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TEST – I

(AFC, Basic elasticity, Differential calculus and GA-Percentage)

Q1. An axial flow compressor has an overall pressure ratio of 4·0 and mass flow of 3 kg/ s. If the Polytrophic efficiency is 88 per cent. Air is entering with an inlet temperature of 288K. Compute the isentropic efficiency of the compressor. (Take ϒ = 1.4) Q2. The first stage of an axial compressor is designed with no inlet guide vanes. The work done factor is 0·93 and the isentropic efficiency of the stage is 0·89. Stage stagnation temperature rise being 25 K. Assuming an inlet velocity of 140 m/s and ambient conditions of 1.01 bar and 288 K. The stage stagnation pressure ratio is _______? (Common data question) 3 and 4 An AFC is designed on free vortex principles, with no inlet guide vanes. The rotational speed is 6000 rev /min. The Mach number relative to the tip is limited to 0-95. The hub-tip ratio is 0.60. Assuming an inlet velocity of 140 m/s and ambient conditions of 1·01 bar and 288 K, calculate; Q3. What is the corresponding Blade angle at the entry at tip? Q4. The height of the blade is? Q5. Absolute velocity across stator in axial flow compressor?

(a) Increase (b) decreases (c) remains constant (d) First increases and then decreases (Common data question) 6 and 7 A compressor of turbojet engine operates in standard sea level air with a pressure ratio of 5.0 and an air consumption of 35kg/s, at an isentropic efficiency of 80%. Take T01 = 16 deg C Q6. Calculate the work per kg of air. Q7. Calculate the total temperature at the compressor discharge. Q8. For an AFC, the condition for low reaction stage (R<1/2) is -

(a) Ct1< Wt2 (b) Ct1 = Wt2 (c) Ct1> Wt2 (d) Ct1 = Ct2 Q9. Total number of independent variables in the linear stress-strain relationship of an isotropic material is-

(a) 1 (b) 2 (c) 3 (d) 4 Q10. As x is increased from -Infinity to + Infinity, the function

f(x) = ex/(1 + ex) (a) Monotonically increases (b) monotonically decreases (c) increases to a max. value and then Decreases (d) decreases to a minimum value then increases



Q11. The state of plane stress in a plate 100mm thickness is given as normal stress in x-direction is 100 N/mm2, Normal Stress in y-direction 200 N/mm2, E = 300 N/mm2, Poisson’s ratio = 0.3, the stress(N/mm2) developed in the direction of thickness is

(a) 0 (b) 90 (c) 100 (d) 200 Q12. The Mach No. at the inlet of a nozzle is 1.1, the shape of nozzle should be

(a) Converging (b) Diverging (c) Converging-Diverging (d) Diverging-Converging Q13. A thin cylinder contained fluid at a pressure of 500 N/m2, the internal diameter of the shell is 0.6m and the tensile stress in the material is to be limited to 9000 N/m2. The shell must have the minimum wall thickness (mm) of

(a) 9 (b) 11 (c) 17 (d) 21 Q14. Consider f(x) = x3 - 3x2 - 45x + 24, the above function (a) is maximum at x = 5 (b) is increasing in the interval (-3,0) (c) is minimum at x = -3 (d) is decreasing in the interval (1,2) Q15. The state of plane stress of point in an isotropic material is given by Normal stress in x -direction = 16 MPa, Normal stress in y -direction = -4 MPa, shear stress = 5 MPa. The inclination of plane of zero shear stress w.r.t. specified plane is (degrees) (a) 31.7 (b) 26.6 (c) 13.3 (d) 63.4 Q16. Evaluate

Lim x π/2

Q17. The length of a longest interval in which the function 3sinx – 4 sin3x is increasing is

(a)

(b)

(c)

(d) π

Q18. If y = a logx + bx2 + x has its extremum values at x = -1 and x = 2, then a and b equals ________ (Common data question) 19 and 20 At a point in a structural member, a 2D stress system exists where Normal stress in x direction is 60 N/mm2, Normal stress in y direction is -40 N/mm2 and shear stress is 50 N/mm2, E =200000 N/mm2 and ν = 0.3

Q19. The principal strains (εI and εII ) at that point are ________

Q20. The inclination of the principal strains to the plane on which σx acts is________ Q21. In the context of flow compressor, choose the correct statement,

(a) For rotor, rothalpy is constant and for stator, stagnation enthalpy is constant.



(b) For rotor, rothalpy is constant and for stator, enthalpy is constant. (c) For rotor, enthalpy is constant and for stator, stagnation enthalpy is constant. (d) All of the above are correct

Q22. Across a normal shock

(a) Velocity decreases, total pressure decreases, static pressure increases (b) Velocity increases, total pressure decreases, static pressure increases (c) Velocity decreases, total pressure decreases, static pressure decreases (d) Anything can happen

Q23. Non-zero stress components in a plane strain problem are _______________ Q24. The number of compatibility conditions for a plane stress problem is _________ Q25. A long thin walled cylindrical shell closed at both ends is subjected to an internal pressure. Ratio of hoop stress to longitudinal stress in the shell is

(a) 1 (b ) 2 (c) 1.5 (d) 4 Q26. For a rectangular section with b = 2 cm and d = 6cm, the MOI perpendicular to the plane of cross section in cm4 is __________________ Q27. The state of 2D-stress at a point is given by the following matrix of stresses:

=

MPa

What is the magnitude of maximum shear stress in MPa? (A) 50 (B) 75 (C) 100 (D) 110 Q28. A thin cylinder of inner radius 500mm and thickness 10mm is subjected to an internal pressure of 5MPa. The average circumferential (hoop) stress in MPa is

(A) 100 (B) 250 (C) 500 (D) 1000 Q29. An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300K and 1500K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures in Kelvin at the end of the compression and expansion processes are respectively

(A) 500 and 900 (B) 900 and 500 (C) 500 and 500 (D) 900 and 900 Q30. The velocity triangles at the inlet and exit of the rotor of a turbo machine are shown. V is the absolute velocity of the fluid, W denotes the relative velocity of the fluid and U denotes the blade velocity. Subscript 1 and 2 denotes the inlet and outlet respectively. If V2 = W1 and V1 = W2 Then the degree of reaction is



. (a) 0 (b) 1 (c) 0.5 (d) 0.25

Q31. At x =0, the function f(x) = x3 + 1 has

(a) A maximum value (b) A minimum value (c) A singularity (d) A point of inflexion Q32. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1% with the internal pressure remaining the same, the % change in the circumferential (hoop) stress is

(a) 0 (b) 1 (c) 1.08 (d) 2.02 Q33. There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters? Q34. In Mathematics examination, a student scored 30% in the first paper of 180 marks. How much

% marks should he score in the second paper of 150 marks if he is to get an overall percentage of at

least 50%

Q35. On account of a hike in the prices of onions by 20%, a housewife decides to reduce her consumption of onions to save her from tears. By what percent should she reduce her consumption so that the expenditure remains unchanged?

Q36. The difference between interest on Rs. 5000 at the rate 5% p.a. for 6 months and on Rs. 3000

at the rate 3% p.a. for 4 months is ___________.

Q37. The population of a town increases by 5% annually. If it is 15435 now, its population 2 years

ago was _____________.

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