Unit Operations
Calculate the ideal available energy produced by the discharge to atmosphere through a nozzle of air stored in a cylinder of capacity 0.1 m3 at a pressure of 5 MN/m2. The initial temperature of the air is 290 K and the ratio of the specific heats is 1.4.
🔺U = -0.84 x 10^6 J or -840 kJ
Calculate the energy stored in 1000 cm3 of gas at 80 MN/m2 at 290 K using STP as the datum.
🔺U = -47.7 kJ
A double-effect forward-feed evaporator is required to give a product consisting of 30 per cent crystals and a mother liquor containing 40 per cent by mass of dissolved solids. Heat transfer coefficients are 2.8 and 1.7 kW/m2 K in the first and second effects respectively. Dry saturated steam is supplied at 375 kN/m2 and the condenser operates at 13.5 kN/m2. (a) What area of heating surface is required in each effect, assuming they are both identical, if the feed rate is 0.6 kg/s of liquor, containing 20 per cent by mass of dissolved solids, and the feed temperature is 313 K? (b) What is the pressure above the boiling liquid in the first effect? The specific heat capacity may be taken as constant at 4.18 kJ/kg K, and the effects of boiling point rise and of hydrostatic head may be neglected.
(A) Area = 5.06 m2 (B) Atmospheric
A saturated solution containing 1500 kg of potassium chloride at 360 K is cooled in an open tank to 290 K. If the density of the solution is 1200 kg/m3, the solubility of potassium chloride/100 parts of water by mass is 53.55 at 360 K and 34.5 at 290 K calculate: (a) the capacity of the tank required, and (b) the mass of crystals obtained, neglecting any loss of water by evaporation.
(A) Capacity of the Tank = 3.58 m2 (B) Mass of Crystals = 534 kg
A three-stage evaporator is fed with 1.25 kg/s of a liquor which is concentrated from 10 to 40 per cent solids. The heat transfer coefficients may be taken as 3.1, 2.5, and 1.7 kW/m2 K in each effect respectively. Calculate the required steam flowrate at 170 kN/m2 and the temperature distribution in the three effects, if: (a) if the feed is at 294 K, and (b) if the feed is at 355 K. Forward feed is used in each case, and the values of U are the same for the two systems. The boiling-point in the third effect is 325 K, and the liquor has no boiling-point rise.
(A) D0 = 0.472 kg/s; T1 = 368 K; T2 = 351 K; T3 = 325 K (B) D0 = 0.331 kg/s; T1 = 371 K; T2 = 353 K; T3 = 325 K
A forward-feed double-effect evaporator, having 10 m2 of heating surface in each effect, is used to concentrate 0.4 kg/s of caustic soda solution from 10 to 50 per cent by mass. During a particular run, when the feed is at 328 K, the pressures in the two calandrias are 375 and 180 kN/m2 respectively, and the condenser operates at 15 kN/m2. For these conditions, calculate: (a) the load on the condenser; (b) the steam economy and (c) the overall heat transfer coefficient in each effect. Would there be any advantages in using backward feed in this case? Heat losses to the surroundings are negligible. Physical properties of caustic soda solutions: Solids (% by mass) 10 20 30 50 Boiling-Point Rise (K) 1.6 6.1 15.0 41.6 Specific heat Capacity (kJ/kgK) 3.85 3.72 3.64 3.22 Heat of Dilution (kJ/kg) 0 2.3 9.3 220
(A) D2 = 0.15 kg/s. (B) Steam Economy = 1.57 (C) U1 = 2.53 kW/m2 K
Glass spheres are fluidised by water at a velocity equal to one half of their terminal falling velocities. Calculate: (a) the density of the fluidised bed, (b) the pressure gradient in the bed attributable to the presence of the particles. The particles are 2 mm in diameter and have a density of 2500 kg/m3. The density and viscosity of water are 1000 kg/m3 and 1 mNs/m2 respectively.
(A) Density of fluidized bed = 1367 kg/m3 (B) Pressure Gradient = 3605 (N/m2)/m
A single-acting air compressor supplies 0.1 m3/s of air measured at, 273 K and 101.3 kN/m2 which is compressed to 380 kN/m2 from 101.3 kN/m2. If the suction temperature is 289 K, the stroke is 0.25 m, and the speed is 4.0 Hz, (A) what is the cylinder diameter? (B) Assuming the cylinder clearance is 4 per cent and compression and re-expansion are isentropic (y = 1.4), what are the theoretical power requirements for the compression?
