101年 - 101 國立嘉義大學_碩士班(乙組)招生考試試題_土木與水資源工程學系：流體力學#146267

(a) Please write the Navier-Stokes equations for the flow of a Newtonian incompressible fluid with constant viscosity, and explain the physical meaning of each term. (10％)

(b) What’s the Reynold number？ Explain the meaning of Reynold number. (10％)

2. In the region just downstream of a sluice gate, the water may develop a reverse flow region as is in Fig-1. The velocity profile is assumed to consist of two uniform regions, one with velocity Va =3 m/s and the other with Vb =0.9 m/s. Determine the net flowrate of water across the portion of the control surface at section (2) if the channel is 6 m wide. (20%)

3. For the inclined-tube manometer of Fig-2 the pressure in pipe A is 4.1 kpa. The fluid in both pipes A and B is water, and the gage fluid in the manometer has a specific gravity of 2.6. What is the pressure in the pipe B corresponding to the differential reading shown？(20%)

Fig-2

4. A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighting 800 lb is held in place by a horizontal flexible cable as shown in Fig-3. Water acts against the gate which is hinged at point A. Friction in the hinge is negligible. Determine the tension in the cable. (20％)

5. Water flows under the sluice gate shown in Fig-4. Determine the flowrate if the gate is 8ft wide. (20％)