BME Fluid Mechanics 2 — Questions and Answers
Question 1: The Navier-Stokes equations describe the motion of which type of fluids?
- Inviscid, incompressible fluids
- Viscous, incompressible Newtonian fluids (Correct answer)
- Non-Newtonian fluids only
- Compressible ideal gases only
Correct answer: Viscous, incompressible Newtonian fluids
The Navier-Stokes equations govern viscous, incompressible Newtonian fluid flow by relating velocity, pressure, and viscous forces.
Question 2: A fluid flows through a pipe that suddenly expands in diameter. Using the continuity equation for incompressible flow, if the diameter doubles, the velocity will:
- Double
- Halve
- Decrease to one-quarter (Correct answer)
- Remain the same
Correct answer: Decrease to one-quarter
Continuity requires A₁V₁ = A₂V₂; doubling diameter quadruples area, so velocity decreases to one-quarter.
Question 3: Which dimensionless number represents the ratio of inertial forces to surface tension forces in fluid flow?
- Reynolds number
- Weber number (Correct answer)
- Froude number
- Bond number
Correct answer: Weber number
The Weber number (We = ρV²L/σ) is the ratio of inertial to surface tension forces.
Question 4: In a laminar boundary layer over a flat plate, the boundary layer thickness δ scales with distance x from the leading edge as:
- δ ∝ x
- δ ∝ x^(1/2) (Correct answer)
- δ ∝ x^(4/5)
- δ ∝ x²
Correct answer: δ ∝ x^(1/2)
For laminar (Blasius) boundary layers, δ ∝ x^(1/2) based on the similarity solution.
Question 5: The head loss in a pipe due to friction (Darcy-Weisbach) is given by h_f = f(L/D)(V²/2g). If flow velocity doubles, the head loss:
- Doubles
- Quadruples (Correct answer)
- Increases by a factor of 8
- Remains constant
Correct answer: Quadruples
Head loss is proportional to V², so doubling velocity quadruples the frictional head loss.
Question 6: A Pitot tube measures fluid velocity by detecting the difference between:
- Static pressure and dynamic pressure
- Total pressure and static pressure (Correct answer)
- Gauge pressure and absolute pressure
- Hydrostatic pressure and atmospheric pressure
Correct answer: Total pressure and static pressure
A Pitot tube measures stagnation (total) pressure; subtracting static pressure gives dynamic pressure, from which velocity is calculated.
Question 7: Which flow regime exhibits a velocity profile that is parabolic across a circular pipe cross-section?
- Turbulent flow
- Transitional flow
- Laminar (Hagen-Poiseuille) flow (Correct answer)
- Plug flow
Correct answer: Laminar (Hagen-Poiseuille) flow
Laminar Hagen-Poiseuille flow in a circular pipe produces a parabolic velocity profile with maximum velocity at the centerline.
BME Fluid Mechanics 2
The Navier-Stokes equations describe the motion of which type of fluids?