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:
AIncrease σ and reduce cavitation risk
BDecrease σ and increase cavitation risk
CKeep σ constant
DIncrease Pv but not affect cavitation
Correct Answer:
B. Decrease σ and increase cavitation risk
EXPLANATION
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.
In centrifugal pump design, the impeller exit diameter D₂ and speed N (rpm) determine the peripheral velocity U₂ = πD₂N/60. For a pump with D₂ = 300 mm running at 1500 rpm, the peripheral velocity is:
A23.56 m/s
B28.45 m/s
C35.62 m/s
D42.78 m/s
Correct Answer:
A. 23.56 m/s
EXPLANATION
U₂ = π × 0.3 × 1500/60 = 23.56 m/s. This velocity is critical in pump design as it affects the Euler's head and pump efficiency in Indian water supply and irrigation projects.
The Froude number Fr = V/√(gD) for channel flow determines the flow type. For Fr = 0.8, the flow is classified as:
ASupercritical
BSubcritical
CCritical
DTransitional
Correct Answer:
B. Subcritical
EXPLANATION
Fr < 1 indicates subcritical (tranquil) flow, Fr = 1 is critical, and Fr > 1 is supercritical (rapid) flow. This classification is essential in open channel hydraulics for dam spillways and canal design.
A submerged gate in a canal discharges water at the bottom. The discharge through the gate is given by Q = Cd × A × √(2g(h₁-h₂)), where Cd is discharge coefficient, A is gate area, and (h₁-h₂) is head difference. Typical value of Cd for a sharp-edged gate is:
A0.55-0.65
B0.75-0.85
C0.95-1.00
D1.05-1.10
Correct Answer:
A. 0.55-0.65
EXPLANATION
For sharp-edged submerged gates, Cd ≈ 0.6. For rounded gates Cd ≈ 0.8. This is crucial in irrigation canal design and water resource management in India.
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:
AEuler's equation
BPrandtl's momentum integral equation
CNavier-Stokes equations with boundary layer approximations
DContinuity equation alone
Correct Answer:
C. Navier-Stokes equations with boundary layer approximations
EXPLANATION
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.
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:
APelton turbine (impulse)
BTurgo turbine
CFrancis turbine (reaction)
DKaplan turbine (axial flow)
Correct Answer:
A. Pelton turbine (impulse)
EXPLANATION
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.
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:
ALaminar region
BFully turbulent region (complete turbulence)
CTransition region
DCreeping flow region
Correct Answer:
B. Fully turbulent region (complete turbulence)
EXPLANATION
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.
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?
AMach number decreases
BMach number remains constant
CMach number increases
DMach number becomes negative
Correct Answer:
C. Mach number increases
EXPLANATION
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.
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):
A6.5 m/s
B8.2 m/s
C10.5 m/s
D12.8 m/s
Correct Answer:
C. 10.5 m/s
EXPLANATION
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.
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:
AOnly the jet velocity
BOnly the deflection angle
CBoth jet velocity and deflection angle (sinθ component)
DThe density of the fluid only
Correct Answer:
C. Both jet velocity and deflection angle (sinθ component)
EXPLANATION
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.
