课程名称︰ 流体力学导论
课程性质︰ 必修
课程教师︰ 李雨
开课学院： 工学院
开课系所︰ 应力所
考试日期（年月日）︰ 2015.05.06
考试时限（分钟）： 120
试题 :
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