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CHEMICAL ENGINEERING GATE 2000
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Question 1 of 73
1. Question
1 pointsCategory: MATHEMATICSA pair of fair dice is rolled simultaneously. The probability that the sum of the numbers from the dice equals six is
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Question 2 of 73
2. Question
1 pointsCategory: MATHEMATICSFor an even function f (x),
Correct
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Question 3 of 73
3. Question
1 pointsCategory: MATHEMATICSThe integrating factor for the differential equation
is
Correct
Incorrect

Question 4 of 73
4. Question
1 pointsCategory: MASS TRANSFERIn a binary liquid solution of components A and B, if component A exhibits positive deviation from Raoult’s law, then components B,
Correct
Incorrect

Question 5 of 73
5. Question
1 pointsCategory: MASS TRANSFERAssume that benzene is insoluble in water. The normal boiling points of benzene and water are 80.1 ºC and 100 ºC, respectively. At a pressure of 1 atm, the boiling point of a mixture of benzene and water is
Correct
Incorrect

Question 6 of 73
6. Question
1 pointsOn a PV diagram of an ideal gas, suppose a reversible adiabatic line intersects a reversible isothermal line at point A. Then at point A, the slope of the reversible adiabatic line and the slope of the reversible isothermal line are related as
Correct
Incorrect

Question 7 of 73
7. Question
1 pointsCategory: PROCESS CALCULATIONSThe molar composition of a gas is 10% H2, 10% O2, 30% CO2 and balance H2O. If 50% H2O condenses, the final mole percent of H2 in the gas on a dry basis will be
Correct
Incorrect

Question 8 of 73
8. Question
1 pointsCategory: FLUID MECHANICSFor a sphere falling in the constant drag coefficient regime, its terminal velocity depends on its diameter (d) as
Correct
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Question 9 of 73
9. Question
1 pointsCategory: FLUID MECHANICSIn a fully turbulent flow (Re > 10^5) in a pipe of diameter d, for a constant pressure gradient, the dependence of volumetric flow rate of an incompressible fluid is
Correct
Incorrect

Question 10 of 73
10. Question
1 pointsIn the laminar boundary layer flow over a flat plate, the ratio (δ/x) varies as :
Where δ is the boundary layer thickness and x is the distance from the leading edge in the direction of flow.
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Question 11 of 73
11. Question
1 pointsCategory: FLUID MECHANICSFor laminar flow of a shearthinning liquid in a pipe, if the volumetric flow rate is doubled, the pressure gradient will increase by a factor of
Correct
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Question 12 of 73
12. Question
1 pointsCategory: HEAT TRANSFERThe Grashof number is defined as the ratio of
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Question 13 of 73
13. Question
1 pointsCategory: HEAT TRANSFERA sphere of radius, R1 is enclosed in a sphere of radius, R2. The view (or shape) factor for radiative heat transfer of the outer sphere with respect to the inner sphere is
Correct
Incorrect

Question 14 of 73
14. Question
1 pointsCategory: MASS TRANSFERThe absorption factor is defined as
Where L = liquid flow rate, G = gas flow rate and m = slope of the equilibrium line
Correct
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Question 15 of 73
15. Question
1 pointsCategory: HEAT TRANSFERAt 750 K and 1 atm, the approximate value of the Schmidt number for air is
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Question 16 of 73
16. Question
1 pointsCategory: MASS TRANSFERFor the nth tray (counted from the bottom of a distillation column), the Murphree tray efficiency is given by
Correct
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Question 17 of 73
17. Question
1 pointsCategory: MASS TRANSFERThe McCabe ΔL law states that the
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Question 18 of 73
18. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGThe experimentally determined overall order for the reaction A + B → C + D is two. Then the
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Question 19 of 73
19. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGThe reaction A→B is conducted in an isothermal batch reactor. If the conversion of A increases linearly with holding time, then the order of the reaction is
Correct
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Question 20 of 73
20. Question
1 pointsFor the liquid phase parallel reactions
the desired product is R. A higher selectivity of R will be achieved if the reaction is conducted at
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Question 21 of 73
21. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGIn solid catalysed reactions the diffusional effects are more likely to affect the overall rate of reaction for
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Question 22 of 73
22. Question
1 pointsCategory: CHEMICAL TECHNOLOGYIn petroleum refining, the process used for conversion of hydrocarbons to aromatics is
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Question 23 of 73
23. Question
1 pointsCategory: CHEMICAL TECHNOLOGYCommercially, ethylene is produced from naphtha by
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Question 24 of 73
24. Question
1 pointsCategory: CHEMICAL TECHNOLOGYTriple superphosphate is manufactured by reacting –
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Question 25 of 73
25. Question
1 pointsCategory: PROCESS CONTROLThe unit step response of the transfer function reaches its final steady state asymptotically after
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Question 26 of 73
26. Question
1 pointsCategory: PROCESS CONTROLThe unit step response of the transfer function
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Question 27 of 73
27. Question
1 pointsCategory: PROCESS CONTROLSelect the correct statement from the following :
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Question 28 of 73
28. Question
1 pointsCategory: PROCESS CONTROLFor a feedback control system to be stable, the
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Question 29 of 73
29. Question
1 pointsFor a typical project, the cumulative cash flow is zero at the
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Question 30 of 73
30. Question
1 pointsCategory: MATHEMATICSThe line integral of where C is the unit circle around the origin traversed once in the counterclockwise direction, is
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Question 31 of 73
31. Question
1 pointsCategory: MATHEMATICSThe inverse of the matrix
Correct
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Question 32 of 73
32. Question
2 pointsCategory: MATHEMATICSThe complex conjugate of is
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Question 33 of 73
33. Question
2 pointsCategory: MATHEMATICSThe general solution of
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Question 34 of 73
34. Question
1 pointsCategory: THERMODYNAMICSThe thermal efficiency of a reversible heat engine operating between two given thermal reservoirs is 0.4. The device is used either as a refrigerator or as a heat pump between the same reservoirs. Then the coefficient of performance as a refrigerator (COP)R and the coefficient of performance as a heat pump (COP)HP are
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Question 35 of 73
35. Question
1 pointsCategory: THERMODYNAMICSAt a given temperature, K1, K2 and K3 are the equilibrium constants for the following reaction 1, 2, 3 respectively :
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Question 36 of 73
36. Question
1 pointsThe sphericity of a solid particle of cubical shape is
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Question 37 of 73
37. Question
1 pointsCategory: FLUID MECHANICSA 30% (by volume) suspension of spherical sand particles in a viscous oil has a hindered settling velocity of 4.44 μm/s. If the RichardsonZaki hindered settling index is 4.5, then the terminal velocity of a sand grain is
Correct
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Question 38 of 73
38. Question
1 pointsCategory: FLUID MECHANICSA 1 m high bed made up of 2 mm particles is to be fluidised by an oil (density 900 kg/m³; viscosity 0.01 Pa s). If at the point of incipient fluidisation, the bed voidage is 39% and the pressure drop across the bed is 10 kPa, then the density of particles is
Correct
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Question 39 of 73
39. Question
1 pointsCategory: FLUID MECHANICSA free jet of water of crosssectional area 0.01 m² and a velocity of 20 m/s strikes a plate and then flows in the plane parallel to the plate as shown in the figure below. The horizontal component of the force on the support is
Correct
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Question 40 of 73
40. Question
1 pointsCategory: FLUID MECHANICSA steel sphere of radius 0.1 m at 400 K is immersed in an oil at 300 K. If the centre of the sphere reaches 350 K in 20 minutes, how long will it take for a 0.05 m radius steel sphere to reach the same temperature (at the centre) under identical conditions? Assume that the convective heat transfer coefficient is infinitely large.
Correct
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Question 41 of 73
41. Question
1 pointsCategory: HEAT TRANSFERA composite flat wall of a furnace is made of two materials A and B. The thermal conductivity of A is twice of that of material B, while the thickness of layer of A is half of that of B. If the temperatures at the two sides of the wall are 400 and 1200 K, then the temperature drop (in K) across the layer of material A is
Correct
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Question 42 of 73
42. Question
1 pointsCategory: FLUID MECHANICSFor turbulent flow in a tube, the heat transfer coefficient is obtained from the DittusBoelter correlation. If the tube diameter is halved and the flow rate is doubled, then the heat transfer coefficient will change by a factor of
Correct
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Question 43 of 73
43. Question
1 pointsCategory: MASS TRANSFERThe individual mass transfer coefficients (mol/m² s) for absorption of a solute from a gas mixture into a liquid solvent are kL =4.5 and kG =1.5. The slope of the equilibrium line is 3. Which of the following resistance(s) is (are) controlling ?
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Question 44 of 73
44. Question
1 pointsCategory: MASS TRANSFERIn a laboratory test run, the rate of drying was found to be 0.5 x 10³ kg/m² s when the moisture content reduced from 0.4 to 0.1 on a dry basis. The critical moisture content of the material is 0.08 on a dry basis. A tray drier is used to dry 100 kg (dry basis) of the same material under identical conditions. The surface area of the material is 0.04 m²/kg of dry solid. The time required (in seconds) to reduce the moisture content of the solids from 0.3 to 0.2 (dry basis) is
Correct
Incorrect

