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MAE420 Applied Fluid Mechanics
Homework #2 (6 problems)
Due: 10:00pm on April 6, 2015.
-----------------------------------------------------------------------------------------------1. Find stream function ψ and velocity potential ϕ of the following axisymmetric flows. X-axis
is the axis of symmetry.
a) Uniform stream U∞ in the x-direction
b) Point source or sink at the origin
2. A 1-m-diameter sphere is being towed at speed V in fresh water at 20°C. Assuming inviscid
theory with an undistorted free surface, estimate the speed V in m/s at which cavitation will
first appear on the sphere surface. Cavitation occurs when the pressure is below 2337 Pa. Where
will cavitation appear? For this condition, what will be the pressure at point A on the sphere,
which is 45o up from the direction of travel? (Don’t neglect hydrostatic pressure term, ρgz in
the Bernoulli equation because of high density of water. You can neglect the effect of the free
surface to obtain the velocity field around the sphere. Use a reference frame fixed in the sphere.)
3. (a) Given the flow velocity distribution around a moving sphere (moving velocity U) in static
U cos  a 3
U sin  a 3
,



), find the fluid kinetic energy of the whole flow field.
fluid ( r  

r3
2r 3
A 22-cm-diameter solid aluminum sphere (specific gravity SG = 2.9) is accelerating at 15 m/s2
in water at 20°C. (b) According to potential theory, what is the hydrodynamic mass of the
sphere? (c) Estimate the force being applied to the sphere at this instant.
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MAE420 Applied Fluid Mechanics
Homework #2 (6 problems)
Due: 10:00pm on April 6, 2015.
-----------------------------------------------------------------------------------------------4. The ultralight plane Gossamer Condor in 1977 was the first to complete the Kremer Prize
figure-eight course under human power. Its wingspan was 29 m, with average chord 2.3 m and
a total mass of 95 kg. The drag coefficient was approximately 0.05. The pilot was able to deliver
power of 186 W to propel the plane. Assuming two-dimensional flow at sea level, estimate (a)
the cruise speed attained, (b) the lift coefficient, and (c) the power required to achieve a speed
of 7.72m/s.
5. A freshwater boat of mass 400 kg is supported by a rectangular hydrofoil of aspect ratio 8, 2
percent camber, and 12 percent thickness. If the boat travels at 7 m/s and  =2.5o, estimate (a)
the chord length, (b) the power required if the drag coefficient of the 2D hydrofoil CD is
0.01.
(Use C L  2 sin(   ) and assume the coefficient of the induced drag CDi 
rectangular hydrofoil. The total drag coefficient C D is equal to CD  CDi . )
CL2
for the
 AR
6. The simplest representation of a three-dimensional aircraft wing in flight is the rectangular
horseshoe vortex.
a) Calculate the induced downwash at the center of the wing.
b) Assuming the result of part a) applies along the entire wingspan, estimate CDi , the liftinduced coefficient of drag, in terms of the wing’s aspect ratio: AR = s2/A, and the wing’s
coefficient of lift CL  L /(1/ 2)U 2 A , where A is the planform area of the wing.
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