NCEES Fluid Mechanics 5 — Questions and Answers
Question 1: A submerged gate 1 m wide and 2 m tall has its top edge at 3 m depth. What is the total hydrostatic force on the gate? (ρ = 1000 kg/m³)
- 58,860 N
- 78,480 N (Correct answer)
- 39,240 N
- 117,720 N
Correct answer: 78,480 N
F = ρg·ȳ·A where ȳ = 3 + 1 = 4 m (centroid depth); F = 1000×9.81×4×(1×2) = 78,480 N.
Question 2: What does the water hammer phenomenon refer to in pipe systems?
- Vibration caused by pump cavitation
- Pressure surge caused by rapid valve closure (Correct answer)
- Noise from pipe expansion due to temperature change
- Turbulent eddies striking pipe walls
Correct answer: Pressure surge caused by rapid valve closure
Water hammer is a pressure surge or wave caused when a fluid in motion is forced to stop or change direction suddenly, typically by rapid valve closure.
Question 3: For a Venturi meter, which principle is used to determine flow rate?
- Momentum equation
- Continuity and Bernoulli equations combined (Correct answer)
- Energy equation with losses only
- Darcy-Weisbach equation
Correct answer: Continuity and Bernoulli equations combined
A Venturi meter uses the continuity equation (A₁V₁ = A₂V₂) combined with Bernoulli's equation to relate pressure difference to flow velocity.
Question 4: The net positive suction head (NPSH) is important in pump design primarily to avoid:
- Pipe corrosion
- Cavitation (Correct answer)
- Water hammer
- Pump overheating
Correct answer: Cavitation
If the available NPSH falls below the required NPSH, the local pressure drops below vapor pressure and cavitation occurs, damaging the pump.
Question 5: For laminar flow in a circular pipe (Hagen-Poiseuille flow), the velocity profile is:
- Uniform (plug flow)
- Parabolic (Correct answer)
- Logarithmic
- Linear
Correct answer: Parabolic
Hagen-Poiseuille flow produces a parabolic velocity profile: u(r) = (ΔP/4μL)(R² - r²), with maximum velocity at the centerline.
Question 6: Which of the following best describes the concept of 'specific energy' in open channel flow?
- Total energy per unit weight relative to the channel bottom (Correct answer)
- Kinetic energy per unit volume
- Potential energy per unit mass
- Total head relative to a fixed datum
Correct answer: Total energy per unit weight relative to the channel bottom
Specific energy E = y + V²/2g, representing total energy per unit weight measured above the channel bed (not a fixed datum).
Question 7: In Stokes' law for a small sphere settling in a viscous fluid, the drag force is proportional to:
- The square of the sphere's velocity
- The sphere's velocity (linear) (Correct answer)
- The cube of the sphere's diameter
- The Reynolds number squared
Correct answer: The sphere's velocity (linear)
Stokes' drag law: F = 3πμDV, showing drag is linearly proportional to velocity for Re < 1 (creeping flow).
NCEES Fluid Mechanics 5
A submerged gate 1 m wide and 2 m tall has its top edge at 3 m depth.
What is the total hydrostatic force on the gate? (ρ = 1000 kg/m³)