Fluid Mechanics Flashcards

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

Answer: Viscosity is neglected

Euler equations are Navier-Stokes equations with the viscous (μ∇²V) term set to zero, i.e., inviscid flow.

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:

Answer: 0.58

Fr = V/√(g·y) = 2/√(9.81×1.2) = 2/3.43 ≈ 0.583; flow is subcritical.

Which of the following correctly describes the vorticity in irrotational flow?

Answer: Vorticity is zero everywhere

By definition, irrotational flow has zero vorticity (curl of velocity = 0) everywhere in the flow field.

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:

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.

The boundary layer thickness δ for laminar flow over a flat plate (Blasius solution) varies with distance x as:

Answer: δ ∝ x^(1/2)

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

For a submerged orifice discharging water, if the head difference between upstream and downstream is doubled, the flow rate changes by a factor of:

Answer: √2

Orifice flow Q = Cd·A·√(2g·Δh); doubling Δh gives Q ∝ √(2Δh)/√(Δh) = √2.

The principle of mass conservation for steady, incompressible flow in a streamtube is expressed as:

Answer: A₁V₁ = A₂V₂

The continuity equation for incompressible steady flow states A₁V₁ = A₂V₂ (constant volumetric flow rate).