(A) Diameter = 0.38 m (B) Theo Power Req = 17.1 kW
0.126 kg/s of a solid product containing 4 per cent water is produced in a dryer from a wet feed containing 42 per cent water on a wet basis. Ambient air at 294 K and of 40 per cent relative humidity is heated to 366 K in a preheater before entering the dryer from which it leaves at 60 per cent relative humidity. Assuming that the dryer operates adiabatically, (A) what must be the flowrate of air to the preheater and (B) how much heat must be added to the preheater? How will these values be affected if the air enters the dryer at 340 K and sufficient heat is supplied within the dryer so that the air again leaves at 340 K with a relative humidity of 60 per cent?
(A) Flowrate of Air to the preheater = 3.16 m3/s (B) Heat added = 276 kW; Total Heat Supplied = 242 kW
Hydrogen is pumped from a reservoir at 2 MN/m2 pressure through a clean horizontal mild steel pipe 50 mm diameter and 500 m long. The downstream pressure is also 2 MN/m2 and the pressure of this gas is raised to 2.6 MN/m2 by a pump at the upstream end of the pipe. The conditions of flow are isothermal and the temperature of the gas is 293 K. (A) What is the flowrate and (B) what is the effective rate of working of the pump? Viscosity of hydrogen D 0.009 mN s/m2 at 293 K.
(A) G = 0.213 kg/s (B) Power Requirement = 1.13 x 10^5 W or 113 kW
A hydrocarbon oil of density 950 kg/m3 and specific heat capacity 2.5 kJ/kg K is cooled in a heat exchanger from 363 to 313 K by water flowing countercurrently. The temperature of the water rises from 293 to 323 K. If the flowrate of the hydrocarbon is 0.56 kg/s, (A) what is the required flowrate of water? (B) After plant modifications, the heat exchanger is incorrectly connected so that the two streams are in co-current flow. What are the new outlet temperatures of hydrocarbon and water, if the overall heat transfer coefficient is unchanged?
(A) G = 0.56 kg/s (B) To = 324.2 K: Tw = 315.8K
A liquor of 0.30 mole fraction of benzene and the rest toluene is fed to a continuous still to give a top product of 0.90 mole fraction benzene and a bottom product of 0.95 mole fraction toluene. If the reflux ratio is 5.0, how many plates are required: (a) if the feed is saturated vapour? (b) if the feed is liquid at 283 K?
(A) Hfs = 16, 425 kJ/kmol or 16.63 MJ/Kmol (B) Hf = 1615 kJ/kmol or 1.615 MJ/kmol
Tests on a small scale tank 0.3 m diameter (Rushton impeller, diameter 0.1 m) have shown that a blending process between two miscible liquids (aqueous solutions, properties approximately the same as water, i.e. viscosity 1 mN s/m2, density 1000 kg/m3) is satisfactorily completed after 1 minute using an impeller speed of 250 rev/min. It is decided to scale up the process to a tank of 2.5 m diameter using the criterion of constant tip-speed. (a) What speed should be chosen for the larger impeller? (b) What power will be required? (c) What will be the blend time in the large tank?
(A) N = 0.346 Hz or 20.8 rev/min (B) P = 9.8 W (C) tm = 4140 s or 1.15 min
By what percentage would the rate of absorption be increased or decreased by increasing the total pressure from 100 to 200 kN/m2 in the following cases? (a) The absorption of ammonia from a mixture of ammonia and air containing 10% of ammonia by volume, using pure water as solvent. Assume that all the resistance to mass transfer lies within the gas phase. (b) The same conditions as (a) but the absorbing solution exerts a partial vapour pressure of ammonia of 5 kN/m2. The diffusivity can be assumed to be inversely proportional to the absolute pressure.
(A) NA = -10.54D/RTL, that is the rate is unchanged (B) rate of diffusion has been increased = 48%
It is desired to separate 1 kg/s of an ammonia solution containing 30 per cent NH3 by mass into 99.5 per cent liquid NH3 and a residual weak solution containing 10 per cent NH3. Assuming the feed to be at its boiling point, a column pressure of 1013 kN/m2, a plate efficiency of 60 per cent and that an 8 per cent excess over the minimum reflux requirements is used, (A) how many plates must be used in the column and (B) how much heat is removed in the condenser and added in the boiler?
(A) Plates = 8.33 = 9 (B) Heat Input to boiler = 617 kW; Condenser Duty = 372 kW
1.25 kg/s of a solution is concentrated from 10 to 50 per cent solids in a triple-effect evaporator using steam at 393 K, and a vacuum such that the boiling point in the last effect is 325 K. If the feed is initially at 297 K and backward feed is used, (A) what is the steam consumption, (B) the temperature distribution in the system and (C) the heat transfer area in each effect, each effect being identical? For the purpose of calculation, it may be assumed that the specific heat capacity is 4.18 kJ/kgK, that there is no boiling point rise, and that the latent heat of vaporisation is constant at 2330 kJ/kg over the temperature range in the system. The overall heat transfer coefficients may be taken as 2.5, 2.0 and 1.6 kW/m2 K in the first, second and third effects, respectively.
