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Posted By: ram Member Level: Diamond Posted Date: 03 Sep 2008
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2007 Jawaharlal Nehru Technological University Aeronautical IV B.Tech. II Semester Regular Examinations, April/May -2006 VISCOUS FLOW THEORY Question paper
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Code No: RR422104 Set No.1
IV B.Tech. II Semester Regular Examinations, April/May -2006
VISCOUS FLOW THEORY
(Aeronautical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
? ? ? ? ?
1. (a) Explain the shearing action of a viscous fluid flow over a surface. What hap-
pens in case of a perfect fluid? Elaborate with sketches/ plots. [8]
(b) Explain the significance of curl of the velocity field and Divergence of the
velocity field. Express these in cartesian and cylindrical co-ordinates. [8]
2. (a) Given the velocity field
-!
V = (6 + 2xy + t2)ˆi - (xy2 + 10t)ˆj + 25ˆk.
What is the acceleration of a particle at (3,0,2) at time t=1? [8]
(b) Sketch velocity profiles of boundary layer flows under following conditions.
i. Favourable pressure gradient
ii. Zero pressure gradient
iii. Weak adverse pressure gradient
iv. Critical adverse pressure gradient
v. Strong adverse pressure gradient.
Explain the phenomenon in each plot. [8]
3. Given a velocity field with components at P(x,y,z)
u(x,y,z) = cx + 2woy + uo
v(x,y,z) = cy + uo
w(x,y,z) = -2cz + wo
Where c, wo, uo, vo and !o are constants.
Determine
(a) Translational velocity
(b) Rotational velocity
(c) Rate of strain. [16]
4. (a) Write Navier-Stokes equations for viscous, incompressible fluid flow in Carte-
sion and vector form. Explain the terms on LHS and RHS. [8]
(b) Show that parallel flow through a straight channel of width ‘2b’ is given by
µ = - 12µdp
dx (b2 - y2). [8]
5. A flat plate is suddenly moved to a velocity U1 in oil with = 920 kg/m3 and
µ = 0.07 kg/ms. Plot the velocity ratio u
U1
as a function of distance form the plate
for t=0.01s, 0.05s, and 0.1s. If U1 = 3m/sec., calculate the shearing stress at the
plate.
6. Consider viscous flow part a wedge of included angle . Shown in figure 1.
Show that the velocity distribution in the laminar boundary layer over the wedge
surface is given by Falkner Scan equation. f000 + f f00 + 1 - f0
2 = 0 [16]
7. (a) Consider viscous flow past a flat plate at zero angle of attack. The temperature
at the plate is maintained constant. Describe the thermal boundary layer in
a laminar flow, if V1 is the free stream velocity and T1 is the free stream
temperature.
[8]
(b) The given velocity profile in laminar boundary layer
U
U1
= 62 - 83 + 34. where = y
Obtain the shape parameter H.
What is the significance of this value of H? [8]
8. (a) Describe the Law of the wall for a turbulent flow along a wall with illustrations.
[8]
(b) Prandtl’s mixing length theory appears better than the ‘apparent kinematic
viscosity "’ concept. Elaborate the statement in regard to the semi-empirical
theories of turbulence.
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