Question 45 of 73
45. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGThe conversion for a firstorder liquidphase reaction A→B in a CSTR is 50%. If another CSTR of the same volume is connected in series, then the % conversion at the exit of the second reactor will be
Correct
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Question 46 of 73
46. Question
2 pointsCategory: CHEMICAL REACTION ENGINEERINGThe following halflife data are available for the irreversible liquid phase reaction, A→products :
The overall order of the reaction is
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Question 47 of 73
47. Question
2 pointsCategory: CHEMICAL REACTION ENGINEERINGThe first order series reaction is conducted in a batch reactor. The initial concentrations of A, B, and C (CA0, CB0, CC0, respectively) are all nonzero. The variation of CB with reaction time will not show a maximum if
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Question 48 of 73
48. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGThe reaction A→B is conducted in an diabatic plug flow reactor (PFR). Pure A at a concentration of 2 kmol/m³ is fed to the reactor at the rate of 0.0 m³/s and at a temperature of 500 K. If the exit conversion is 20%, then the exit temperature (in K) is
Data: Heat of reaction at 298 K = 50,000 kJ/kmol of A reacted
Heat capacities, CPA = CPB = 100 kJ/kmol K (may be assumed to be independent of temperature).Correct
Incorrect

Question 49 of 73
49. Question
2 pointsCategory: MODERATEThe rate controlling step for the heterogeneous irreversible catalytic reaction A (g) + B (g) → C (g) is the surface reaction of adsorbed A with adsorbed B to give adsorbed C. The rate expression for this reaction can then be written as
where KA, KB, and KC are the adsorption ;equilibrium constants and k is the rate constant of the rate controlling step.
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Question 50 of 73
50. Question
2 pointsCategory: CHEMICAL TECHNOLOGYSelect the process from the righthand column which matches with the catalyst given in the lefthand column (write both answers in Box No. 2.21)
I. Nicked, A) Hydrogenation of vegetable oils,
II. Zeolites, B) Ammonia synthesis,
C) Catalytic cracking of gas oil,
D) Alkylation,
E) Sulphuric acid manufacture,
F) Nitric acid manmufacture,
G) Methanol synthesis,
H) Ethylene oxide manufacture,Correct
Incorrect

Question 51 of 73
51. Question
1 pointsCategory: EASYThe initial value (t = 0+) of the unit step response of the transfer function
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Question 52 of 73
52. Question
1 pointsCategory: PROCESS CONTROLThe time constant of unity gain, first order plus time delay process is 5 min. If the phase lag at a frequency of 0.2 rad/min is 60º, then the dead time (in minutes) is
Correct
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Question 53 of 73
53. Question
1 pointsCategory: MATHEMATICSFind the directional derivative of u = xyz at the point (1,2,3) in the direction from (1,2,3) to (1,1,3).
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Question 54 of 73
54. Question
1 pointsCategory: MATHEMATICSFind whether or not the vectors (1,1,2), (1,2,1) and (0,3,3) are linearly independent.
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Question 55 of 73
55. Question
1 pointsIndustrial grade methanol can be produced according to the reaction
CO (g) + 2H2 (g) ⇔ CH3OH (g)
For this reaction ΔGº400 = – 1.3484 kJ. If an equimolal mixture of CO and H2 is fed to a reactor maintained at 400 K and 10 bar, determine the fraction of CO that is converted into CH3OH at equilibrium. Assume that the reaction mixture behaves like an ideal gas.Correct
Incorrect

