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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