Questions and Answers of Unit Operations Of Chemical Engineering

An aqueous solution of a volatile component A containing 7.94 mol % A preheated to its boiling point is to be fed to the top of a continuous stripping column operated at atmospheric pressure. Vapor
A tower containing six ideal plates, a reboiler, and a total condenser is used to separate, partially, oxygen from air at 65 lbƒ/in.2 gauge. It is desired to operate at reflux ratio (reflux to
A rectifying column containing the equivalent of three ideal plates is to be supplied continuously with a feed consisting of 0.4 mol % ammonia and 99.6 mol % water Before entering the column, the
It is desired to produce an overhead product containing 80 mol % benzene from a feed mixture of 68 mol % benzene and 32 mol % toluene. The following methods are considered for this operation. All are
The operation of a fractionating column is circumscribed by two limiting reflux ratios: one corresponding to the use of an infinite number of plates and the other a total reflux, or infinite reflux,
A laboratory still is charged with 10 L of a methanol-water mixture containing 0.70 mole fraction methanol. This is to be distilled batchwise without reflux at 1 atm pressure until 5 L of liquid
A solution containing 10 g/L of a valuable protein and 1 g/L of a protein impurity is extracted in a stirred vessel using an organic solvent. Distribution coefficient K = 8 for the valuable protein
To show the effect of particle-size distribution on the rate of extraction, consider an oil-containing solid containing some particles half the average size and some 15 times the average size (say 25
An organic solute is to be extracted from a dilute aqueous solution using a solvent with a distribution coefficient of 6.8. For a continuous counterflow extractor, bow many ideal stages are needed if
Wastewater from a 750-m3 tank flows by gravity through a 150-mm steel pipe 1,000 m long that ends 15 m below the bottom of the tank. If the normal tank depth is 3.5 m, what is the discharge rate, in
From the following data, calculate the drag coefficients for benzene drops rising through water. Plot the results against the Reynolds number and compare with the drag coefficients for solid spheres.
Spherical particles 1 mm in diameter are to be fluidized with water at twice the minimum velocity. The particles have an internal porosity of 40 percent, an average pore diameter of 10 μm, and a
A 15 percent slurry of 20- to 28-mesh limestone in water is to be kept in suspension in a 20-ft-diameter tank using a six-blade 45° turbine.(a) If Da / Dt = 1/3 and W/Da = 0.2, what stirrer speed
A partial oxidation is carried out by bubbling air through an organic solution in a baffled laboratory reactor 12 cm in diameter with a liquid depth of 15 cm. The stirrer is a 6-blade turbine 6 cm in
A stirred hydrogenation reactor 1.5 m in diameter with a liquid depth of 1.8 m is equipped with a 0.5-m six-blade turbine. The liquid viscosity is 2.3 cP and the density is 950 kg/m3. The catalyst is
A furnace wall consists of 200 mm of refractory fireclay brick, 100 mm of kaolin brick, and 6 mm of steel plate. The fire side of the refractory is at 1.150°C, and the outside of the steel is at
A standard 1-in. Schedule 40 steel pipe carries saturated steam at 250°F. The pipe is lagged (insulated) with a 2-in, layer of 85 percent magnesia pipe covering, and out-side this magnesia there is
Derive the equation for steady-state heat transfer through a spherical shell of inner radius r1 and outer radius r2. Arrange the result for easy comparison with the solution for a thick-walled
A very long, wide sheet of plastic 4 mm thick and initially at 20°C is suddenly exposed on both sides to an atmosphere of steam at 102°C. (a) If there is negligible thermal resistance between the
A long steel rod 1 in. in diameter is initially at a uniform temperature of 1.200°F. It is suddenly immersed in a quenching bath of oil at 150°F. In 4 min its average temperature drops to 250°F.
