Questions and Answers of Unit Operations Of Chemical Engineering

A vertical-tube two-pass heater is used for heating gas oil. Saturated steam at 100 lbƒ/in.2 gauge is used as a heating medium. The tubes are 1 in. OD by BWG 16 and are made of mild steel. The oil
A shell-and-tube exchanger is used to cool an aqueous stream from 95 to 30°C using cooling water at 20°C. If the flow rate of the cooling water is twice that of the process stream, would a higher
A steam-heated natural-circulation calandria is to be designed to boil 5,000 kg/h of chlorobenzene at atmospheric pressure. (a) Approximately how much heat-transfer surface will be required?(b) How
Liquid styrene at 60°C is being heated in a 2-m-diameter steam-jacketed kettle equipped with a standard six-blade turbine. (a) Calculate the film coefficient for the inside wall hj if the stirrer
The thickness of the laminar boundary layer on a flat plate Zx is approximately given by the equation Zx = 5.5[μx/(u∞ρ)]1/2. Show that at the transition to the turbulent flow the Reynolds number
(a) Estimate the transition length at the entrance to a 15-mm tube through which 100 percent glycerol at 60°C is flowing at a velocity of 0.3 m/s. The density of glycerol is 1.240 kg/m3.(b) Repeat
(a) Estimate the Reynolds number for flow in an automobile exhaust pipe if the 2-L 4-cycle engine is operating at 3,000 rpm. (b) If the catalytic converter has 4 times the cross section of the
Plot the viscosity of water, hexane, and 100 percent glycerol on semilog coordinates, and discuss how nearly the viscosity follows an Arrhenius relationship (μ = Ae-E/RT).
Plot the viscosity at moderate pressures of the halogen gases at 20°C versus their molecular weight. Make a similar plot for some of the normal paraffins, and discuss the trends shown by these plots.
Air at 30C and 5 bars, is flowing inside a ½-in. Schedule 40 steel pipe. If the flow is at 4.0 ft3/min at standard temperature and pressure (0°C and I atm), is the flow likely to be laminar or
Crude oil is pumped at 1.5 m/s through a pipeline 1 m in diameter. Above what value of the oil viscosity would laminar flow exist? Give your answer in both SI and cgs units.
The apparent viscosity of a non-newtonian liquid at a given shear rate is the value indicated by a viscometer operating on the liquid at that shear rate. It is the viscosity that would be indicated
Air at 3 atm and 100°C is flowing at 1.0 m/s in a 1.5-cm tube. Calculations indicate that the flow is laminar, with a Reynolds number very near the critical value. Would the flow become turbulent
A liquid is flowing in steady flow through a 75-mm pipe. The local velocity varies with distance from the pipe axis as shown in Table 4.1. Calculate (a) Average velocity V̅, (b) Kinetic energy
For a given fluid and a given distance between plates in a system like that shown in Fig. 4.5, velocity ν0 must be large enough to counteract the effect of gravity; other- wise, some of the fluid
A vertical cylinder 15 cm in diameter is placed inside and concentric with a cylinder 15.8 cm in diameter. Oil with a viscosity of 0.21 Pa-s fills the space between the cylinders. If the inner
(a) A water tank is 30 ft in diameter, and the normal depth is 25 ft. The outlet is a 4-in, horizontal pipe at the bottom. If this pipe is sheared off close to the tank, what is the initial flow rate
Water at 20°C is pumped at a constant rate of 9 m3/h from a large reservoir resting on the floor to the open top of an experimental absorption tower. The point of discharge is 5 m above the floor,
Water enters a 100-mm-ID 90° elbow, positioned in a horizontal plane, at a velocity of 6 m/s and a pressure of 70 kN/m2 gauge. Neglecting friction, what are the magnitude and the direction of the
A vertical cylindrical reactor 2.5 m in diameter and 4 m high is cooled by spraying water on the top and allowing the water to flow down the outside wall. The water flow rate is 0.15 m3/min, and the
An aqueous solution with a density of 1040 kg/m3 and a viscosity of 1.25 mPa-s is sprayed above the top of a column packed with 2.5 x 2.5 cm Raschig rings. The liquid flow rate is 4,500 kg/m2
A pump storage facility takes water from a river at night when demand is low and pumps it to a hilltop reservoir 500 ft above the river. The water is returned through turbines in the daytime to help
Prove that the flow of a liquid in laminar flow between infinite parallel flat plates is given by where L = length of plate in direction of flow b= distance between plates Neglect end effects.
The velocity profile in a fluid stream is approximated using a three-part model, where the velocity is 1.6 m/s in 15 percent of the cross-sectional area, 3.2 m/s in 35 percent of the area, and 4.5
For flow of water in a smooth 60-mm pipe at Re = 5 x 104. what is the thickness of the viscous sublayer? What fraction of the cross-sectional area of the pipe does this represent? About what fraction
A newtonian fluid is in laminar flow in a rectangular channel with a large aspect ratio. Derive the relationship between local and maximum velocity, and determine the ratio umax/V̅.
