(c) Consider a steady, incom npressible, three-dimensional flow. The x and z velocity components are given by u = ax²+by²+cz² and w= e axz + byz², where a, b, c are constants. Find the y velocity component (v) as a function of x, y, and z. (7 points)

3.(3%)請指出上面第一大题的譜例第1小節内的各個和聲外音分別為哪一種?(需註明拍位、音高 及和聲外音種類方能給分;答錯倒扣) 

4.(2%)下方譜例中，第三行是給Clarinetti inA 的譜,請問其在第一小節中吹奏出来的音高分別為何?(需全部正確才給分)

(a) Write down the statement of mass conservation (i.e. the continuity equation) for fluid flow and explain the physical meaning of each terms. (6 points)

(b) If the fluid of interest is nearly incompressible, the mass conservation in (a) can be simplified. Write down this simplified equation, provide justifications for your simplification, and explain the physical meaning. (7 points)

(a) What is the Newtonian fluid? (5 points)

(b) Write down the differential form of momentum conservation (i.e. the Navier- Stokes equation) for incompressible flows. Interpret the physical meaning of each terms. (9 points)

(c) What is the Reynolds number? Interpret its physical meaning and its significance in characterizing flow properties. (6 points)

(d) Consider a fully developed pipe flow, describe the differences in time-mean velocity structure (e.g. velocity across the pipe) between laminar and turbulent flow regimes. (5 points)

(a) As illustrated in Fig. 1a, consider a steady, incompressible. laminar flow (with a constant viscosity) confined by two infinite parallel plates. One plate is moving at speed U, while the other plate is held fixed. Assuming that the flow is parallel (y = 0) and is purely two-dimensional (in x and y direction). The boundary conditions are (1) at y= 0, น = v=w = 0. (2) at y = Ly, น = U, y=w=0. Based on the above assumptions, develop the simplified continuity and momentum equations (please provide reasons for why certain terms can be neglected) (7 points)

(b) Following (a), solve for the velocity field and estimate the shear force per unit area acting on the fixed plate. (8 points)