Fluid Mechanics Flashcards

The Navier-Stokes equations describe the motion of which type of fluids?

Answer: Viscous, incompressible Newtonian fluids

The Navier-Stokes equations govern viscous, incompressible Newtonian fluid flow by relating velocity, pressure, and viscous forces.

A fluid flows through a pipe that suddenly expands in diameter. Using the continuity equation for incompressible flow, if the diameter doubles, the velocity will:

Answer: Decrease to one-quarter

Continuity requires A₁V₁ = A₂V₂; doubling diameter quadruples area, so velocity decreases to one-quarter.

Which dimensionless number represents the ratio of inertial forces to surface tension forces in fluid flow?

Answer: Weber number

The Weber number (We = ρV²L/σ) is the ratio of inertial to surface tension forces.

In a laminar boundary layer over a flat plate, the boundary layer thickness δ scales with distance x from the leading edge as:

Answer: δ ∝ x^(1/2)

For laminar (Blasius) boundary layers, δ ∝ x^(1/2) based on the similarity solution.

The head loss in a pipe due to friction (Darcy-Weisbach) is given by h_f = f(L/D)(V²/2g). If flow velocity doubles, the head loss:

Answer: Quadruples

Head loss is proportional to V², so doubling velocity quadruples the frictional head loss.

A Pitot tube measures fluid velocity by detecting the difference between:

Answer: Total pressure and static pressure

A Pitot tube measures stagnation (total) pressure; subtracting static pressure gives dynamic pressure, from which velocity is calculated.

Which flow regime exhibits a velocity profile that is parabolic across a circular pipe cross-section?

Answer: Laminar (Hagen-Poiseuille) flow

Laminar Hagen-Poiseuille flow in a circular pipe produces a parabolic velocity profile with maximum velocity at the centerline.