The Institution of Engineers,India 2011 M.E Product Design and Development Amie pg - Question Paper
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3. (a) Write short notes on any two of the following : 5 + 5
through the nozzle, () exit pressure, (iii) exit temperature, (iv) exit Mach number and (v) exit velocity for the following two conditions, i.e., sonic velocity at thethroat with divergent section acting as a nozzle and sonic velocity at the throat with divergent section acting as a diffuser.
2.J (a) A normal shock wave occurs in air flowing at a Mach number of 15. The static pressure and temperature of the air upstream of a shock wave are 1 bar and 300 K. Determine Mach number, pressure and temperature downstream of the shock wave. Also, estimate the shock strength.
(b) Derive the Rankine-Hugoniot relations for the plane stationary normal shocks.
(0 Moving shock waves (//) Rayleigh line (Hi) Prandtl-Glauert rule (/v) Tangent gas approximation.
(b) What is meant by a doublet ? Show that the combination of a doublet, with uniform stream, gives the potential flow around a circular cylinder corresponding to the stream line i|/ = 0. 10
4. (a) State and explain the Croccos theorem for
two-dimensional flows. Furnish a proof of the theorem. What are the two conditions necessary for a flow to be isentropic ? 10
(b) A horizontal pipe conveys a gas at a temperature of 5C. At a section 1-1 of the pipe, the diameter is 6 cm and the gas pressure is 2-75 kg-/cm2 (gauge). At a
SI1:2FN: 5302/5314(68) ( 2 )
(Continued)
section 2-2 of the pipe, the diameter is 3 cm and the gas pressure is 1-60 kg/cm2 (gauge). Assuming an isothermal change, find the velocity of the gas at these sections. Take R = 20-27 m/K. 10
5. (a) Discuss the Busemann and pressure-turning angle
shock polar diagram and its significance. 10
(b) Explain Karman-Tsien pressure correction formula for two-dimensional subsonic flows. 10
(a) Define diffuser efficiency with normal shock and derive the expression for the same. 10
(b) Derive the partial differential equation of velocity potential function for two-dimensional steady irrotational isentropic motion with V and 0 as independent variable and velocity potential function
as dependent variable. 10
7. (a) Discuss the mass flow rate through a convergent
nozzle with respect to critical pressure ratio and maximum mass flow. 10
(b) Explain the effectiveness and simplicity of the shock polar in the interpretation and solution of the characteristics of flow behind the shock wave. 10
8. (a) Discuss the performance characteristics of supersonic
profile. 10
(b) What is an oblique shock ? Give practical examples where such shocks occur. Make a theoretical analysis of such a shock. 10
( Turn Over)
S11:2FN: 5302/5314(68) ( 3 )
Group C
Write short notes on the following :
(/) Strength of shock waves
(ii) Reflection of oblique shock
(iii) Supersonic aerofoils
(iv) Hodograph method for two-dimensional subsonic flow.
ADVANCED FLUID MECHANICS
PG
Time : Three hours
Maximum Marks : 100
Answer FIVE questions, taking ANY TWO from Group A, ANY TWO from Group B and ALL from Group C.
All parts of a question ( a, b, etc.) should be answered at one place.
Answer should be brief and to-the-point and be supplemented with neat sketches. Unnecessary long answers may result in loss of marks.
Any missing or wrong data may be assumed suitably giving
proper justification.
Figures on the right-hand side margin indicate full marks.
Group A
(a) Define compressibility correction factor to be used
with pitot-static tube with a neat sketch. Derive the expression for compressibility correction factor. 8
(b) The exit area to threat area ratio for a convergent divergent nozzle is 2-5, the throat being 12-5x 10'4 m2.
Air enters this nozzle from a reservoir where the absolute pressure is 680 kN/m2 and temperature is 24C. Air discharge from the exit area into atmosphere where the local barometric pressure is 101 kN/m2. Assume the flow to be isentropic with R = 287J/kg.K and K - 14. Calculate the (/) mass rate of air flow
( Turn Over)
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| Earning: Approval pending. |
