EIT Fluid Mechanics 3

Question 1

The Navier-Stokes equations for incompressible Newtonian flow reduce to the Euler equations when:

Accepted Answer

Viscosity is neglected

Answer

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:

Accepted Answer

0.58

Answer

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?

Accepted Answer

Vorticity is zero everywhere

Answer

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:

Accepted Answer

50,900

Answer

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:

Accepted Answer

δ ∝ x^(1/2)

Answer

The Blasius solution gives δ = 5x/√Re_x = 5x/(Vx/ν)^(1/2), so δ ∝ x^(1/2).

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