# GATE 2007 AEROSPACE ENGINEERING (Q 41-50)

1. A turbulent boundary layer remais attached over a longer distance on the upper surface of an airfoil than does a laminar boundary layer, because
1. the turbulent boundary layer is more enegetic and hence can overcome the adverse pressure gradient better
2. the laminar boundary layer developes more skin friction and hence slow down more rapidly
3. turbulence causes the effective coefficient of viscosity to reduce, resulting in less loss of momentum in the boundary layer
4. the turbulent boundary layer is thicker, hence the velocity fradient in it are smaller, therefore viscous losses are less

Answer:- the turbulent boundary layer is more enegetic and hence can overcome the adverse pressure gradient better

2. The laminar boundary layer over a large flat plate held parellel to the freestream is 5 mm thick at a point 0.2 m downstream of the leading edge. The thickness of the boundary layer at a point 0.8 m downstream of the leading edge will be
1. 20 mm
2. 10 mm
3. 5 mm
4. 2.5 mm

For laminar boundary layer, δ ∝ x0.5
⇒δ21 = (x2/x1)0.5
⇒δ2 = δ1 (x2/x1)0.5 = 10 mm

3. If horizontal tail area is increased while elevator to horizontal tail area ratio is kept same, then
1. both longitudinal static stability and elevator control power will increase
2. only longitudinal static stability will increase
3. only elevator control power will increase
4. neither stabilty nor control power changes

4. A circular shaft is made-up of two materials A and B. The inner core is made-up of material A with diameter dA, torsion constant JA and shear modulus GA. The outer sleeve is made-up of material B with diameter dB, torsion constant JB and shear modulus GB. The composite shaft is of length L and is subjected to pure tension moment T. The torsional stiffness, T/φ where φ is the angle of twist, of this composite shaft is then

5. Air enters through the eye of a centrifugal compressor with a stagnation temperature 300 K and exits the compressor with a stagnation temperature 424 K. If the isentropic efficiency of the compressor is 0.81 and the ratio of specific heats of he flowing gas (assumed as constant) is 1.4, then the pressure ratio across the compressor is
1. 2.75
2. 5.60
3. 65.00
4. 228.00

ηi = ΔTi / ΔTa
⇒ΔTi = ηiΔTa = 0.81*(424-300) = 100.44 K
⇒T2i = 400.44 K
(p2 / p1) = (T2 / T1)(γ/(γ−1))
⇒(p2 / p1) = (400.44/300)3.5 = 2.748 = 2.75

6. The boundary conditions for an Euler-Bernoulli column are given in column X and the critical buckling loads are given in column Y. Match the boundary condition of the column to its corresponding buckling load. Pcr is the critical buckling load, E is the Young’s modulus of the column material, I its sectional moment of area, and Lis the length of the column.
X. Boundary Condition Y. Critical Buckling Load
X1. Pinned-pinned column Y1. Pcr =
X2. Fixed-free (cantilevered) column Y2. Pcr =
X3. Fixed-fixed column Y3. Pcr =
X4. Fixed-pinned column Y4. Pcr =
1. X1-Y4, X2-Y3, X3-Y1, X4-Y2
2. X1-Y4, X2-Y2, X3-Y3, X4-Y1
3. X1-Y4, X2-Y1, X3-Y2, X4-Y3
4. X1-Y4, X2-Y3, X3-Y2, X4-Y1

7. For an impulse turbine with identical stages, the hot gas exits from the stator blades at the mean blade height at an absolute angle of 70 degrees with the axis of the turbine. If the absolute inlet blade angle with the axis of the turbine at the mean blade height for the rotor blades is 37 degrees, then the absolute exit blade angle with the axis of the turbine at the mean blade height of the rotor blades is
1. 33 degrees
2. 37 degrees
3. 53 degrees
4. 53.5 degrees

8. Which one of the following materials should be selected to design an axial flow turbine operating at high temperatures?
1. Steel alloy
2. Titanium alloy
3. Nickel alloy
4. Aluminum alloy

9. Which one of the following statements is true?
1. The isentropic efficiency of a compressor is constant throughout the compressor.
2. Flow separation problems are more critical for the axial compressor than for the centrifugal compressors.
3. The pressure ratio of the centrifugal compressor approaches zero as the compressor mass flow rate approaches zero.
4. Centrifugal compressors are always designed with multiple stages.

Answer:- The isentropic efficiency of a compressor is constant throughout the compressor.

10. An athlete starts running with a speed V0. Subsequently, his speed decreases by an amount that is proportional to the distance that he has already covered. The distance covered will be
1. Linear in time