For compressible flow through a convergent nozzle, chocking occurs when:
Answer: B
Chocking in a convergent nozzle occurs when the Mach number reaches unity (sonic condition) at the throat. Beyond this, exit velocity cannot increase further regardless of downstream pressure decrease.
Q.22Hard
In open channel flow, the critical depth occurs when:
Answer: B
Critical depth in open channel flow corresponds to Fr = 1, minimum specific energy condition.
Q.23Hard
For a submerged curved vane deflecting a jet, the component of force in the direction of jet is:
Answer: B
Force component = ρQv(1 - cos θ) where θ is deflection angle from momentum equation.
Q.24Hard
The equivalent length method for minor losses in pipes replaces a fitting with an equivalent length of pipe. For a 90° elbow with diameter 50 mm, typical equivalent length is:
Answer: C
Equivalent length L_e = K × (d/f) ≈ 0.9 × (0.005.02) ≈ 2.25 m for typical elbow
Q.25Hard
In a centrifugal pump, the impeller diameter is doubled while keeping speed constant. The head capacity changes by factor of:
Answer: B
Head H ∝ D²N² at constant N, so head increases by 2² = 4 times
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Q.26Hard
For a weir with discharge Q = C_w × L × H^(23), if the length is doubled and head is halved, the new discharge becomes:
A vertical pipe of diameter 40 mm has water flowing upward at 2.5 m/s. If the friction factor is 0.035 and pipe length is 50 m, what is the total head loss (friction + elevation)?
Answer: C
h_f = 0.035 × (050.04) × (6.1925.62) = 1.12 m; total = 1.12 + 50 = 51.12 m
Q.28Hard
A circular jet impinges on a 45° inclined flat plate and splits equally. If jet velocity is 15 m/s and diameter is 30 mm, what is the magnitude of the resultant force?
Answer: C
Using momentum equation with 45° deflection, the resultant force = ρAV² × √2 = 1000 × 0.000707 × 225 × 1.414 = 2648 N
Q.29Hard
In a venturi meter, if the area ratio is 4:1 and the pressure difference is 8 kPa, what is the velocity in the throat? (ρ_water = 1000 kg/m³)
Answer: B
From Bernoulli and continuity: V₂ = √(2ΔP/(ρ(A₁²/A₂² - 1))) = √(16000/(1000 × 15)) = 4.12 m/s
Q.30Hard
A horizontal jet of 0.02 m² cross-section with velocity 8 m/s strikes a curved vane and is deflected 60°. What is the force on the vane in the direction of jet?
Answer: C
Force = ρAV²(1 - cos60°) = 1000 × 0.02 × 64 × 0.5 = 6.4 kN. The deflection angle affects the force component.
Q.31Hard
The momentum equation for a control volume states that ΣF = d(mV)/dt. For a fluid jet deflected by a flat plate at angle θ to the horizontal, the force perpendicular to the original jet direction depends on:
Answer: C
The perpendicular force component = ρQV²sin(θ), where Q is discharge and V is velocity. This principle is used in water turbines and industrial jet applications.
Q.32Hard
For a Venturi tube with throat area ratio A₁/A₂ = 3 and upstream pressure P₁ = 200 kPa, assuming inviscid flow (Bernoulli applicable), if the pressure at throat P₂ drops to 80 kPa, the upstream velocity V₁ is (ρ = 1000 kg/m³):
Answer: C
From Bernoulli: P₁/ρg + V₁²/2g = P₂/ρg + V₂²/2g. Using continuity A₁V₁ = A₂V₂, and solving: V₁ = √(2(P₁-P₂)/(ρ(A₂²/A₁²-1))) ≈ 10.5 m/s. Venturi tubes are standard in flow measurement systems.
Q.33Hard
The Mach number M = V/a represents the ratio of flow velocity to the speed of sound. For subsonic compressible flow in a converging nozzle, what occurs to the Mach number as the flow accelerates?
Answer: C
In a converging nozzle with subsonic inlet flow, velocity increases and Mach number increases as flow approaches throat. This principle is critical in rocket propulsion and aerospace applications in India.
Q.34Hard
For pipe flow, the friction factor f in the Moody diagram depends on both Reynolds number and relative roughness (ε/D). For a rough pipe with high Re, f approaches an asymptotic value independent of Re. This region is called:
Answer: B
At very high Reynolds numbers in rough pipes, friction factor depends only on relative roughness, not Re. This region is called the 'fully turbulent' or 'zone of complete turbulence' region in the Moody diagram.
Q.35Hard
The specific speed of a turbine is Ns = N√Q/H^1.25, where N is speed in rpm, Q is discharge in m³/s, and H is head in meters. A turbine with Ns < 50 is classified as:
Answer: A
Specific speed Ns < 50 indicates Pelton turbines, 50-250 indicates Francis turbines, and >250 indicates Kaplan turbines. This classification is essential in hydroelectric projects across Indian dams.
Q.36Hard
According to the theory of boundary layer flow, the boundary layer thickness δ grows along a flat plate as δ ∝ √(νx/V). This relationship is derived from:
Answer: C
The √x dependence comes from solving the Navier-Stokes equations with boundary layer approximations (Blasius solution). This is fundamental to aerodynamic design in Indian aircraft industries.
Q.37Hard
The cavitation parameter σ = (P - Pv)/(0.5ρV²) indicates the tendency of a flowing fluid to cavitate. Cavitation occurs when σ drops below a critical value σc. For a given pump, lowering the inlet pressure or raising the fluid temperature will:
Answer: B
Lowering inlet pressure decreases (P - Pv), reducing σ. Raising temperature increases Pv, also reducing σ. Both conditions increase cavitation risk in turbomachinery. This is critical in high-speed pump operations.
Q.38Hard
In a riveted joint, if the shear strength of rivet material is 300 MPa and bearing strength is 400 MPa, which failure mode would occur first for a single rivet with 16 mm diameter?
Answer: A
Shear area = π/4 × 16² ≈ 201 mm². Shear failure load = 300 × 201 = 60,300 N. Bearing depends on thickness; shear typically governs for isolated rivet analysis.
Q.39Hard
What is the significance of the 'Hertzian stress' in rolling contact bearings?
Answer: B
Hertzian contact stress is the maximum compressive stress that occurs at the contact surface between rolling elements and raceways, critical for fatigue analysis.
Q.40Hard
A ball bearing with dynamic load rating C = 8000 N is subjected to a radial load of 2000 N. What is the approximate L10 life in millions of revolutions?
Answer: B
Using L10 = (C/P)³, where C = 8000 N and P = 2000 N: L10 = (20008000)³ = 4³ = 64. However, this gives 64 million revolutions. Re-calculating: (20008000)^3 = 64, which represents the life multiplier, resulting in approximately 512 million revolutions for typical bearing calculations.
