NCEES Fluid Mechanics 2 — Questions and Answers
Question 1: A pipe suddenly expands from a diameter of 0.1 m to 0.2 m. If the velocity in the smaller pipe is 4 m/s, what is the head loss due to the sudden expansion?
- 0.046 m (Correct answer)
- 0.183 m
- 0.459 m
- 0.092 m
Correct answer: 0.046 m
Using the Borda-Carnot equation: hL = (V1 - V2)²/2g; V2 = 4×(0.1/0.2)² = 1 m/s; hL = (4-1)²/(2×9.81) ≈ 0.459 m.
Question 2: Which dimensionless number represents the ratio of inertial forces to viscous forces in fluid flow?
- Froude number
- Reynolds number (Correct answer)
- Weber number
- Euler number
Correct answer: Reynolds number
The Reynolds number (Re = ρVL/μ) is the ratio of inertial to viscous forces and governs laminar vs. turbulent flow.
Question 3: For a Newtonian fluid, the shear stress is proportional to:
- The velocity gradient squared
- The velocity gradient (Correct answer)
- The pressure gradient
- The fluid density
Correct answer: The velocity gradient
For a Newtonian fluid, τ = μ(du/dy), where shear stress is directly proportional to the velocity gradient.
Question 4: Water flows at 2 m/s through a 0.05 m diameter pipe. What is the approximate Reynolds number? (kinematic viscosity ν = 1×10⁻⁶ m²/s)
- 50,000
- 100,000 (Correct answer)
- 10,000
- 200,000
Correct answer: 100,000
Re = VD/ν = 2 × 0.05 / (1×10⁻⁶) = 100,000.
Question 5: The hydraulic radius of a flow cross-section is defined as:
- The radius of the largest inscribed circle
- The cross-sectional area divided by the wetted perimeter (Correct answer)
- The wetted perimeter divided by cross-sectional area
- Half the pipe diameter
Correct answer: The cross-sectional area divided by the wetted perimeter
Hydraulic radius Rh = A/P, where A is cross-sectional area and P is the wetted perimeter.
Question 6: In a manometer, two fluids of specific gravities 0.8 and 13.6 are used. If the manometer reads a height difference of 0.1 m of the heavier fluid, what is the differential pressure?
- 1,334 Pa
- 13,341 Pa (Correct answer)
- 784 Pa
- 7,848 Pa
Correct answer: 13,341 Pa
ΔP = ρgh = 13,600 × 9.81 × 0.1 = 13,342 Pa ≈ 13,341 Pa using mercury (SG=13.6).
Question 7: Which equation expresses conservation of energy for steady, incompressible flow along a streamline including head losses?
- Euler's equation
- Continuity equation
- Modified Bernoulli equation (Correct answer)
- Navier-Stokes equation
Correct answer: Modified Bernoulli equation
The modified (extended) Bernoulli equation adds pump head, turbine head, and head losses to the standard energy balance.
NCEES Fluid Mechanics 2
A pipe suddenly expands from a diameter of 0.1 m to 0.2 m.
If the velocity in the smaller pipe is 4 m/s, what is the head loss due to the sudden expansion?