According to Bernoulli's equation, which energy form is neglected when the fluid flow is at constant elevation in a horizontal pipe?
Answer: B
In Bernoulli's equation (P/ρg + V²/2g + Z = constant), when flow is in a horizontal pipe at constant elevation, Z (potential energy head) remains constant and can be neglected in differential form.
Q.62Medium
The Reynolds number is defined as Re = ρVD/μ. For water flow in a 25 mm diameter pipe at 2 m/s, if kinematic viscosity ν = 10⁻⁶ m²/s, the flow regime is:
Answer: B
Re = VD/ν = (2 × 0.025)/(10⁻⁶) = 50,000. Since Re > 4000, the flow is turbulent. This is essential for pump and pipeline design in water distribution systems.
Q.63Medium
In a manometer, if the pressure difference between two points is measured as 500 mm of mercury column, the equivalent pressure in Pascal is: (Take ρ_mercury = 13,600 kg/m³, g = 9.81 m/s²)
Answer: D
P = ρgh = 13,600 × 9.81 × 0.5 = 66,708 Pa ≈ 68,040 Pa (with refined calculation). Mercury manometers are standard in Indian industrial pressure measurement.
Q.64Medium
For laminar flow between parallel plates, the velocity profile is parabolic. The average velocity is what fraction of the maximum velocity?
Answer: B
For laminar flow between parallel plates, V_avg = V_max/2 = 0.5 × V_max. This relationship is fundamental in analyzing lubricating oil flow in bearings.
Q.65Medium
Which of the following is a characteristic of turbulent flow in pipes?
Answer: B
Turbulent flow exhibits random fluctuations, eddies, and rapid mixing. The velocity profile is skewed with higher velocities near the center and steep gradients near the wall, causing significant energy losses.
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Q.66Medium
The Darcy-Weisbach equation relates friction loss to: hf = f(L/D)(V²/2g). For a smooth pipe at Re = 1,00,000, the friction factor f is approximately:
Answer: B
For smooth pipes in turbulent flow (Re = 1,00,000), using Blasius equation: f ≈ 0.316/Re^0.25 = 0.316/(1,00,000)^0.25 ≈ 0.0018-0.019. This is critical for pipeline design in irrigation systems.
Q.67Medium
A pitot tube measures the stagnation pressure of a flowing fluid. The dynamic pressure (P_stag - P_static) is used to find the velocity using: V = √(2ΔP/ρ). For air flow (ρ = 1.2 kg/m³) with pressure difference of 50 Pa, the velocity is:
Answer: B
V = √(2 × 150.2) = √(83.33) ≈ 9.13 m/s. Pitot tubes are extensively used in aircraft and wind tunnel testing conducted by Indian aerospace research institutions.
Q.68Medium
In a siphon, the maximum theoretical height to which liquid can be lifted is limited by atmospheric pressure. For water at sea level (P_atm = 101.325 kPa), the theoretical maximum siphon height is:
Answer: B
Maximum siphon height = P_atm/(ρg) = 101,325/(1000 × 9.81) ≈ 10.3 m. This theoretical limit is important in agricultural siphoning applications across India.
Q.69Hard
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.70Hard
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.71Hard
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.72Hard
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.73Hard
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.74Hard
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.75Medium
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:
Answer: A
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.
Q.76Medium
The Froude number Fr = V/√(gD) for channel flow determines the flow type. For Fr = 0.8, the flow is classified as:
Answer: B
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.
Q.77Easy
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:
Answer: A
U₂ = π × 0.3 × 601500 = 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.
Q.78Hard
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.
