BME Fluid Mechanics 4 — Questions and Answers
Question 1: Cavitation in hydraulic machinery occurs when the local fluid pressure drops below the:
- Atmospheric pressure
- Vapor pressure of the fluid (Correct answer)
- Critical pressure of the fluid
- Stagnation pressure
Correct answer: Vapor pressure of the fluid
Cavitation occurs when local static pressure falls below the fluid's vapor pressure, causing vapor bubble formation.
Question 2: For compressible flow in a converging-diverging nozzle, a normal shock wave can appear in the:
- Converging section only
- Throat only
- Diverging section at supersonic conditions (Correct answer)
- Inlet plenum
Correct answer: Diverging section at supersonic conditions
Normal shocks form in the diverging section when back pressure is between the design (fully supersonic) and subsonic exit conditions.
Question 3: The concept of 'fully developed flow' in a pipe means that:
- Velocity and pressure are both uniform across the cross-section
- The velocity profile no longer changes with downstream distance (Correct answer)
- Turbulence intensity has reached zero
- The boundary layer has just started forming
Correct answer: The velocity profile no longer changes with downstream distance
Fully developed flow means the velocity profile shape is constant with axial position; only pressure continues to drop linearly.
Question 4: The vorticity vector ω in a fluid flow field is defined as:
- ω = ∇·V (divergence of velocity)
- ω = ∇×V (curl of velocity) (Correct answer)
- ω = ∂V/∂t (time derivative)
- ω = ∫V dt (integral of velocity)
Correct answer: ω = ∇×V (curl of velocity)
Vorticity is ω = ∇×V, representing the local angular rotation rate of a fluid element.
Question 5: Stokes' Law for the drag force on a slowly moving sphere in a viscous fluid is:
- F_D = 0.5ρV²ACD
- F_D = 3πμVD (Correct answer)
- F_D = πD²μV/4
- F_D = 6πρVD²
Correct answer: F_D = 3πμVD
For creeping (Stokes) flow (Re ≪ 1), the drag on a sphere is F_D = 3πμVD where D is diameter.
Question 6: The critical depth in open channel flow is defined as the depth at which:
- Flow velocity equals the wave speed (Froude number = 1) (Correct answer)
- The channel slope equals the friction slope
- Energy losses are maximized
- The hydraulic radius is minimized
Correct answer: Flow velocity equals the wave speed (Froude number = 1)
Critical depth occurs when Fr = V/√(gy) = 1, meaning flow velocity equals the shallow-water wave speed.
Question 7: The Euler turbine equation relates the torque produced by a turbomachine to:
- Change in fluid temperature across the rotor
- Change in the tangential component of fluid velocity between inlet and outlet (Correct answer)
- Pressure drop across the impeller only
- Change in fluid density through the machine
Correct answer: Change in the tangential component of fluid velocity between inlet and outlet
Euler's equation T = ρQ(r₂Vθ₂ − r₁Vθ₁) shows torque depends on the change in angular momentum (tangential velocity × radius).
BME Fluid Mechanics 4
Cavitation in hydraulic machinery occurs when the local fluid pressure drops below the: