EIT Fluid Mechanics 3 — Questions and Answers
Question 1: The Navier-Stokes equations for incompressible Newtonian flow reduce to the Euler equations when:
- The flow is laminar
- Viscosity is neglected (Correct answer)
- The flow is steady
- The fluid is compressible
Correct answer: Viscosity is neglected
Euler equations are Navier-Stokes equations with the viscous (μ∇²V) term set to zero, i.e., inviscid flow.
Question 2: A rectangular channel 3 m wide carries water at a depth of 1.2 m with a velocity of 2 m/s. The Froude number is approximately:
- 0.58 (Correct answer)
- 1.00
- 1.73
- 0.29
Correct answer: 0.58
Fr = V/√(g·y) = 2/√(9.81×1.2) = 2/3.43 ≈ 0.583; flow is subcritical.
Question 3: Which of the following correctly describes the vorticity in irrotational flow?
- Vorticity equals the velocity
- Vorticity is zero everywhere (Correct answer)
- Vorticity equals the pressure gradient
- Vorticity is constant but nonzero
Correct answer: Vorticity is zero everywhere
By definition, irrotational flow has zero vorticity (curl of velocity = 0) everywhere in the flow field.
Question 4: Water at 20°C flows through a 50 mm diameter pipe at 0.002 m³/s. The kinematic viscosity is 1×10⁻⁶ m²/s. The Reynolds number is:
- 50,900 (Correct answer)
- 25,400
- 12,700
- 101,800
Correct answer: 50,900
V = Q/A = 0.002/(π×0.05²/4) = 1.019 m/s; Re = VD/ν = 1.019×0.05/1×10⁻⁶ ≈ 50,900.
Question 5: The boundary layer thickness δ for laminar flow over a flat plate (Blasius solution) varies with distance x as:
- δ ∝ x^(1/2) (Correct answer)
- δ ∝ x^(4/5)
- δ ∝ x^(1/3)
- δ ∝ x
Correct answer: δ ∝ x^(1/2)
The Blasius solution gives δ = 5x/√Re_x = 5x/(Vx/ν)^(1/2), so δ ∝ x^(1/2).
Question 6: For a submerged orifice discharging water, if the head difference between upstream and downstream is doubled, the flow rate changes by a factor of:
- √2 (Correct answer)
- 2
- 4
- 1/√2
Correct answer: √2
Orifice flow Q = Cd·A·√(2g·Δh); doubling Δh gives Q ∝ √(2Δh)/√(Δh) = √2.
Question 7: The principle of mass conservation for steady, incompressible flow in a streamtube is expressed as:
- A₁V₁ = A₂V₂ (Correct answer)
- P₁ + ½ρV₁² = P₂ + ½ρV₂²
- F = ṁ(V₂ − V₁)
- τ = μ(dV/dy)
Correct answer: A₁V₁ = A₂V₂
The continuity equation for incompressible steady flow states A₁V₁ = A₂V₂ (constant volumetric flow rate).
EIT Fluid Mechanics 3
The Navier-Stokes equations for incompressible Newtonian flow reduce to the Euler equations when: