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）︰2008.4.25 考試時限（分鐘）：100 mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : (15%)(1)Write both of the conservation of mass and linear momentum equations with the Reynolds transport theorem , and explain the difference in a non-deforming control volume and deforming control volume for a moving control volume . (20%)(2)Please explain the following terms : (a)Source (b)Force Vortex (c)Vorticity (d)The relation between stream function Ψ and velocity potential Φ (e)Angular deformation (15%)(3)A static thrust as sketched in the following figure is to be designed for testing a jet engine . The following conditions are known for a typical test : Intake air velocity = 300 m/s ; exhaust gas velocity = 500 m/s ; intake cross-section area = 1 m^2 ; intake static pressure = -22.5 kPa = 78.5 kPa(abs) ; intake temperature = 268K ; exhaust static pressure = 0 kPa = 101 kPa(abs) . Estimate the nominal trust for which to design . ┌───╮ │ ╰─────┐ u1 ─→│ │ u2 ──→ │ │ │ ╭──┬──┘ └─┬─╯ │ │ ─→ │ │ Fth │ ────┴────┴───── (10%)(4)A general statement of the second law of thermodynamics . Please describe " The time rate of increase of the entropy of a system " . (20%)(5)Five liters/s of water enter the rotor along the axis of rotation . The cross-sectional area of each three nozzle exits normal to the relative velocity is 18 mm^2 . How large is the resisting torque required to hold the rotor stationary ? How fast will the rotor spin steadily if the resisting torque is reduced to zero and θ = 30度 . (20%)(6)A fluid flows past a circular cylinder of radius a with an upstresm speed of Vo . A more advanced theory indicates that if viscous effects are negligible , the velocity of the fluid along the surface of the cylinder is given by V = Vosinθ . (a)Determine the streamline and normal components of acceleration (an and as)on the surface of the cylinder as a function of Vo,a,θ. (b)When Vo = 10 m/s and a = 0.1 m ＆ 1.0 m , please plot an and as for 0度 ≦ θ ≦ 90度 . --

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