(A) Steam Consumption = D0 = 0.432 kg/s (B) Effect 1 = 374K; Effect 2 = 350K; Effect 3 = 325 K (C) Area = 18.0 m2
A single-stage double-acting compressor running at 3 Hz is used to compress air from 110 kN/m2 and 282 K to 1150 kN/m2. If the internal diameter of the cylinder is 20 cm, the length of stroke 25 cm, and the piston clearance 5%, calculate: (a) the maximum capacity of the machine, referred to air at the initial temperature and pressure, and (b) the theoretical power requirements under isentropic conditions.
(A) The capacity = 0.047 m3/s (B) Theo Power Requirement = 17.3 kW
Water flows at 2 m/s through a 2.5 m length of a 25 mm diameter tube. If the tube is at 320 K and the water enters and leaves at 293 and 295 K respectively, (A) what is the value of the heat transfer coefficient? (B) How would the outlet temperature change if the velocity was increased by 50%?
(A) U = 1.612 kW/m2 K (B) T = 294.5 K
A smooth tube in a condenser which is 25 mm internal diameter and 10 m long is carrying cooling water and the pressure drop over the length of the tube is 2 ð 104 N/m2. If vapour at a temperature of 353 K is condensing on the outside of the tube and the temperature of the cooling water rises from 293 K at inlet to 333 K at outlet, (A) what is the value of the overall heat transfer coefficient based on the inside area of the tube? (B) If the coefficient for the condensing vapour is 15,000 W/m2 K, what is the film coefficient for the water? (C) If the latent heat of vaporisation is 800 kJ/kg, what is the rate of condensation of vapour?
(A) U = 6.57 kW/m2 K. (B) hi = 11.68 kW/m2 K (C)rate of condensation = 0.235 kg/s
A single-effect evaporator with a heating surface area of 10 m2 is used to concentrate a NaOH solution flowing at 0.38 kg/s from 10 per cent to 33.3 per cent. The feed enters at 338 K and its specific heat capacity is 3.2 kJ/kg K. The pressure in the vapour space is 13.5 kN/m2 and 0.3 kg/s of steam is used from a supply at 375 K. Calculate: (a) The apparent overall heat transfer coefficient. (b) The coefficient corrected for boiling point rise of dissolved solids. (c) The corrected coefficient if the depth of liquid is 1.5 m.
(A) U1 = 1.28 kW/m2 K (B) U1 = 2.21 kW/m2 K (C) U1 = 1.89 kW/m2 K
Soda ash is mixed with lime and the liquor from the second of three thickeners and passed to the first thickener where separation is effected. The quantity of this caustic solution leaving the first thickener is such as to yield 10 Mg of caustic soda per day of 24 hours. The solution contains 95 kg of caustic soda/1000 kg of water, whilst the sludge leaving each of the thickeners consists of one part of solids to one of liquid. Determine: (a) the mass of solids in the sludge, (b) the mass of water admitted to the third thickener and (c) the percentages of caustic soda in the sludges leaving the respective thickeners.
(A) mass of CaCO3 in sludge = 13.7 Mg/day (B) The mass of water fed to third thickener = 129 Mg/day (C) thickener 1 = 4.34 per cent; thickener 2 = 0.47 per cent; thickener 3 = 0.05 per cent
A slurry containing 100 kg of whiting, of density 3000 kg/m3, per m3 of water, and, is filtered in a plate and frame press, which takes 900 s to dismantle, clean, and re-assemble. (A) If the cake is incompressible and has a voidage of 0.4, what is the optimum thickness of cake for a filtration pressure (−P) of 1000 kN/m2? (B) The density of the whiting is 3000 kg/m3. If the cake is washed at 500 kN/m2 and the total volume of wash water employed is 25 per cent of that of the filtrate, how is the optimum thickness of the cake affected? The resistance of the filter medium may be neglected and the viscosity of water is 1 mNs/m2. In an experiment, a pressure difference of 165 kN/m2 produced a flow of water of 0.02 cm3/s through a centimetre cube of filter cake.
(A) optimum frame thickness = 70 mm (B) Frame thickness = 59.2 ≈ 60 mm
A rotary drum filter, 1.2 m diameter and 1.2 m long, handles 6.0 kg/s of slurry containing 10 per cent of solids when rotated at 0.005 Hz. By increasing the speed to 0.008 Hz it is found that it can then handle 7.2 kg/s. (A) What will be the percentage change in the amount of wash water which may be applied to each kilogram of cake caused by the increased speed of rotation of the drum, and (B) what is the theoretical maximum quantity of slurry which can be handled?
