Question

Fluid Mechanics. Please answer as many as you can.

Short answer questions 1) Explain the physical meaning of the acceleration term uVu, where u is the velocity vector in a fluid. 2) Name the two equations that are required to describe the flow of an inertial jet in an incompressible, unstratified fluid. 3) What is the “Continuum Hypothesis”? 4) Describe how a viscous boundary layer adjacent to a solid surface results in transfer of momentum to/from that surface. 5) What is the difference between the Eulerian and Lagrangian reference frames? 6) Describe physically what is meant by the “hydrostatic approximation”. 7) Considering the vertical momentum equation, give a key condition that must be met for the hydrostatic approximation to hold. 8) Which assumptions are required for Bernoulli's equation to be valid? 9) The horizontal pressure gradient required to drive flow along an open channel (of rectangular cross-section, but with a free-surface) is set by the volume flow rate, the flow depth, the width of the channel and the fluid viscosity. How many dimensionless groups are needed to specify the flow? 10) Fluid of density p and viscosity v flows through a pipe of cross-sectional area A at a volume flow rate Q. If the flow is steady and incompressible, what parameter group gives the ratio of inertial to viscous forces? 11) What is the physical meaning of the expression du/dx+ðv/dy, where (u, v) is a two- dimensional velocity field in the x, y plane? 12) Explain the physical meaning of the Froude number, Fr, for free-surface flows, with reference to flows having Fr < 1 or Fr> 1. 13) The dispersion relation for surface gravity waves is w = (gk tanh(kH) 1/2. Derive an expression for the phase speed. Evaluate this expression in the deep water and shallow water limits.

Answer 1

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