Steel spheres 3 in. in diameter heated to 700°F are to be cooled by immersion in an oil bath at 125°F. If there is negligible thermal resistance between the oil and the steel surfaces, (a)
For the same initial temperatures Ts and Ta and at the same Fourier number, would the average temperature of a sphere be higher or lower than that of a cylinder or a slab? (See Fig. 10.5.) What are
Under the conditions described in Example 10.6, what is the average rate of heat loss per unit area from the ground to the air during the 12-h period? The thermal conductivity of soil is 0.7
The heat-transfer rate to the jacket of an agitated polymerization kettle is 7.4 kW/m2 when the polymerization temperature is 50°C and the water in the jacket is at 20°C. The kettle is made of
(a) Compare the thermal conductivities and thermal diffusivities of air and water at 100°F. (b) Calculate the penetration distances in a stagnant mass of air and one of water, at 50°F and 1 atm,
An oil storage tank has 20-mm steel walls covered with 50 mm of fiberglass insulation. If the oil temperature is kept at 150°C, (a) What is the rate of heat loss when the outside temperature is
An incinerator with 1/2-in. steel walls is lined with 4 in. of firebrick to protect the steel and has 3 in. of magnesia insulation on the outside. When the gas temperature is 1,400°F, the inside
Show that for a given Biot number, the approximate unaccomplished temperature change for a sphere given by Eq. (10.32) can be expressed as a function of Fo and Bi. Compare the values found from the
Particles of coal about 50 micrometers (μm) in size are injected into a stream of air at 300°C that carries them to a boiler. How long will it take to heat the particles from 25°C to within 5°C
A slab of polymer 1.6 cm thick, originally at 30°C, is heated between steel plates with a surface temperature of 70°C. The density of the solid is 950 kg/m3, its thermal conductivity is 0.12 W/m ·
A thermopane window has two panes of glass 3 mm thick separated by a space of 1 cm. How much difference would it make in the overall heat transfer coefficient if the space were filled with argon
The temperature of a flowing gas stream is measured using a bare thermocouple. which is a spherical metal bead 1.2 mm in diameter. The properties of the metal are: ρ = 8,000 kg/m3, cp = 450 J/kg ·
Sketch the temperature gradients in and near a slab being cooled by immersion in a flowing liquid, when the thermal conductivity of the solid is twice that of the liquid. Show typical gradients for a
Calculate the overall heat-transfer coefficients based on both inside and outside areas for the following cases. Case 1 Water at 10°C flowing in a 3/4-in. 16 BWG condenser tube and saturated
Aniline is to be cooled from 200 to 150°F in a double-pipe heat exchanger having a total outside area of 70 ft2. For cooling, a stream of toluene amounting to 8,600 lb/h at a temperature of 100°F
In the exchanger described in Prob. 11.3, how much aniline can be cooled if the overall heal-transfer coefficient is 70 Btu/ft2 · h · F?Prob. 11.3Aniline is to be cooled from 200 to 150°F in a
Carbon tetrachloride flowing at 19.000 kg/h is to be cooled from 85 to 40°C using 13.500 kg/h of cooling water at 20°C. The film coefficient for carbon tetrachloride, outside the tubes, is 1,700
In a double-pipe heat exchanger used to cool a slurry, the overall coefficient Ui is 1.84 kW/m2 · °C. Water flows in the inner pipe, which is 1-in. Schedule 40 steel pipe; the slurry flows in the
A tubular condenser with 120 3/4-in. BWG 16 copper tubes 8 ft long condenses 22,100 lb/h of saturated steam at 120°C using 870 gal/min of cooling water. The measured inlet and exit water
In a counterflow heat exchanger, the hot stream is cooled from 120 to 30°C while the cold stream temperature changes from 20 to 60°C. If the same exchanger were operated with parallel flow, what
An organic vapor is to be condensed at 80°C and 1.2 atm in a water-cooled condenser, and the condensed organic liquid cooled to 35°C in the same condenser. Cooling water is available at 25°C, and
A hot stream is cooled from 200°C to 60°C in a counterflow exchanger using water that enters at 20°C and leaves at 55°C. The overall coefficient at the warm end of the exchanger is 800 W/m2 ·
A counterflow shell-and-tube exchanger is used to cool 2.500 kg/h of oil from 160°C to a temperature below 80°C. Cooling water enters the tubes at 20°C at a flow rate of 4.000 kg/h. The predicted
For the conditions of Problem 11.10, estimate the outlet temperatures allowing for fouling factors of 4.000 W/m2 · °C on both sides of the tubes.Prob. 11.10A counterflow shell-and-tube exchanger is
An aqueous solution with a boiling point 3°C above that of water is heated and partially vaporized in the tubes of a shell-and-tube exchanger. Steam on the shell side of the exchanger is at 1.70 atm
Benzene vapor at 100°C is cooled and condensed at atmospheric pressure in a shell-and-tube exchanger. The cooling water enters at 20°C and leaves at 45°C. For countercurrent flow, calculate
Oil at 50°F is heated in a horizontal 2-in. Schedule 40 steel pipe 60 ft long having a surface temperature of 120°F. The oil flow rate is 150 gal/h at inlet temperature. What will be the oil
Repeat Problem 11.14 for parallel flow in the exchanger and discuss the differences between parallel and countercurrent flow.Prob. 11.14Benzene vapor at 100°C is cooled and condensed at atmospheric
Glycerin is flowing at the rate of 700 kg/h through a 30-mm-ID pipe. It enters a heated section 2.5 m long, the walls of which are at a uniform temperature of 115°C. The temperature of the glycerin
Oil is flowing through a 75-mm-ID iron pipe at 1 m/s. It is being heated by steam out-side the pipe, and the steam-film coefficient may be taken as 11 kW/m2 · C. At a particular point along the
Kerosene is heated by hot water in a shell-and-tube heater. The kerosene is inside the tubes, and the water is outside. The flow is countercurrent. The average temperature of the kerosene is 110°F,
Assume that the kerosene of Prob. 12.4 is replaced with water at 110ºF and flowing at a velocity of 8 ft/s. What percentage increase in overall coefficient may be expected if the tube surfaces
Both surfaces of the tube of Prob. 12.5 become fouled with deposits from the water. The fouling factors are 330 on the inside and 200 on the outside surfaces, both in Btu/ft2 · h · °F. What
From the Colburn analogy, how much would the heat-transfer coefficient inside a 1-in. Schedule 40 steel pipe differ from that inside a 1-in. BWG 16 copper tube if the same fluid were flowing in each
Water must be heated from 15 to 50°C in a simple double-pipe heat exchanger at a rate of 3,500 kg/h. The water is flowing inside the inner tube with steam condensing at 110°C on the outside. The
Since the Prandtl number and the heat capacity of air are nearly independent of temperature, Eq. (12.34) seems to indicate that hi for air increases with μ0.2(a) Explain this anomaly and determine
Air is flowing through a steam-heated tubular heater under such conditions that the steam and wall resistances are negligible in comparison with the air-side resistance. Assuming that each of the
A sodium-potassium alloy (78 percent K) is to be circulated through 1/2-in.-ID tubes in a reactor core for cooling. The liquid-metal inlet temperature and velocity are to be 580°F and 32 ft/s. If
In a catalytic cracking regenerator, catalyst particles at 600°C are injected into air at 700°C in a fluidized bed. Neglecting the chemical reaction, how long will it take for a 50·μm particle to
In a pilot plant, a viscous oil is being cooled from 200 to 110°C in a 1.0-in. jacketed pipe with water flowing in the jacket at an average temperature of 30°C. To get greater cooling of the oil,
In the manufacture of nitric acid, air containing 10 percent ammonia is passed through a pack of fine-mesh wire screens of Pt/Rh alloy. (a) Calculate the heat- transfer coefficient for air at 500°C
Water at 15°C is flowing at right angles across a heated 25-mm-OD cylinder, the surface temperature of which is 120°C. The approach velocity of the water is 1 m/s. (a) What is the heat flux, in
Water is heated from 15 to 65°C in a steam-heated horizontal 50-mm-ID tube. The steam temperature is 120°C. The average Reynolds number of the water is 45. The individual coefficient of the water
A large tank of water is heated by natural convection from submerged horizontal steam pipes. The pipes are 3-in. Schedule 40 steel. When the steam pressure is atmospheric and the water temperature is
(a) Compare the film coefficients for heat transfer to water and to oil flowing at 1 m/s in a 10-cm pipe at about 50°C. Assume the oil has the properties given in Table 12.5.(b) Show that the ratio
(a) Calculate the overall coefficient U for heat transfer through a vertical glass window from a room at 70°F to still air at 0°F. Assume that a single pane of glass is 1/8 in. thick and 4 ft
How does U for a thermopane window depend on the spacing between the panes?
Air at 1 atm and 20°C flows at 10 m/s past a horizontal flat plate which has a surface temperature of 80°C. The length of the plate is 1.6 m. (a) Calculate the average heat flux in W/m2 and the
(a) If the Sieder-Tate equation were used to predict the coefficients for air in turbufent flow at 200°C, how much difference would there be in the coefficients for heating and for cooling if ΔT =
An organic liquid flows at 25 cm/s through a heated tube 1.5 cm in diameter and 15 cm long. The liquid properties are: ρ 900 kg/m3, μ = 1.7 cP, k = 0.135 W/m·°C, and = Cp 2.0 J/g · °C. (a)
A 1-in. BWG 14 copper condenser tube, 3 m long, is to condense ethyl alcohol at atmospheric pressure. Cooling water inside the tube keeps the metal surface at an essentially constant temperature of
A study of heat transmission from condensing steam to cooling water in a single-tube condenser gave results for both clean and fouled tubes. For each tube the overall co-efficient U was determined at
A vertical tubular condenser is to be used to condense 2,100 kg/h of ethyl alcohol. which enters at atmospheric pressure. Cooling water is to flow through the tubes at an average temperature of
A horizontal shell-and-tube condenser is to be used to condense saturated ammonia vapor at 145 lbƒ/in.2 abs (Th = 82°F). The condenser has 19 steel tubes (1.5-in. OD 1.3-in. ID) 14 ft long through