(A) per cent increase = 4.17 per cent (B) 18.0 kg/s
1 Mg of dry mass of a non-porous solid is dried under constant drying conditions in an air stream flowing at 0.75 m/s. The area of surface drying is 55 m2. (A) If the initial rate of drying is 0.3 g/m2s, how long will it take to dry the material from 0.15 to 0.025 kg water/kg dry solid? (B) The critical moisture content of the material may be taken as 0.125 kg water/kg dry solid. If the air velocity were increased to 4.0 m/s, what would be the anticipated saving in time if the process were surface-evaporation controlled?
(A) t = 10.96 ks (3 h) (B) Time Saved = 8.10 ks (2.25 h)
Water is pumped at 1.4 m3/s from a tank at a treatment plant to a tank at a local works through two parallel pipes, 0.3 m and 0.6 m diameter respectively. (A) What is the velocity in each pipe and, (B) if a single pipe is used, what diameter will be needed if this flow of water is to be transported, the pressure drop being the same? Assume turbulent flow with the friction factor inversely proportional to the one quarter power of the Reynolds number.
(A) u1 = 2.62 m/s; u2 = 4.30 m/s (B) Required Diameter = 0.63 m
In order to extract acetic acid from dilute aqueous solution with isopropyl ether, the two immiscible phases are passed countercurrently through a packed column 3 m in length and 75 mm in diameter. acid by mass, then the ether phase leaves the column with a concentration of 1.0 per cent acid by mass. Calculate: (a) the number of overall transfer units based on the raffinate phase, and (b) the overall extraction coefficient based on the raffinate phase. The equilibrium relationship is given by: (kg acid/kg isopropyl ether) = 0.3 (kg acid/kg water).
(a) KRa = 0.461 kg/m3s(kg/kg) (b) number of overall transfer units = 5.53
Gas, from a petroleum distillation column, has its concentration of H2S reduced from 0.03 kmol H2S/kmol of inert hydrocarbon gas to 1 per cent of this value, by scrubbing with a triethanolamine-water solvent in a countercurrent tower, operating at 300 K and at atmospheric pressure. H2S is soluble in such a solution and the equilibrium relation may be taken as Y = 2X, where Y is kmol of H2S kmol inert gas and X is kmol of H2S/kmol of solvent. The solvent enters the tower free of H2S and leaves containing 0.013 kmol of H2S/kmol of solvent. If the flow of inert hydrocarbon gas is 0.015 kmol/m2s of tower cross-section and the gas-phase resistance controls the process, calculate: (a) the height of the absorber necessary, and (b) the number of transfer units required. The overall coefficient for absorption K"Ga may be taken as 0.04 kmol/sm3 of tower volume (unit driving force in Y ).
(a) Z = 7.8 m (b) NOG = NTU = 21
A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m3/s and is delivered at atmospheric pressure. Calculate the pressure required to maintain this rate of flow under isothermal conditions. The volume occupied by 1 kmol at 273 K and 101.3 kN/m2 is 22.4 m3. What would be the effect on the required pressure if the gas were to be delivered at a height of 150 m (i) above, and (ii) below its point of entry into the pipe?
(i) P1 = 110.94 kN/m2 (ii) P1 = 111.26 kN/m2
A petroleum product of viscosity 0.5 m Ns/m2 and density 700 kg/m3 is pumped through a pipe of 0.15 m diameter to storage tanks situated 100 m away. The pressure drop along the pipe is 70 kN/m2. The pipeline has to be repaired and it is necessary to pump the liquid by an alternative route consisting of 70 m of 200 mm pipe followed by 50 m of 100 mm pipe. If the existing pump is capable of developing a pressure of 300 kN/m2, will it be suitable for use during the period required for the repairs? Take the roughness of the pipe surface as 0.05 mm.
-🔺Pf = 255.6 kN/m2 Thus the existing pump is satisfactory for this duty.
In a packed column, operating at approximately atmospheric pressure and 295 K, a 10% ammonia-air mixture is scrubbed with water and the concentration is reduced to 0.1%. If the whole of the resistance to mass transfer may be regarded as lying within a thin laminar film on the gas side of the gas-liquid interface, derive from first principles an expression for the rate of absorption at any position in the column. At some intermediate point where the ammonia concentration in the gas phase has been reduced to 5%, the partial pressure of ammonia in equilibrium with the aqueous solution is 660 N/m2 and the transfer rate is 103 kmol/m2s. What is the thickness of the hypothetical gas film if the diffusivity of ammonia in air is 0.24 cm2/s?
