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110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:流體力學(D)#105721

科目：研究所、轉學考(插大)-流體力學 | 年份：110年 | 選擇題數：0 | 申論題數：15

試卷資訊

所屬科目：研究所、轉學考(插大)-流體力學

選擇題 (0)

申論題 (15)

(1) (5%) Let the scales of the streamwise and radial velocities of the lymph flow be U and W, respectively. Let the streamwise and radial positions in the lymph flow be scaled by R0 and L, respectively. From scale analysis of the continuity equation, what can you tell about the magnitudes of U and W?
(2) (5%) From scale analysis of the momentum equation in the 2 direction, under what condition can the momentum equation in the z direction be reduced to the equation of Poiseuille flow? What should the scale of pressure be?
(3) (5%) From scale analysis of the momentum equation in the r direction, what conclusion can be drawn about the pressure distribution with the results from part (b)?

(4) (5%) Consider a control volume in the micro-tube that has a cross-sectional area A(z,t) = πR2(z,t) and an intinitesimal length dz. From control volume analysis, show that61de226415e4d.jpgdr is the volume flow rate. 
(5) (10%) In the case of part (b), write down the boundary conditions of the Poiseuille flow in the micro-tube and solve for นz(r, z,t). Compute Q(z,t) by integrating นz(r,z,t) directly.

(6) (10%) Since R(z, t) is in a form of a traveling wave, A(z,t) and Q(z,t) are too in a form of traveling wave. From the results in part (d) show that Q(z,t) = cA(z,t) + Q0(t) . Together with the results from part (e), derive an expression of the pressure gradient in the z direction in terms of Q0(t), R0, △R, c, andμ.

(7) (10%) Consider the deformation of the wall is small, ie, △R<< R0. Perform the Taylor expansion of the pressure gradient about △R = 0 to the first order and show that it is possible to obtain a pressure rise when there is a traveling wave propagating on the deformable wall.
(1) (10%) Formulate a general dynamic equation to describe the sphere transient unsteady motion u(t) from time zero with a proper initial condition. Explain the physical meaning of every term in your equation.
(2) (5%) If the sphere motion falls in the low-Re flow regime (Regime A), C, the drag coefficient can be described by CD=24/Re. Determine the sphere terminal velocity U.

(3) (7%) Based on the Navier-Stokes equation, use scaling arguments to explain why the tolal drag in the low-Re regime (Regime A) always follows the same relation that logCD~ -log(Re), or equivalently, FD~ μRU.
(4) (8%) Perform dimension analysis to find all the relevant non-dimensional flow variables with one that involves the transient timescale T as a dimensionless time scale, T'.

(5) (5%) Now, we consider the motion of a spherical liquid droplet of identical radius R, density pu (ρ＜ρL-ρs)and viscosity iL that also falls at its terminal velocity ULin the low-Re regime. Do you expect a greater or a lower Co than that of the solid sphere if the liquid droplet falls at the same speed as the solid sphere? Why?
(6) (5%) Compare the terninal velocity of the spherical liquid droplet and the solid sphere. Under what condition they may fall at the same speed?
(7) (5%) If the sphere now moves in Regime B, the experienced CD decays with Re at a slower rate than the decay rate in Regime A. Can you explain it use the flow process?
(8) (5%) Use flow process to explain why CD remains nearly constant in Regime C. What happens when there is a sudden drop of CD in Regimes D and explain its flow process.