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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.4
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 significance of curl of the velocity field and Divergence of the
velocity field. Express these in Cartesian and cylindrical co-ordinates [8]
(b) A velocity field is given by u = y
x2+y2 , = -x
x2+y2
Calculate the circulation around a circular path of radius 5m. u and v are
given in the units of m/sec. [8]
2. (a) A flat plate is kept in a viscous fluid flow. Depict the Velocity Boundary
Layer and Thermal Boundary Layer over this flat plate in one plot. Explain
the physics of the flow field. [8]
(b) A velocity field is given by
-!
V = axˆi - ayˆi; x and y are in meters, a =
0.1/sec. At (2,8,0) evaluate the equation of stream line, equation of pathline
and velocity. What would be the position of the particle at (2,8,0) at t=20.
[8]
3. (a) Show that the following velocity components represent a rigid body rotation.
u = a + by - cz; v = d - bx + ez; w = f + cx-ey
(b) Write Navier-Stokes equations for visions, incompressible fluid flow in carte-
sian co-ordinates and vector form. How does the Euler equation differ from
this. [8]
4. Consider flow near a flat plate suddenly accelerated from rest, moving in its own
plane with constant velocity Vo. Work out and plot the velocity distribution above
this suddenly acceleerated plane wall. [16]
5. Starting from Navier-stokes equation, verify for plane Poiscnille flow that the shear-
ing stress becomes zero at the middle plane and that @Tyx
@y = dp
dx [16]
6. Prove that karman’s momentum Integral relation for flat plate Boundary layer flow
is given by w = U2 ddx
If u (x, y) =, U 2y - y2
2 , 0 y (x)
then show that the shear stress estimate along the plate is given by
Cf = 2 wU2 0.73Re
1/2x[16]
7. Consider viscous flow past a circular cylinder shown in figure 4.
Sketch and explain the velocity profiles at = 0o, 30o, 60o, 90o, 1200 and 150o.
Hence explain the phenomenon of separation.
8. Consider turbulent flow past a plane wall. Describe various regimes of flow, (due
to the velocity profile) in this flow field. Hence show that the universal flow profile
is given by¯uu= 5.5 + 5.75 log10uy and explain it with a plot.
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