BME Fluid Mechanics 5 — Questions and Answers
Question 1: Reynolds Transport Theorem relates the time rate of change of an extensive property in a:
- Control volume to a system (material volume) (Correct answer)
- Pipe cross-section to its inlet conditions
- Turbulent flow to its laminar equivalent
- Rotating frame to a stationary observer
Correct answer: Control volume to a system (material volume)
Reynolds Transport Theorem converts conservation laws from a Lagrangian system (fixed mass) to an Eulerian control volume formulation.
Question 2: In pipe network analysis using the Hardy-Cross method, iterations are performed to satisfy:
- Mass continuity at each node and energy balance around each loop (Correct answer)
- Momentum balance at each junction only
- Maximum entropy production at each node
- Minimum pipe length in each loop
Correct answer: Mass continuity at each node and energy balance around each loop
Hardy-Cross iterates flow corrections until both nodal flow continuity and loop head-loss balance (∑h_f = 0) are satisfied simultaneously.
Question 3: The 'no-slip condition' in viscous fluid mechanics states that:
- Pressure is continuous across a solid boundary
- The fluid velocity at a solid wall equals the wall velocity (Correct answer)
- Turbulent fluctuations vanish at the wall
- Density is constant near the boundary layer
Correct answer: The fluid velocity at a solid wall equals the wall velocity
The no-slip condition requires that viscous fluid immediately adjacent to a solid surface moves at the same velocity as the surface.
Question 4: Which statement correctly describes the difference between Newtonian and non-Newtonian fluids?
- Newtonian fluids have viscosity that varies with shear rate; non-Newtonian fluids do not
- Newtonian fluids have constant viscosity; non-Newtonian fluids have viscosity that depends on shear rate (Correct answer)
- Non-Newtonian fluids obey Bernoulli's equation; Newtonian fluids do not
- Newtonian fluids are always turbulent; non-Newtonian fluids are always laminar
Correct answer: Newtonian fluids have constant viscosity; non-Newtonian fluids have viscosity that depends on shear rate
Newtonian fluids have a linear stress–strain rate relationship (constant μ); non-Newtonian fluids (e.g., blood, paint) exhibit shear-dependent viscosity.
Question 5: The Buckingham π theorem states that if a physical problem involves n variables and k fundamental dimensions, the number of independent dimensionless groups is:
- n + k
- n × k
- n − k (Correct answer)
- k − n
Correct answer: n − k
Buckingham π theorem: the number of independent dimensionless Π groups equals n (variables) minus k (fundamental dimensions).
Question 6: In the k-ε turbulence model, the variable ε represents:
- Turbulent kinetic energy
- Rate of dissipation of turbulent kinetic energy (Correct answer)
- Eddy viscosity ratio
- Turbulent Prandtl number
Correct answer: Rate of dissipation of turbulent kinetic energy
In the k-ε model, k is turbulent kinetic energy and ε is the rate at which k is dissipated into heat by viscous action.
Question 7: A manometer uses a U-tube filled with a denser fluid to measure pressure differences. If the manometer fluid is mercury (SG = 13.6) and the height difference is 15 cm, the pressure difference is approximately:
- 1.47 kPa
- 14.7 kPa
- 20.0 kPa (Correct answer)
- 147 kPa
Correct answer: 20.0 kPa
ΔP = ρgh = 13.6×1000×9.81×0.15 ≈ 20,012 Pa ≈ 20.0 kPa.
BME Fluid Mechanics 5
Reynolds Transport Theorem relates the time rate of change of an extensive property in a: