Multiple-choice questions on principles of chemical engineering

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I. Multiple-choice Questions 1. A liquid flows stably in a straight pipe with constant diameter. If the volumetric flow rate remains unchanged and the inner diameter of the pipe is reduced to half of its original value, assuming that the relative roughness inside the pipe stays the same, then (1) in laminar flow, the flow resistance becomes C times the original value. A. 4 times B. 8 times C. 16 times D. 32 times (2) In fully turbulent flow (the drag square region), the flow resistance becomes D times the original value. A. 4 times B. 8 times C. 16 times D. 32 times Solution: (1) From this, we get …; (2) From this, we get … 2. Water flows from the feed tank into the storage tank. If the total length of the pipes (including the equivalent length due to local resistances) is reduced by 25%, while the height difference between the surface of the feed tank and that of the storage tank remains unchanged, and assuming that the flow is completely turbulent (i.e., in the regime where resistance is proportional to the square of velocity), then the flow rate of water becomes A times the original value. A. 1.155 times B. 1.165 times C. 1.175 times D. 1.185 times. Solution: From … it follows that …; moreover, for fully turbulent flow, it is given that …; therefore, … 3. Two glass balls with different diameters sink freely at the same speed in water and in air respectively. It is known that the density of a glass ball is 2500 kg/m3, the density of water is 998.2 kg/m3, the viscosity of water is 1.005×10-3 Pa·s, the density of air is 1.205 kg/m3, and the viscosity of air is 1.81×10-5 Pa·s. (1) If gravity sedimentation occurs in the laminar flow region, the ratio of the particle diameter in water to that in air is B. A. 8.612 B. 9.612 C. 10.612 D. 11.612 (2) If centrifugal sedimentation occurs in the laminar flow region, and it is known that the ratio of the cyclone separation factor to the hydrocyclone separation factor is 2, then the ratio of the particle diameter in water to that in air is D. A. 10.593 B. 11.593 C. 12.593 D. 13.593 Solution: (1) From this, it follows that … therefore. (2) From , we get , so … 4. A spherical particle is undergoing free gravitational sedimentation in air. It is known that the density of this particle is 5000 kg/m3, the density of air is 1.205 kg/m3, and the viscosity of air is 1.81×10-5 Pa·s. Then, (1) the maximum particle diameter that can settle in the laminar flow region is B × 10-5 m. A. 3.639 B. 4.639 C. 5.639 D. 6.639 (2) The minimum particle diameter that can settle in the turbulent region is C × 10-3 m. A. 1.024 B. 1.124 C. 1.224 D. 1.324 Solution: (1) From this, it follows that; and since, therefore. (2) From this, it follows that; hence. 5. For incompressible filter cakes, filtration is first carried out at a constant velocity and then at a constant pressure. (1) During constant-speed filtration, it is known that when the filtration time is 100 s, the filtration pressure difference is 3104 Pa ； At a filtration time of 500 s, the filtration pressure difference is 9104 Pa. Then, when the filtration time is 300 s, the filtration pressure difference is C. A. 4×104 Pa B. 5×104 Pa C. 6×104 Pa D. 7×104 Pa (2) If filtering is continued at a constant rate for 300 seconds before switching to filtration at a constant pressure, and it is known that the volume of filtrate obtained at the end of the constant-rate filtration phase is 0.75 m3, with a filtration area of 1 m2, the constant for constant-pressure filtration is K = 5×10-3 m2/s, and qe = 0 m3/m2 (the resistance of the filtering medium can be ignored). Then, after further pressure-controlled filtration for 300 seconds, the volume of the filtrate is again D. A. 0.386 m3 B. 0.486 m3 C. 0.586 m3 D. 0.686 m3 Solution: (1) From …, we obtain …; by subtracting these two equations, we get …, so therefore … (2) From …, we get 6. Constant-pressure filtration is performed on a certain suspension. It is known that when the filtration time is 300 s, the volume of the filtrate obtained is 0.75 m3, the filtration area is 1 m2, and the constant for pressure-driven filtration K = 5×10-3 m2/s. To obtain another 0.75 m3 of filtrate, an additional filtration time of C is required. A. 505s B. 515s C. 525s D. 535s Solution: From this, it follows that … 7. Water vapor condenses outside a horizontal pipe with an outer diameter of 25 mm and a length of 2.5 m. (3) If the outer diameter of the tube is doubled, the condensation heat transfer coefficient becomes C of the original value. A. 0.641 times B. 0.741 times C. 0.841 times D. 0.941 times (4) If the original horizontal pipe is placed vertically, and it is assumed that the condensate flows in a laminar manner, then the condensation heat transfer coefficient will be A times that of the original case. A. 0.493 times B. 0.593 times C. 0.693 times D. 0.793 times Solution: (1) From this, we get …; (2) From this, we get … 8. Hot water and cold water exchange heat through a heat exchanger. The inlet temperature of the hot water is 90C and its outlet temperature is 50C, while the inlet temperature of the cold water is 15C and its outlet temperature is 53C. The flow rates of hot water and cold water are the same, and it is assumed that their physical properties are identical. Then, the heat loss accounts for C% of the total heat transfer. A. 5% B. 6% C. 7% D. 8% Solution: From , we have