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.
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:
A8.2 m
B10.3 m
C12.5 m
D14.8 m
Correct Answer:
B. 10.3 m
EXPLANATION
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.
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:
A7.45 m/s
B9.13 m/s
C10.2 m/s
D12.5 m/s
Correct Answer:
B. 9.13 m/s
EXPLANATION
V = √(2 × 50/1.2) = √(83.33) ≈ 9.13 m/s. Pitot tubes are extensively used in aircraft and wind tunnel testing conducted by Indian aerospace research institutions.
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:
A0.032
B0.018
C0.008
D0.004
Correct Answer:
B. 0.018
EXPLANATION
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.
Which of the following is a characteristic of turbulent flow in pipes?
AFluid particles move in straight parallel lines with no mixing
BVelocity profile is highly skewed near the wall with rapid mixing
CShear stress is independent of velocity gradient
DEnergy loss is proportional to velocity
Correct Answer:
B. Velocity profile is highly skewed near the wall with rapid mixing
EXPLANATION
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.
For laminar flow between parallel plates, the velocity profile is parabolic. The average velocity is what fraction of the maximum velocity?
A0.25 times
B0.50 times
C0.75 times
D0.90 times
Correct Answer:
B. 0.50 times
EXPLANATION
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.
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)
A65,340 Pa
B66,666 Pa
C67,500 Pa
D68,040 Pa
Correct Answer:
D. 68,040 Pa
EXPLANATION
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.
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:
ALaminar (Re < 2300)
BTurbulent (Re > 4000)
CTransitional (2300 < Re < 4000)
DCreeping flow (Re < 1)
Correct Answer:
B. Turbulent (Re > 4000)
EXPLANATION
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.