A 25-mm-OD copper tube is to be used to boil water at atmospheric pressure. (a) Estimate the maximum heat flux obtainable as the temperature of the copper surface is increased. (b) If the
Steam containing 2 percent air is condensed at atmospheric pressure inside 25-mm tubes in a water-cooled condenser. The vertical tubes are 3 m long; the coefficient and temperature of the cooling
(a) Calculate the heat-transfer coefficient for film boiling of water at 1 atm on submerged horizontal tubes. 1/2, 1, and 2 in. in diameter, with a surface temperature of 180°C. (b) How does the
Benzene vapor is condensed at atmospheric pressure in a shell-and-tube condenser with horizontal 7/8-in. BWG 16 copper tubes, Predict the film coefficient for the top row of tubes and the average
At a low overall ΔT the boiling heat flux for a tube bundle is about 4 times that for a single tube, but at a high ΔT the flux is much lower than that for a single tube. Give a logical explanation
Saturated steam at 1.2 lbƒ/in.2 is condensed on the outside of 3/4-in. horizontal steel tubes. Cooling water enters the tubes at 60°F and leaves at 75°F at a velocity of 6 ft/s. What are the film
A plant uses methyl isobutyl ketone (MIBK) as a solvent and discharges a gas stream containing 0.25 percent MIBK at 70°C and 1 atm. The melting point of MIBK is -85°C. (a) What fraction of the
In answering questions such as those in Problem 13.13. why is it important to know the melting point of the condensing substance?Prob. 13.13A plant uses methyl isobutyl ketone (MIBK) as a solvent and
Determine the net heat transfer by radiation between two surfaces A and B. expressed as watts per square meter of area B, if the temperatures of A and B are 500 and 200°C, respectively, and the
The black flat roof of a building has an emissivity of 0.9 and an absorptivity of 0.8 for solar radiation. The sun beats down at midday with an intensity of 300 Btu/ft2·h. (a) If the temperature of
The roof of Prob. 14.2 is painted with an aluminum paint, which has an emissivity of 0.9 and an absorptivity for solar radiation of 0.5. What is the equilibrium temperature of the painted roof?Prob.
A 3-in. Schedule 40 iron pipeline carries steam at 6 atm gauge. The line is uninsulated and is 70 m long. The surrounding air is at 25°C. The emissivity of the pipe wall is 0.70. How many kilograms
A radiant heating system is installed in the plaster ceiling of a room 18 ft long by 18 ft wide by 8 ft high. The temperature of the concrete floor is maintained at 65°F. Assume that no heat flows
On a clear night, when the effective blackbody temperature of space is -70°C, the air is at 15°C and contains water vapor at a partial pressure equal to that of ice or liquid water at 0°C. A very
Air leaves a heat exchanger at about 300°C and 1.5 atm, and the temperature is measured using a thermocouple inside a 1/2-in.-diameter thermowell mounted normal to the airflow. If the gas velocity
In an uninsulated house, there is a 90-mm air gap between the plaster wall and the wood siding. When the inside wall is at 18°C and the outer wall at -9°C, what is the heat loss in watts per square
In boiling water at 1 atm pressure outside a stainless-steel tube with a surface temperature of 410°F, the heat-transfer coefficient h in the absence of radiation is 32 Btu/h·ft2·°F. If the
A greenhouse 20 m long and 15 m wide has a nearly flat roof 3 m above the floor level. When the sun is directly overhead the solar flux is 1,000 W/m2. If the glass roof has an emissivity of 0.9 and
In Problem 14.10, if the sun's rays are at 45° from the vertical, what is the greenhouse temperature?Prob. 14.10A greenhouse 20 m long and 15 m wide has a nearly flat roof 3 m above the floor level.
Catalyst particles in the outer layer of a tubular reactor exchange heat with the wall by radiation as well as by convection (a) For 1/4-inch spherical catalyst beads at 390°C and a wall
Two large parallel plates are at temperatures T1 = 500 K and T2= 300 K. Their emissivities are ε1 = 0.85 and ε2 = 0.90. What is the radiant flux between the plates?
A polished aluminum sheet is placed between the plates of Problem 14.12 as a radiation shield. The emissivity of the aluminum is 0.1. How much does the shield lower the flux to plate 2?Prob. 14.12Two
Crude oil at the rate of 150,000 kg/h is to be heated from 20 to 57°C by heat exchange with the bottom product from a distillation unit. The product at 129,000 kg/h is to be cooled from 146 to
Air is blown at a rate of 3 m3/s (measured at 0°C and 1 atm) at right angles to a tube bank 10 pipes and 10 spaces wide and 10 rows deep. The length of each pipe is 3.5 m. The tubes are on
A petroleum oil having the properties given in Table 15.3 is to be heated in a horizontal multipass heater with steam at 60 lbƒ/in.2 gauge. The tubes are to be steel, 3/4-in. OD by BWG 16, and their
Compare the coefficients predicted by the Donohue equation [Eq. (15.6)] with those found from Eq. (12.63) for flow normal to a single cylinder. Can the difference be reconciled by considering the

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