AAE 333 Exam 2
Wed Dec 2 , 8PM-10PM
Open Book (Closed notes)
1 Crib Sheet (two sided)
Calculator allowed
Hand in Scratch work
Do not staple to Scantron
PUT YOUR Purdue ID ON THE SCANTRON !!!
Include 00
1) For what value of the constant “b” does the velocity potential φ = x^2 + b y^2 represent an
incompressible flow?
a. 1
b. 2
c. -1
d. -2
e. 0
2) What are the {x,y} velocity components corresponding to the stream function ψ = 2 x y.
a.
b.
c.
d.
e.
u=2 y , v=2 x
u=2 x , v=-2 y
u=-2 x , v= 2 y
u=x^2 y, v=x y^2
u=x y^2 , v=-x^2 y
3) The minimum gage pressure on the surface of an airfoil is -200 Pa when
the free stream velocity is 10 m/s. If the free stream velocity is
increased to 20 m/s, the minimum gage pressure will change (neglecting
viscous effects) to
a. 0 Pa
b. 200 Pa
c. -400 Pa
d. -600 Pa
e. -800 Pa
4) The NACA 3412 airfoil has a maximum distance between the chord line and the camber line of
a. 12% of chord
b. 3 % of chord
c. 4% of chord
d. 1% of chord
e. 2% of chord
5) An airplane flies through sea level air. Its pitot tube reads a gage pressure of 0.2 atm. The air
speed (in m/s) is closest to
a. 10
b. 50
c. 100
d. 200
e. 400
6) Incompressible potential flow over a circular cylinder has a max speed of twice the free stream
without circulation. If sufficient circulation is a added to make the max velocity 3 times free
stream, the lift coefficient would be closest to
a. 0
b. 2
c. 4
d. 6
e. 8
7) In a two-D laminar Channel flow (Poiseuille flow), the velocity in the x direction is given by
u=3*y*(2-y). The upper wall (at y=2) must be restrained from moving by an external force
acting along the wall.
If the viscosity is μ=0.5, the required force (per unit area of the top wall, positive in the +x
direction) is:
a. -3
b. 3
c. 0
d. 6
e. -6
8) In the same channel as Pb 7), the pressure gradient along the channel, dp/dx, is :
a. -3
b. 3
c. 0
d. 6
e. -6
9) Consider a vertical fixed wall at x=0 and a parallel moving wall at x=1mm. The moving wall has a
velocity of 1m/s in the +y direction. The viscosity of the fluid in the gap is .02 Pa-s. The fluid
exerts a force (in the y direction, per unit area, in N/m^2) on the fixed wall of :
a. 0
b. 10
c. -10
d. 20
e. -20
10) In a 2D flow, u=2 x^2 + 2 y^2; v=-4*x*y, the viscous shear stress , 𝜏𝑥𝑦 , is
a. 4 μy
b. 0
c. 4 μ x
d. -4 μy
e. -4 μx
11) The 2D velocity field u=2 x^2 + 2 y^2; v=4*x*y is equivalent to which of the following velocity
potentials:
a. None exists
b. 2 (3 x^2+y^2) y/3
c. 2(x^2+3 y^2)x/3
d. 2(x+y)xy
e. 2 X^2 y^2
12) Cp, dx and dy are 300*1 column vectors coming out of the airfoil source/vortex panel method
used in class. The angle of attack is zero. (x and y are measured in units of chord and are
ordered clockwise around the perimeter of the airfoil). The lift coefficient can be computed by
which of the following matlab commands:
a. Cl=cp’*dx
b. Cl=cp’*dy
c. Cl=-cp’*dx
d. Cl=-cp’*dy
e. Cl=-cp*dx’
13) Which of the five figures shown below could represent a contour plot of streamlines and the
corresponding quiver plot of the velocity field?
(a) :
(b):
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.2
0.4
0.6
0.8
0
1
0
0.2
0.4
0.6
0.8
(c ) :
(d):
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.2
0.4
1
0.6
0.8
0
1
0
0.2
0.4
0.6
0.8
1
(e):
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
14) Which of the five figures shown in Pb 13 could represent a contour plot of velocity potential
and the corresponding quiver plot of the velocity field?
a.
b.
c.
d.
e. yes
15) The velocity potential of a uniform flow in the y direction with speed 2 and a source of strength
0.1π located at x=y=0 is:
a. 2 x + .05 ln(r)
b. 2 y + .05 ln(r)
c. 2 x + .05 θ
d. 2 y - .05 θ
e. 2 y - .05 ln(r)
(where r and θ are polar coordinates centered at x=y=0)
16) Water flows through a circular tube with a radius of 2cm. A constriction is placed in the tube
with a minimum radius of 1 cm. Upstream from the constriction the flow speed is 100 cm/s and
the gage pressure is 0. At the minimum area, the flow speed and gage pressure are:
a. 200 cm/s and -15Pa
b. 400 cm/s and -15Pa
c. 400 cm/s and -75Pa
d. 25 cm/s and -75Pa
e. 50 cm/s and 37.5Pa
(Note: this problem had a typo… the pressures are 100 times too small.. 15Pa should have been
1500 Pa. I messed up the makeup exams too by changing 100cm/s to 10cm/s but forgetting to
change the velocity answers down by a factor of 10 too. )
I will decide what to do about these mistakes when I see how people answered.