0.043 mm
A mixture of alcohol and water containing 0.45 mole fraction of alcohol is to be continuously distilled in a column to give a top product of 0.825 mole fraction alcohol and a liquor at the bottom containing 0.05 mole fraction alcohol. How many theoretical plates are required if the reflux ratio used is 3? Indicate on a diagram what is meant by the Murphree plate efficiency.
10 theoretical plates
Seeds, containing 20 per cent by mass of oil, are extracted in a countercurrent plant, and 90 per cent of the oil is recovered in a solution containing 50 per cent by mass of oil. If the seeds are extracted with fresh solvent and 1 kg of solution is removed in the underflow in association with every 2 kg of insoluble matter, how many ideal stages are required?
5 thickeners
A single effect evaporator operates at 13 kN/m2. What will be the heating surface necessary to concentrate 1.25 kg/s of 10 per cent caustic soda to 41 per cent, assuming a value of U of 1.25 kW/m2 K, using steam at 390 K? The heating surface is 1.2 m below the liquid level. The boiling-point rise of the solution is 30 deg K, the feed temperature is 291 K, the specific heat capacity of the feed is 4.0 kJ/kg deg K, the specific heat capacity of the product is 3.26 kJ/kg degK and the density of the boiling liquid is 1390 kg/m3.
A = 106.6 m2
A single-effect evaporator is used to concentrate 7 kg/s of a solution from 10 to 50 per cent of solids. Steam is available at 205 kN/m2 and evaporation takes place at 13.5 kN/m2. If the overall heat transfer coefficient is 3 kW/m2 K, calculate the heating surface required and the amount of steam used if the feed to the evaporator is at 294 K and the condensate leaves the heating space at 352.7 K. The specific heat capacity of a 10 per cent solution is 3.76 kJ/kgK, the specific heat capacity of a 50 per cent solution is 3.14 kJ/kg K.
A = 68.6 m2
A liquor containing 15 per cent solids is concentrated to 55 per cent solids in a doubleeffect evaporator operating at a pressure of 18 kN/m2 in the second effect. No crystals are formed. The feedrate is 2.5 kg/s at a temperature of 375 K with a specific heat capacity of 3.75 kJ/kgK. The boiling-point rise of the concentrated liquor is 6 degK and the pressure of the steam fed to the first effect is 240 kN/m2. The overall heat transfer coefficients in the first and second effects are 1.8 and 0.63 kW/m2 K, respectively. If the heat transfer area is to be the same in each effect, what areas should be specified?
Area in each effect = 67.5 m2
A forward-feed double-effect standard vertical evaporator with equal heating areas in each effect is fed with 5 kg/s of a liquor of specific heat capacity of 4.18 kJ/kgK, and with no boiling-point rise, so that 50 per cent of the feed liquor is evaporated. The overall heat transfer coefficient in the second effect is 75 per cent of that in the first effect. Steam is fed at 395 K and the boiling-point in the second effect is 373 K. The feed is heated to its boiling point by an external heater in the first effect. It is decided to bleed off 0.25 kg/s of vapour from the vapour line to the second effect for use in another process. If the feed is still heated to the boiling-point of the first effect by external means, what will be the change in the steam consumption of the evaporator unit? For the purposes of calculation, the latent heat of the vapours and of the live steam may be taken as 2230 kJ/kg.
Change in steam consumption = D0 = 1.33kg/s Increase of 0.12 kg/s
Caustic soda is manufactured by the lime-soda process. A solution of sodium carbonate in water containing 0.25 kg/s Na2CO3 is treated with the theoretical requirement of lime and, after the reaction is complete, the CaCO3 sludge, containing by mass 1 part of CaCO3 per 9 parts of water is fed continuously to three thickeners in series and is washed countercurrently. Calculate the necessary rate of feed of neutral water to the thickeners, so that the calcium carbonate, on drying, contains only 1 per cent of sodium hydroxide. The solid discharged from each thickener contains one part by mass of calcium carbonate to three of water. The concentrated wash liquid is mixed with the contents of the agitated before being fed to the first thickeners.
