110年 - 110 國立中央大學_碩士班招生考試_化學工程與材料工程學系/甲組(一般生):輸送現象與單元操作#103873

2. (8%) Introduce the following dimensionless terms into the Navior-Stokes equation:
 u* =u/u∞, dimensionless velocity
P* =P/ρu∞², dimensionless pressure
 t*=t u∞/L, dimensionless time
 x* =x/L, dimensionless distance
 The operator∇ may then written ∇*/L. Show that the Navior-Stokes equation becomes

4. (10%) Please recreate the diagram provided below in your answer sheet, and draw the "'minimumn reflux ratio" and ''minimum operating ratio" operating lines. Clearly label the two lines.

(1) In the steady-state operation, steam leaving the turbine is condensed and recycled back to the boiler. For the sake of efficacy, steam from the outlet of the turbine is set to 1 bar and 100℃. Given the steam fow rate of 20 kgs, determine the minimal temperature and pressure of steam entering the turbine (assuming entropy generation). (4 pts)

(2) Given that compressed water of 100℃ and 10 MPa is steadily supplied to the boiler, determine the operation temperature of the boiler and the heat generation rate which must be achieved by the nuclear reaction to maintain the steady and saturated state of steam at the pressure determined in (1). (4 pts)

(4) You decide to employ a counterflow, concentric tube heat exchanger for the purpose. Given the condition that the cooling fluid - water - is at 10℃ and the diameters of the outer annulus and inner tube are to be 45 cm and 25 cm, respectively, determine the respective convection heat transfer coefficients for cooling water and stean. (9 pts) Explain the physical meanings of Reynolds and Nusselt numbers, which are relevant for addressing the question. (2 pts)

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