課程名稱︰ 流體力學導論 課程性質︰ 必修 課程教師︰ 李雨 開課學院： 工學院 開課系所︰ 應力所 考試日期（年月日）︰ 2015.05.06 考試時限（分鐘）： 120 試題 : Fluid Mechanics Mid-term Examination(open book) (1) The followings are short questions, aiming to examine some of your basic knowledge in fluid mechanics. (a) Tell the differences/similarities between solid/liquid/gas. (5%) (b) Why it is convenient to use Lagarangian approach to derive the equations governing the continuum fluid flow, but use the Eulerian approach to solve the problems? (5%) (c) Give two examples that we need to consider the molecular effect fluid flows. (5%) (d) What is the physics background for the theoretical model of continuum fluid mechanics? (5%) (e) What are the roles of thermodynamics in fluid mechanics? (5%) (f) When the temperature field is decoupled from the velocity and pressure field of fluid flow? (5%) (2) Considered a two dimensional layer of incompressible fluid contained between two infinite flat plates with gap h. (a) The fluid motion is driven by an harmonic oscillation of the lower plate on its own plane, with velocity u(t)=u sinΩt. Find the 0 quasi-steady velocity and vorticity profiles in the fluid. (10%) (b) Redo the problem of (a) if the upper plate is removed. (Hint: What boundary condition would you apply on the upper free surface if it is assume to remain calm?) (10%) (c) Solve for the velocity field if both the upper and the lower plates are undergoing harmonic oscillations, but with different angular frequencies. (i.e., one with Ω and the other with Ω . Hint: the 1 2 problem is linear.) (10%) (3) Extend the plane Poiseille flow analysis (i.e., solve for the velocity field) to describe incompressible stratified flow. One fluid, filling half the channel, has density ρ and viscosity μ ; the other fluid has 1 1 ρ and μ . Check your result against the single fluid result by setting 2 2 ρ =ρ and μ =μ . What happens if the upper fluid is much less dense 1 2 1 2 and less viscous than the lower fluid, as would be the case with air flowing over water? (Hint: let the velocity and the shear stress be continuous at the interface) (20%) (4) The surface temperature of a lake changes from one location to another as T(x ,x ). If you attach a thermometer to a boat and take a path through 1 2 the lake given by x =b (t), with i=1 and 2. Find an expression for the i i rate of change of the thermometer temperature in terms of the lake temperature. (15%) (5) The thermal energy equation is de _ ρ一 = -P▽‧u + ▽‧(k▽T) + Ф dt By using the definition of enthalpy, h, show that an equivalent form of this equation is dh dP ρ一 = 一 + ▽‧(k▽T) + Ф (15%) dt dt --

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