Feed = 0.23 kg/s
A solution of 5 per cent acetaldehyde in toluene is to be extracted with water in a five stage co-current unit. If 25 kg water/100 kg feed is used, what is the mass of acetaldehyde extracted and the final concentration? The equilibrium relation is given by: (kg acetaldehyde/kg water) = 2.20 (kg acetaldehyde/kg toluene)
Final Concentration = 0.536 per cent Mass of Acetaldehyde extracted = 4.489 kg/100 kg feed
A granular material containing 40 per cent moisture is fed to a countercurrent rotary dryer at a temperature of 295 K and is withdrawn at 305 K, containing 5 per cent moisture. The air supplied, which contains 0.006 kg water vapour/kg dry air, enters at 385 K and leaves at 310 K. The dryer handles 0.125 kg/s wet stock. Assuming that radiation losses amount to 20 kJ/kg dry air used, determine the mass flowrate of dry air supplied to the dryer and the humidity of the exit air. The latent heat of water vapour at 295 K = 2449 kJ/kg, specific heat capacity of dried material = 0.88 kJ/kg K, the specific heat capacity of dry air = 1.00 kJ/kg K, and the specific heat capacity of water vapour = 2.01 kJ/kg K.
G = 2.07 kg/s Humidity = 0.0284 kg/kg dry air
The heat required when 1 kmol of MgSO4.7H2O is dissolved isothermally at 291 K in a large mass of water is 13.3 MJ. What is the heat of crystallisation per unit mass of the salt?
Heat of crystallization = 53.9 kJ/kg
In the extraction of acetic acid from an aqueous solution with benzene a packed column of height 1.4 m and cross-sectional area 0.0045 m2, the concentrations measured at the inlet and the outlet of the column are: acid concentration in the inlet water phase, CW2 = 0.69 kmol/m3. acid concentration in the outlet water phase, CW1 = 0.684 kmol/m3. flowrate of benzene phase = 5.6 × 10−6 m3/s = 1.24 × 10−3 m3/m2s. inlet benzene phase concentration, CB1 = 0.0040 kmol/m3. outlet benzene phase concentration, CB2 = 0.0115 kmol/m3. Determine the overall transfer coefficient and the height of the transfer unit.
KBa = 7.66 × 10−4 kmol/sm3 (kmol/m3) HOB = 1.618 m
In the extraction of acetic acid from an aqueous solution with benzene in a packed column of height 1.4 m and of cross-sectional area 0.0045 m2, the concentrations measured at the inlet and outlet of the column are as shown in Figure 13.22. Determine the overall transfer coefficient and the height of the transfer unit. Acid concentration in inlet water phase, CW2 = 0.690 kmol/m3 Acid concentration in outlet water phase, CW1 = 0.685 kmol/m3 Flowrate of benzene phase = 5.7 cm3s or 1.27 × 10−3 m3/m2s Inlet benzene phase concentration, CB1 = 0.0040 kmol/m3 Outlet benzene phase concentration, CB2 = 0.0115 kmol/m3 The equilibrium relationship for this system is: C*B/C*W= 0.0247
KBa = 7.8 × 10−4 kmol/s m3(kmol/m3) HOB = 1.63 m
A rotary filter, operating at 0.03 Hz, filters at the rate of 0.0075 m3/s. Operating under the same vacuum and neglecting the resistance of the filter cloth, at what speed must the filter be operated to give a filtration rate of 0.0160 m3/s?
N2 = 0.136 Hz (7.2 rpm)
Sulphuric acid is pumped at 3 kg/s through a 60 m length of smooth 25 mm pipe. Calculate the drop in pressure. If the pressure drop falls by one half, what will be the new flowrate? Density of acid D 1840 kg/m3. Viscosity of acid D 25 mN s/m2.
New flowrate = 1.86 kg/s
600 litres/s of water at 320 K is pumped in a 40 mm i.d. pipe through a length of 150 m in a horizontal direction and up through a vertical height of 10 m. In the pipe there is a control valve which may be taken as equivalent to 200 pipe diameters and other pipe fittings equivalent to 60 pipe diameters. Also in the line there is a heat exchanger across which there is a loss in head of 1.5 m of water. If the main pipe has a roughness of 0.0002 m, what power must be delivered to the pump if the unit is 60% efficient?
Power Req = 128 W
In a synthetic ammonia plant the hydrogen is fed through a 50 mm steel pipe to the converters. The pressure drop over the 30 m length of pipe is 500 kN/m2, the pressure at the downstream end being 7.5 MN/m2. What power is required in order to overcome friction losses in the pipe? Assume isothermal expansion of the gas at 298 K. What error is introduced by assuming the gas to be an incompressible fluid of density equal to that at the mean pressure in the pipe? ϻ = 0.02 mNs/m2.
Power Requirement = 1.69 x 10^5 W or 169 kW
A 150 mm gas main is used for transferring gas (molecular weight 13 kg/kmol and kinematic viscosity 0.25 cm2/s) at 295 K from a plant to a storage station 100 m away, at a rate of 1 m3/s. Calculate the pressure drop if the pipe can be considered to be smooth. If the maximum permissible pressure drop is 10 kN/m2, is it possible to increase the flowrate by 25%?