Question 56 of 73
56. Question
1 pointsCategory: THERMODYNAMICSIn a binary mixture the activity coefficient y1 of component 1, in the entire range of composition, is given by where R, A and B are constants. Derive the expression for the activity coefficient of component 2.
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Question 57 of 73
57. Question
2 pointsCategory: THERMODYNAMICSA hydrocarbon oil (viscosity 0.025 Pa s and density 900 kg/m³) is transported using a 0.6 m diameter, 10 km long pipe. The maximum allowable pressure drop across the pipe length is 1 MPa. Due to a maintenance schedule on this pipeline, it is required to use a 0.4 m diameter, 10 km long pipe to pump the oil at the same volumetric flow rate as in the previous case. Estimate the pressure drop for the 0.4 m diameter pipe. Assume both pipes to be hydrodynamically smooth and in the range of operating conditions, the Fanning friction factor is given by
Correct
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Question 58 of 73
58. Question
2 pointsCategory: FLUID MECHANICSA free jet of water is produced using a 75 mm diameter nozzle attached to a 200 mm diameter pipe, as shown in the figure. If the average velocity of water at plane B is 3.8 m/s, calculate the velocity of water at point A in the free jet. Neglect friction losses in the nozzle and pipe.
Correct
Incorrect

Question 59 of 73
59. Question
1 pointsObtain the equation for the qline given that the operating lines are
Where L and L are the liquid flow rates in the enriching and stripping sections, D and B are the top and bottom product flow rates, and xD and xB are the mole fractions of top and bottom products, respectively.
Correct
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Question 60 of 73
60. Question
2 pointsCategory: MASS TRANSFERA continuous – contact extraction column is used to extract a solute from an aqueous stream (F) using an organic solvent (S). The distribution coefficient (y/x) is 1.0, where x and y are the mass fractions of solute in raffinate and extract phases, respectively. The height of transfer unit based on the extract phase is 1.0 m. The rest of the data are given in the figure. Assuming that the phase flow rates are constant, find the height of the tower.
Correct
Incorrect

Question 61 of 73
61. Question
2 pointsCategory: MASS TRANSFERAir at 1 atm is blown past the bulb of a mercury thermometer. The bulb is covered with a wick. The wick is immersed in an organic liquid (molecular weight = 58). The reading of the thermometer is 7.6 0C. At this temperature, the vapour pressure of the liquid is 5 kPa. Find the air temperature, given that the ratio of the heat transfer coefficient to the mass transfer coefficient (psychrometric ratio) is 2 kJ/kg K and the latent heat of vapourisation of the liquid is 360 kJ/kg. Assume that the air, which is blown, is free from the organic vapour.
Correct
Incorrect

Question 62 of 73
62. Question
2 pointsCategory: ECONOMICSA plant is designed to produce 1.2 x 10^8 kg/yr of an agrochemical. The estimated fixed capital investment is Rs 1.5 x 10^9. The working capital is Rs. 2 x 108 and the startup cost (only in the first year of commissioning and to be accounted for in the first year) is Rs. 1.5 x 10^8. The following cost data are available :
Raw materials : Rs 0.80/kg product.
Labour and utilities, etc. : Rs. 0.27/kg product.
Selling price of product : Rs. 10/kg.Other costs (on per year basis) including maintenance, insurance, etc. @ 10% of fixed capital.
Indirect costs of administration, R & D, marketing, etc. @ 20% of sale proceeds.
The plant will be fully depreciated over a period of 5 years using the straightline method. The rate of income tax is 40%. Calculate
a) the net profit at the end of first year,
b) the payout period,Correct
Incorrect

Question 63 of 73
63. Question
1 pointsCategory: PROCESS CONTROLThe response of a thermocouple can be modelled as a first order process to changes in the temperature of the environment. If such a thermocouple at 25ºC is immersed suddenly in a fluid at 80ºC and held there, it is found that the thermocouple reading (in ºC) reaches 63.2% of the final steady state value in 40 seconds. Find the time constant of the thermocouple
Correct
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Question 64 of 73
64. Question
2 pointsCategory: PROCESS CONTROLA feedback control loop with a proportional controller has an open loop transfer function
Where time is in minutes. Obtain the crossover frequency and the ultimate controller gain.Correct
Incorrect

