110年 - 110 國立清華大學碩士班考試入學試題_化學工程學系:輸送現象及單元操作#104976

選擇題 (20)

1. The outbreak of coronavirus disease 2019 (COVID-19) has caused a global pandemic and significant impact on society, economy, and human life. To combat the virus, wearing the mask and keep a safe social distance can help prevent the spread of COVID-19. However, it was still broadly debated regarding "what is the safe social distance". Some studies recommended that at least 2 m of physical distance should be kept from others, while others suggested that 2 m may not be adequate. To answer this question, it is vital to fully understand the mechanism of virus spreading. The respiratory infections occur usually through the transmission of virus-containing droplets and aerosols exhaled from infected individuals during breathing, speaking, coughing, and sneezing. Therefore, we can assume the spreading of the droplet is similar to a falling particle in the air. Please identify the kinetic force (F.) acting on the droplet. Assume u is the dynamic viscosity of airflow, R is the radius of the droplet, n is the falling (terminal) velocity. (A) (B)(C)(D) (E)

2. Please obtain the falling velocity of the droplet. [Hint] Use the force balance of gravity force, buoyance force, and kinetic force. pu is the density of the droplet and p is the density of the air. (A) (B) (C) (D) (E)

3. Assume the diameter, density, viscosity of the droplet is 5 um, 0.997 g/cm³, and kg/m s, respectively. The density of the air is 1.184 kg/m³ and gravity is 9.8 m/s². If the initial height of the droplet is set as 1.5 m, please calculate the falling time of the droplet. Choose the closest answer. (A) l min, (B) 2 min, (C) 10 min, (D) 30 min, (E) 60 min

4. If the evaporation of the droplet is considered, obviously, the small droplets would evaporate first before falling on the ground. However, the evidence demonstrates that large droplets are not affected by evaporation. Please calculate the minimum size (in diamcter) of the droplet before it falls on the groud. Assume the initial horizontal velocity of the droplet is 2 m/s and the initial height of the droplet is set as 1.5 m. The transmission distance is 2 m. (A) 134 um, (B) 226 um, (C) 474 um, (D) 508 um, (E) 668 um

5. As we know, the falling velocity of the particle can also be determined by introducing the friction factor fconcept when we assume kinetic force F& = AKf. A is a characteristic area and K is a characteristic kinetic energy. D is the diameter of the particle. Please identify the correct answer. (A) (B) (C) (D)(E)

6. If we try to introduce the kinetic force Ft from question I, the correlation between fand Re can be: 24 32 (A)(B) (C) (D) (E)

7. Please calculate the falling time of the droplet using the equation from question 5. The initial height of the droplet is set as 1.5 m. Please choose the closest answer. (A) l min, (B) 2 min, (C) 10 min, (D) 30 min, (E) 60 min

8. The falling velocity of the droplet may or may not be the same when using the force balance method or friction factor method. If not the same, there should be a reason behind that. Please choose the CORRECT answer. (A) The falling velocities are the same, so there is no reason behind that. (B) The falling velocities are not the same because the airflow is the creeping flow. (C) The falling velocities are not the same because the air friction is dominant. (D) The falling velocities are not the same because the density of the air can be ignored. (E) The falling velocities are not the same because the viscosity of the air is not considered when using the friction factor method.

9. Cough can increase the initial horizontal velocity of the droplets, allowing the longer travel distance of the droplets. Usually, the average velocity of cough flow is 10 m/s. Please calculate the Reynolds number of the cough flow. Assume the opening of the mouth is 1 cm in diameter. Choose the closest answer. (A)500,(B) 1000, (C) 3000, (D) 5000, (E) 6000

10. Wearing the face mask can provide a critical barrier, reducing most infectious viruses during coughing, especially of asymptomatic people and those with mild symptoms of COVID-19. Please calculate the force of cough flow acting on the mask. Assume the mask perfectly covers the mouth. The velocity of cough flow is 10 m/s and the opening of the mouth is 1 cm in diameter. (A)0.001 N (B) 0.01 N (C) 0.1 N (D)1N (E) 10 N

11. What is the SI unit of mass flux? (A) Kg/s, (B) g((s/ cm²), (C) Kg(s /m²), (D) g/s

12. Concerning the SI units of kinematic viscosity, thermal diffusivity, and mass diffusivity, which of the following statements is true? (A) All three are different. (B) All three are the same as m²/s. (C) All three are the same as s/m². (D) All three are the same as s/cm².