Pressure Drop = 4.33 kN/m2
A centrifuge with a phosphor bronze basket, 380 mm in diameter, is to be run at 67 Hz with a 75 mm layer of liquid of density 1200 kg/m3 in the basket. What thickness of walls are required in the basket? The density of phosphor bronze is 8900 kg/m3 and the maximum safe stress for phosphor bronze is 87.6 MN/m2.
Wall thickness = 15.1 mm
In a mixture of quartz of density 2650 kg/m3 and galena of density 7500 kg/m3, the sizes of the particles range from 0.0052 to 0.025 mm. On separation in a hydraulic classifier under free settling conditions, three fractions are obtained, one consisting of quartz only, one a mixture of quartz and galena, and one of galena only. What are the ranges of sizes of particles of the two substances in the original mixture?
Size ranges = 0.0103-0.0126 mm
If a centrifuge is 0.9 m diameter and rotates at 20 Hz, at what speed should a laboratory centrifuge of 150 mm diameter be run if it is to duplicate the performance of the large unit?
Speed of Rotation = 49 Hz (2940 rpm)
The radiation received by the earth's surface on a clear day with the sun overhead is 1 kW/m2 and an additional 0.3 kW/m2 is absorbed by the earth's atmosphere. Calculate approximately the temperature of the sun, assuming its radius to be 700,000 km and the distance between the sun and the earth to be 150,000,000 km. The sun may be assumed to behave as a black body.
T = 5710 K
A liquid with no appreciable elevation of boiling-point is concentrated in a triple-effect evaporator. If the temperature of the steam to the first effect is 395 K and vacuum is applied to the third effect so that the boiling-point is 325 K, what are the approximate boiling-points in the three effects? The overall transfer coefficients may be taken as 3.1, 2.3, and 1.1 kW/m2 K in the three effects respectively.
T1 = 381.5 K T2 = 363.2 K T3 = 325 K
A wet solid is dried from 40 to 8 per cent moisture in 20 ks. If the critical and the equilibrium moisture contents are 15 and 4 per cent respectively, how long will it take to dry the solid to 5 per cent moisture under the some drying conditions? All moisture contents are on a dry basis.
Total Drying time = 28.48 ks (7.9 h)
Calculate the thickness of the laminar sub-layer when benzene flows through a pipe 50 mm in diameter at 2 1/s. What is the velocity of the benzene at the edge of the laminar sub-layer? Assume that fully developed flow exists within the pipe and that for benzene, p — 870 kg/m3 and /z = 0.7 mN s/m2.
Ub = 0.637 m/s
Glycerol is pumped from storage tanks to rail cars through a single 50 mm diameter main 10 m long, which must be used for all grades of glycerol. After the line has been used for commercial material, how much pure glycerol must be pumped before the issuing liquid contains not more than 1% of the commercial material? The flow in the pipeline is streamline and the two grades of glycerol have identical densities and viscosities.
Volume to be pumped = 0.10 m3
10 Mg of a solution containing 0.3 kg Na2CO3/kg solution is cooled slowly to 293 K to form crystals of Na2CO3.10H2O. What is the yield of crystals if the solubility of Na2CO3 at 293 K is 21.5 kg/100 kg water and during cooling 3 per cent of the original solution is lost by evaporation?
Yield of Crystals = 6536 kg
Calculate the thickness of the boundary layer at a distance of 150 mm from the leading edge of a surface over which oil, of viscosity 0.05 N s/m2 and density 1000 kg/m3 flows with a velocity of 0.3 m/s. What is the displacement thickness of the boundary layer?
displacement thickness = 8.7 mm
An open bowl, 0.3 m in diameter, contains water at 350 K evaporating into the atmosphere. If the air currents are sufficiently strong to remove the water vapour as it is formed and if the resistance to its mass transfer in air is equivalent to that of a 1 mm layer for conditions of molecular diffusion, what will be the rate of cooling due to evaporation? The water can be considered as well mixed and the water equivalent of the system is equal to 10 kg. The diffusivity of water vapour in air may be taken as 0.20 cm2/s and the kilogram molecular volume at NTP as 22.4 m3.
d⊖/dt = 0.026 deg K/s
A wetted-wall column is used for absorbing sulphur dioxide from air by means of a caustic soda solution. At an air flow of 2 kg/m2s, corresponding to a Reynolds number of 5160, the friction factor R/ρu2 is 0.0200. Calculate the mass transfer coefficient in kg SO2/s m2(kN/m2) under these conditions if the tower is at atmospheric pressure. At the temperature of absorption the following values may be used: The diffusion coefficient for SO2 = 0.116 × 10−4 m2/s, the viscosity of gas = 0.018 mNs/m2, and the density of gas stream = 1.154 kg/m3.
