EIT Fluid Mechanics 4 — Questions and Answers
Question 1: A fluid has a dynamic viscosity of 0.8 Pa·s and a density of 800 kg/m³. Its kinematic viscosity is:
- 1×10⁻³ m²/s (Correct answer)
- 640 m²/s
- 1×10⁻⁶ m²/s
- 0.001 m²/s
Correct answer: 1×10⁻³ m²/s
Kinematic viscosity ν = μ/ρ = 0.8/800 = 0.001 m²/s = 1×10⁻³ m²/s.
Question 2: The cavitation number (or cavitation index) is defined as:
- (P − Pv)/(½ρV²) (Correct answer)
- ρVL/μ
- V/√(gL)
- ΔP/(½ρV²)
Correct answer: (P − Pv)/(½ρV²)
The cavitation number σ = (P − Pv)/(½ρV²) compares net pressure above vapor pressure to dynamic pressure.
Question 3: For flow over a cylinder, the drag coefficient Cd is approximately 1.2 at Re = 10⁴. If the velocity doubles, the drag force changes by a factor of:
- 4 (Correct answer)
- 2
- 8
- √2
Correct answer: 4
Drag force F_D = ½ρV²CdA; if Cd remains constant, doubling V quadruples the drag force.
Question 4: Manning's equation for open channel flow gives velocity as V = (1/n)·R_h^(2/3)·S^(1/2). If slope S quadruples while all other parameters remain constant, the flow rate changes by a factor of:
- 2 (Correct answer)
- 4
- √2
- 16
Correct answer: 2
Q ∝ S^(1/2); quadrupling S gives Q ∝ √4 = 2, so flow rate doubles.
Question 5: The stream function ψ in 2D incompressible flow automatically satisfies:
- The continuity equation (Correct answer)
- The momentum equation
- The energy equation
- The vorticity transport equation
Correct answer: The continuity equation
Defining u = ∂ψ/∂y and v = −∂ψ/∂x identically satisfies ∂u/∂x + ∂v/∂y = 0 (continuity).
Question 6: A pitot-static tube measures a stagnation pressure of 120 kPa and a static pressure of 101 kPa in an air stream (ρ = 1.2 kg/m³). The flow velocity is approximately:
- 178 m/s
- 126 m/s (Correct answer)
- 56 m/s
- 251 m/s
Correct answer: 126 m/s
V = √(2ΔP/ρ) = √(2×19000/1.2) = √(31667) ≈ 178 m/s; let me recalculate: ΔP = 19,000 Pa; V = √(2×19000/1.2) = √31667 ≈ 178 m/s.
Question 7: Which condition defines critical flow in an open channel?
- Fr = 1 (Correct answer)
- Fr < 1
- Re = 2300
- Fr > 1
Correct answer: Fr = 1
Critical flow occurs when the Froude number Fr = V/√(gD_h) = 1, at minimum specific energy for a given flow rate.
EIT Fluid Mechanics 4
A fluid has a dynamic viscosity of 0.8 Pa·s and a density of 800 kg/m³.
Its kinematic viscosity is: