課程名稱︰流體力學
課程性質︰大二必修
課程教師︰馬小康
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2008.06.20
考試時限（分鐘）：120 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(10%)(1) In the description of turbulent flow , please write the time average
of the fluctuations , the square of a fluctuation quantity , and
explain them.
(15%)(2) Please explain the following terms:
(a) Froude number
(b) Boundary Layer Momentum Thickness
(c) Circulation
(d) Minor Losses
(e) Aspect ratio
(10%)(3) What is the effect of pressure gradient for the flow over the body
surface ? Please discuss it.
(Hint: Does a flow separation occur ?)
(15%)(4) An oil with a viscosity of μ=0.40 Ns/m^2 and density ρ =900 kg/m^3
flows in a pipe of diameter D =0.20 m.
(a) What pressure drop , P1-P2 , is needed to produce a flowrate Q =
2.0x10^-5 m^3/s if the pipe is horizontal with X1 =0 and X2 =15m ?
(b) How steep a hill , θ , must the pipe be on if the oil is to flow
through the pipe at the same rate as in part(a) , but with P1=P2?
(c) For the conditions of part(b) , if P1 =250 kPa , what is the
pressure at section , X3 =8m ,where X is measured along the pipe ?
(10%)(5) Show that for un-powered flight (for which the drag , lift , and
weight forces are in equilibrium) the glide slope angle , Θ , is
given by tanΘ = CD/CL. If the lift coefficient for a Boing 777 is 15
times greater than its drag coefficient , can it is glide from an
attitude 30000 ft to an airport 80 miles away if it loses power from
its engines ? Explain. (A statute mile is 5280 feet)
(10%)(6) For steady , two dimensional laminar flow with negligible
gravitational effects , the governing Navier-Stokes Equations reduce
to the following
du du 1 dp d^2u d^2u
u─ + v─ = -── + ν(── + ──)
dx dy ρdx dx^2 dy^2
dv dv 1 dp d^2v d^2v
u─ + v─ = -── + ν(── + ──)
dx dy ρdy dx^2 dy^2
What are the assumptions and simplified equationa by Blasius ?
(15%)(7) Air under standard conditions flows through a 4.0-mm-diameter drawn
tubing with an average velocity of V =50 m/s. For such conditions the
flow would normally be turbulent. However , if precautions are taken
to eliminate disturbances to the flow (the entrance to the tube is
very smooth , the air is dust free , the tube does not vibrate , etc.)
, it may be possible to maintain laminar flow.
(a) Determine the pressure drop in a 0.1-m section of the tube if the
flow is laminar.
(b) Repeat the calculations if the flow is turbulent.
(Under standard temperature and pressure conditions ,ρair =1.23kg/m^3
;μ =1.79x10^-5 Ns/m)
(15%)(8) (a) What is the reason for dimples on golf balls ?
(b) A well-hit golf ball (diameter D =1.69 in , weight W =0.0992 lb)
can travel at U =200 ft/s as it leaves the tee. Determine the drag
on a standard golf ball ,and a smooth golf ball for the conditions
ginen. Also determine the acceleration of each ball for these
conditions. (For standard νair =1.57x10^-4 ft^2/s)
(10%)(9) Pease explain the physical meaning for each term in z-direction of
three Navier-Stokes Equations of motion.
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