13. For the following mixtures, (a) H₂-Oz at 1 atm and 273 K, (b) N₂-O₂ at I atm and 273 K, (c) dilute aqucous ethanol solution at 298 K, and (d) Cd in Cu at 293 K, place them in the order of increasing mass diffusivity. (A) (a)(b)(c)(d), (B) (c)(d)(a)(b), (C) (d)(c)(a)(b), (D) (d)(c)(b)(a)

14. For flow of a binary gas mixture over a flat plate, boundary layers of velocity and concentration develop. Which of the following statements concerning the thicknesses of the velocity (δ) and concentration boundary layers is true? (A) (B) (C) (D) none of the above

15. Consider a spherical particle A of radius R dissolving in a stagnant liquid B. Once dissolved, A and B react to form C with an irreversible first-order reaction reaction rate constant k). The solubility of A in B, CAo, is small and the system can be approximated as a dilute binary system. The diffusivity of A in B is DAB. The system can be treated as in a pseudo-steady state. Let b2 denote (k,R/DAB). What is the molar flux of A at the particle surface? (A) (B) (C) (D)

16. Continued from the above problem, what is dmaldr? (-molecular weight of A, ma-mass of particle (A) (B) (C) (D)

17. Consider the absorption of gas A by a laminar falling film of liquid B. Gas A is only
slightly soluble in B, and the diffusion takes place so slowly in the liquid film that A
will not penetrate very far into B. The concentration of A at the interface is maintained
at CAo and the maximum velocity of the fluid is Vmar. Let x be the coordinate into the
liquid film, z the coordinate down the liquid film, and DAB the mass diffusivity of A in
B. The molar concentration of A, CA, is a function of x and z. Which of the following
statements is true?(A) CA increases with increasing x.(B) CA decreases with increasing z.(C) CA increases with decreasing at fixed x and z.(D) CA decreases with increasing at fixed x and z.

18. Continued from the above problem, what is the molar absorption rate of A at the gas/iquid interface? Here, W and L are the width and length of the liquid film exposed to gas A. (A) (B) (C) (D)

19. The equation of continuity of A in a dilute binary solution can be written as

Here, is the mass average velocity and is the molar reaction rate of A. For the
situation of pure diffusion in solids, what will the above equation be reduced to?(A) (B)(C)(D)

20. Which of the following statements is true? (A) Eddy diffusivity is a physical property of a fluid. (B) Eddy diffusivity depends on turbulent intensity of the flow. (C) Nusselt number of heat transfer is analogous to Schmidt number of mass transfer. (D) Chilton-Colburn analogy applies to laminar tube flow.

申論題 (20)

(a) Provide the definitions of forced convection and natural (free) convection.

(b) Give the definitions s and physical meanings of PrandtI number (Pr), Nusselt number (Nu), and Grashof number (Gr).

(a) What are the partial differential equations that must be satisfied by Eq. (1) and (2)?

(b) Write down the boundary conditions that apply at r = R.

(d) Show that Eqs. (1) and (2) satisfy the boundary conditions in (b).

(a) Calculate the membrane coefficient,.

(b) Calculate the overall mass transfer coefficient, K and the percent resistance of membrane.

(d) By increasing the mixing intensity of both liquid phases, we manage to increase the mass coefficients to double their current values. What will be the percent increase in NA?