1
(a) Derive Archimedes principle using a body of general shape. (4 Marks)

(b)
Prove that in a velocity field, the curl of the velocity is equal to the
vorticity. (8 Marks)

(c)
Write the continuity equation in terms of substantial derivative. ( 4 Marks)

(d)
The velocity field is given by u = y/(x

^{2}+y^{2}) and v = -x/(x^{2}+y^{2}) . Calculate the equation of the streamline passing through the point (0, 5). (4 Marks)
2
(a) Explain how Pitot tubes are used for the measurement of airspeed. (6 Marks)

(b)
Write a note on Kutta-Joukowski theorem. (6 Marks)

(c)
Explain double-surface airfoil. (4 marks)

(d)
Consider an airfoil in a flow at standard sea level conditions with a
freestream velocity of 50 m/s. At a given point on the airfoil, the pressure is
0.9×10

^{5}N/m^{2}. Determine the velocity at this point. (4 Marks)
3
(a) What is elliptical lift distribution? (4 marks)

(b)
A vortex filament of strength S assumes shape of closed circular loop of radius
R. Obtain an expression for the velocity induced at the centre of the loop in
terms of S and R. (6 Marks)

(c)
Explain the variation of drag coefficient with Reynolds number for a sphere
with the help of a graph. (6 Marks)

(d)
Prove that three-dimensional source flow is irrotational. (4 Marks)

4
(a) Write a note on isentropic relations. (4 Marks)

(b)
Show that total temperature is constant across a stationary normal shock wave.
(6 Marks)

(c)
Write and explain Rayleigh Pitot tube formula. (4 Marks)

(d)
Consider a room with rectangular floor that is 5m by 7m and a 3.3 m high
ceiling. The air pressure and temperature in the room are 1 atm and 25

^{0}C respectively. Calculate the internal energy and enthalpy of the air in the room temp. (6 Marks)
5
(a) Write a note on supersonic nozzle flow with a normal shock inside the
nozzle. (6 Marks)

(b)
What are Prandtl-Meyer expansion waves? (4 Marks)

(c)
Write a note on SCRAMjet engines. (4 Marks)

(d)
An oblique shock wave has wave angle 30

^{0}. The upstream flow Mach number is 2.4. Calculate the deflection angle of the flow, the pressure and temperature ratios across the shock wave and the Mach number behind the wave. (6 Marks)
6
(a) Define critical Mach number. How will you estimate critical Mach number? (6
Marks)

(b)
Write a note on linearized supersonic flow. (6 Marks)

(c)
Explain predictor-corrector process. (4 Marks)

(d)
A flat plate at α = 20

^{0}is in a Mach 20 freestream. Calculate the lift and wave drag coefficients using Newtonian theory. (4 Marks)
7
(a) Deduce Naiver-Stokes equations for an unsteady, compressible, three
dimensional viscous flow. (8 Marks)

(b)
What is Couette flow? Explain. (4 Marks)

(c)
What is Poiseuille flow? Explain. (4 Marks)

(d)
Explain the terms adiabatic wall temperature and Reynolds analogy. (4 Marks)

8
(a) What are boundary layer equations? Explain the method of solving boundary
layer equations. (8 Marks)

(b)
What is stagnation region? Explain. (4 Marks)

(c)
Write a note on Baldwin-Lomax turbulence model. (4 Marks)

(d)
What is skin friction drag? Explain. (4 Marks)

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