kG = 7.56 × 10−4 kg SO2/m2s(kN/m2)
In a countercurrent-flow heat exchanger, 1.25 kg/s of benzene (specific heat 1.9 kJ/kg K and density 880 kg/m3) is to be cooled from 350 K to 300 K with water which is available at 290 K. In the heat exchanger, tubes of 25 mm external and 22 mm internal diameter are employed and the water passes through the tubes. If the film coefficients for the water and benzene are 0.85 and 1.70 kW/m2 K respectively and the scale resistance can be neglected, what total length of tube will be required if the minimum quantity of water is to be used and its temperature is not to be allowed to rise above 320 K?
length of tubing required = (1302/0.0785) = 165.8 m
A still contains a liquor composition of o-xylene 10 per cent, m-xylene 65 per cent, pxylene 17 per cent, benzene 4 per cent and ethyl benzene 4 per cent. How many plates are required at total reflux to give a product of 80 per cent m-xylene, and 14 per cent p-xylene? The data are given as mass per cent.
n = 39 plates
Two tanks, the bottoms of which are at the same level, are connected with one another by a horizontal pipe 75 mm diameter and 300 m long. The pipe is bell-mouthed at each end so that losses on entry and exit are negligible. One tank is 7 m diameter and contains water to a depth of 7 m. The other tank is 5 m diameter and contains water to a depth of 3 m. If the tanks are connected to each other by means of the pipe, how long will it take before the water level in the larger tank has fallen to 6 m? Assume the pipe to be of aged mild steel.
t = 10590 s (2.94 h)
Strips of a material 10 mm thick are dried under constant drying conditions from 28 per cent to 13 per cent moisture in 25 ks. If the equilibrium moisture content is 7 per cent, what is the time taken to dry 60 mm planks from 22 to 10 per cent moisture under the same conditions, assuming no loss from the edges? All moisture contents are expressed on the wet basis. The relation between E, the ratio of the average free moisture content at time t to the initial free moisture content, and the parameter f is given by: E 1 0.64 0.49 0.38 0.295 0.22 0.14 f 0 0.1 0.2 0.3 0.5 0.6 0.7 where f = kt/l2, k is a constant, t is the time in ks and 2l is the thickness of the sheet of material in mm.
t = 1090ks = 12.6 days
A 100 kg batch of granular solids containing 30 per cent moisture is to be dried in a tray drier to 15.5 per cent of moisture by passing a current of air at 350 K tangentially across its surface at a velocity of 1.8 m/s. If the constant rate of drying under these conditions is 0.0007 kg/s m2 and the critical moisture content is 15 per cent, calculate the approximate drying time. Assume the drying surface to be 0.03 m2/kg dry mass.
t = 11.7 ks (3.25 h)
An aqueous suspension consisting of particles of density 2500 kg/m3 in the size range 1-10 μm is introduced into a centrifuge with a basket 450 mm diameter rotating at 80 Hz. If the suspension forms a layer 75 mm thick in the basket, approximately how long will it take for the smallest particle to settle out?
t = 19.3 s
A chamber, of volume 1 m3, contains air at a temperature of 293 K and a pressure of 101.3 kN/m2, with a partial pressure of water vapour of 0.8 kN/m2. A bowl of liquid with a free surface of 0.01 m2 and maintained at a temperature of 303 K is introduced into the chamber. How long will it take for the air to become 90% saturated at 293 K and how much water must be evaporated? The diffusivity of water vapour in air is 2.4 ð 105 m2/s and the mass transfer resistance is equivalent to that of a stagnant gas film of thickness 0.25 mm. Neglect the effects of bulk flow. Saturation vapour pressure of water D 4.3 kN/m2 at 303 K and 2.3 kN/m2 at 293 K.
t = 604 s = 10 min
A plate and frame press gave a total of 8 m3 of filtrate in 1800 s and 11.3 m3 in 3600 s when filtration was stopped. Estimate the washing time if 3 m3 of wash water is used. The resistance of the cloth may be neglected and a constant pressure is used throughout.
time of washing = 8400 s (2.3 h)
In a shell-and-tube type of heat exchanger with horizontal tubes 25 mm external diameter and 22 mm internal diameter, benzene is condensed on the outside of the tubes by means of water flowing through the tubes at the rate of 0.03 m3/s. If the water enters at 290 K and leaves at 300 K and the heat transfer coefficient on the water side is 850 W/m2 K, what total length of tubing will be required?
total length of tubing required = (41.3/0.0785) = 526 m