Question 65 of 73
65. Question
2 pointsCategory: PROCESS CONTROLGiven the following block diagram,
a) Express the transfer function (Y/X) as a ratio of polynomials in s,
b) Calculate the offset in C due to a unit step change in the reference signal
(set – point) R.Correct
Incorrect

Question 66 of 73
66. Question
2 pointsCategory: CHEMICAL REACTION ENGINEERINGThe elementary, secondorder, liquid phase reaction A + B → C + D is conducted in an isothermal plug flow reactor of 1 m³ capacity. The inlet volumetric flow rate is 10 m³/h and CAO = CBO = 2 kmol/m³. At these conditions, conversion of A is 50%. Now, if a stirred tank reactor of 2 m³ capacity is installed in series, upstream of the plug flow reactor, then what conversion can be expected in the new system of reactors ?
Correct
Incorrect

Question 67 of 73
67. Question
1 pointsCategory: CHEMICAL REACTION ENGINEERINGThe following liquid phase reactions are carried out in a PFR :
A + C → 2B + P; rP = k1 CA Cc
A → D ; rD = k2 CA
What is the ratio of moles of P formed to moles of D formed at the reactor exit if the conversion of C is 50%? No product is present in the feed.
Data : CA0 = Cc0 = 2 kmol/m³; k1 = 1 m³/(kmol s); k2 = 1 s¹Correct
Incorrect

Question 68 of 73
68. Question
1 pointsCategory: CHEMICAL TECHNOLOGYEach of the products mentioned in the lefthand column requires one or more of the reactants mentioned in the righthand column. Match the products with the appropriate reactant(s).
I) Phthalic anhydride A) Benzene,
II) Cumene, B) Naphthalene,
C) Carbon monoxide
D) Phenol,
E) Propylene,
F) A i r,
G) Ethyl benzene,
H) Hydrogen,Correct
Incorrect

Question 69 of 73
69. Question
1 pointsCategory: CHEMICAL TECHNOLOGYSynthesis gas is a mixture of
Correct
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Question 70 of 73
70. Question
1 pointsCategory: PROCESS CALCULATIONSThe reaction A → 2B + C takes place in a catalytic reactor (see diagram below). The reactor effluent is sent to a separator. The overall conversion of A is 95%. The product stream from the separator consists of B, C and 0.5% of A entering the separator, while the recycle stream consists of the remainder of the unreacted A and 1% of B entering the separator.
Calculate the
a) single pass conversion of A in the reactor.
b) molar ratio of recycle to feed.Correct
Incorrect

Question 71 of 73
71. Question
2 pointsCategory: HEAT TRANSFERThe outside surface temperature of a pipe (radius = 0.1 m) is 400 K. The pipe is losing heat to atmosphere, which is at 300 K. The film heat transfer coefficient is 10 W/m² K. To reduce the rate of heat loss, the pipe is insulated by a 50 mm thick layer of asbestos (k = 0.5 W/m K). Calculate the percentage reduction in the rate of heat loss.
Correct
Incorrect

Question 72 of 73
72. Question
1 pointsCategory: HEAT TRANSFERIn a 1 – 1 counter flow shell and tube heat exchanger, process stream (Cp = 4.2 kJ/kg K) is cooled from 450 to 350 K using water (Cp = 4.2 kJ/kg K) at 300 K. The process stream flows on the shellside at a rate of 1 kg/s and the water on the tubeside at a rate of 5 kg/s. If heat transfer coefficients on the shell and tube sides are 1000 W/m² K and 1500 W/m² K, respectively, determine —
a) the required heat transfer area,
b) by what factor will the required area change if the flow is cocurrent ?
Neglect tube wall resistance and fouling resistances.Correct
Incorrect

Question 73 of 73
73. Question
2 pointsCategory: HEAT TRANSFERAn aqueous solution of a solute is concentrated from 5% to 20% (mass basis) in a singleeffect shorttube evaporator. The feed enters the evaporator at a rate of 10 kg/s and at a temperature of 300 K. Stream is available at a saturation pressure of 1.3 bar. The pressure in the vapour space of the evaporator is 0.13 bar and the corresponding saturation temperature of stream is 320 K. If the overall heat transfer coefficient is 5000 W/m2 K, calculate the
a) steam economy,
b) heat transfer surface area,Correct
Incorrect