flow tunnel. What should the flow
speed be in this tunnel?
(5 marks)
Page 7 of 7.