課程名稱︰流體力學 課程性質︰必修 課程教師︰陳瑤明 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2012/6/22 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.Please answer the following questions (a)What flow property determines whether a region of flow is rotational or irrotational? (b)Write the Bernoulli equation, and discuss how it differs between an invisid, rotational region of flow and an irrotational region of flow. (c)In the nondimensionalized incompressible Navier-Stokes equation, there are four nondimensional parameters. Name each one, explain its physical significance, and discuss what it means when the parameters is very small or very large. (d)Explain how flow rate is measured with obstruction-type flow meters. Compare orifice meters, flow nozzles, and venturi meters with respect to cost, size, head loss, and accuracy. (e)What is the difference between laser Doppler velocimetry (LDV) and particle image velocimetry (PIV)? 2.Consider the flow field represented by the potential function ψ=Ax^2+Bxy-Ay^2. Verify that this is an incompressible flow and determine the corresponding stream function. 3.The power, P, required to drive a fan is assumed to depend on the fluid density ρ, volume flow rate Q, impeller diameter D, and angular speed ω. If a fan with D1=200 mm delivers Q1=0.4 m3/s of air at ω1=2500 rpm, what size diameter fan could be expected to deliver Q2=2.38 m3/s of air at ω2=1800 rpm, provided they were geometrically and dynamically similar? (此題須先求出Buckingham pi equation 再用相似性求出 D2) 4.Consider fully developed laminar flow in a circular pipe. Use a cylindrical control volume as shown. Indicate the forces acting on the control volume. Using the momentum equation, develop an expression for the velocity distribution( u=f(∂p/∂x,μ,r,R) ). (此題的control volume為一圓柱，半徑r 長度dx，pipe半徑R，) 5.Dimensions of a centrifugal pump impeller are Parameter Inlet,Section1 Outlet,Section2 Radius,r(mm) 380 1140 Blade width,b(mm) 120 80 Blade angle,β(deg) 40 60 The pump is driven at 575 rpm and the fluid is water. Calculate the theoretical head and mechanical power if the flow rate is 18000 m3/h. 附表公式 Navier-Stokes equation --

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