Calculate the power required per meter of width of stream to force lubricating oil through the gap between two horizontal flat plates under the following conditions:Distance between plates, 6 mmFlow
What would be the temperature rise in the oil from viscous dissipation under the conditions of Prob. 5.4 if the specific heat of the oil is 0.5 cal/g.°C and its density is 820 kg/m3?Prob.
A liquid with a specific gravity of 2.6 and a viscosity of 2.0 cP flows through a smooth pipe of unknown diameter, resulting in a pressure drop of 0.183 lbƒ/in.2 for 1.73 mi. What is the pipe
Water flows through an 8-in. steel pipe at an average velocity of 6 ft/s. Downstream the pipe divides into an 8-in. main and a 2-in. bypass. The equivalent length of the bypass is 22 ft; the length
A steel pipe 2 ft in diameter carries water at about 15 ft/s. If the pipe has a roughness of 0.0003 ft, could the capacity be increased by inserting a smooth plastic liner that reduces the inside
Water at 60°F is pumped from a reservoir to the top of a mountain through a 6-in. Schedule 120 pipe at an average velocity of 12 ft/s. The pipe discharges into the atmosphere at a level 3,000 ft
A reverse-osmosis unit for purifying brackish water has about 900,000 hollow fibers that permit the diffusion of water but reject most of the salt. The fibers are 85 μm in outside diameter, 42 μm
Chlorine gas leaving a reactor at 200°C and 1.5 atm with a flow of 4 lb/min is to be compressed and recycled to the reactor, where the pressure is 1.6 atm. The length of pipe needed is about 80 ft,
Exhaust gas from a power plant passes through a 15- by 20-ft rectangular duct at an average velocity of 50 ft/s. The total length of duct is 250 ft, and there are two 90° bends. The gas is at 180°F
A centrifugal pump takes brine from the bottom of a supply tank and delivers it into the bottom of another tank. The brine level in the discharge tank is 150 ft above that in the supply tank. The
Cooling water for a chemical plant must be pumped from a river 2,500 ft from the plant site. Preliminary design calls for a flow of 600 gal/min and 6-in. steel pipe. Calculate the pressure drop and
A fan draws air at rest and sends it through a 200- by 300-mm rectangular duct 45 m long. The air enters at 15°C and 750 mm Hg absolute pressure at a rate of 0.6 m3/s. What is the theoretical power
The laminar flow of a certain aqueous polystyrene sulfonate solution can be represented by the Ostwald-de Waele model with an exponent of 0.500. The solution is contained in a tank that is a vertical
A portion of a fire protection system can be modeled as a smooth tube with a diameter of 0.12 m, a length of 600 m, and a total drop in elevation of 12 m. End effects can be neglected. How much
(a) What is the maximum flow rate in gal/min through 120 ft of a 2.5-in. fire hose, if the pump discharge pressure is 125 lbƒ/in2. gauge? Assume the canvas hose is twice as rough as steel pipe. (b)
A device for chemical analysis of small amount of aqueous solution (a "lab on a chip") has channels 100 μm wide and 10 μm deep. With a solution viscosity of 1.3 cP and a density of 1,050 kg/m3,
Use the universal velocity distribution to calculate the ratio V̅/umax for Re = 104 ,105 and 106. Use the properties of water at 20°C to simplify the calculation. Compare your ratios with the
For flow in a chip with square channels 300 μm on a side, what fluid velocity, in m/s, corresponds to a Reynolds number of 10, if the fluid is water at 20°C? What if it is air at 70°C?
Gas from a municipal incinerator flows in a square duct 3 m on a side at 800°C and about 1 atm. The viscosity and density are close to the values for air at 800°C. (a) For a gas velocity of 4.0
For the inlet conditions of Example 6.2, what is the maximum length of pipe that may be used if the pipe is 2 in. in diameter? What is it for the inlet conditions of Example 6.3?Example 6.2Air flows
A divergent-convergent nozzle has the proportions shown in Table 6.1. Air (γ= 1.40, M= 29.0) enters the nozzle from a reservoir in which the pressure is 20 atm abs and the temperature is 550 K. Plot
Natural gas consisting essentially of methane is to be transported through a 20-in.-ID pipeline over flat terrain. Each pumping station increases the pressure to 100 lbƒ/in.2 abs, and the pressure
A standard 1-in. Schedule 40 horizontal steel pipe is used to conduct chlorine gas. The gas enters the pipe through a rounded entrance at a pressure of 6 atm abs, a temperature of 120°C, and a
Air at 25°C enters a section of 2-in. Schedule 40 steel pipe at a gauge pressure of 310 kN/m2 and a flow rate of 1,200 kg/h. Assuming isothermal flow, what is the pressure drop in 60 m of pipe?
Calculate the stagnation temperature for air flowing at 200°C and 1.5 atm if the velocity is 0.9 of the sonic velocity.
Air enters a 25-mm (1-in.) Schedule 40 steel pipe at 350 K and p = 5 x 105 N/m2. The velocity is 120 m/s. Assuming flow is adiabatic, for what length of pipe would the air leave at sonic velocity?
Calculate the source pressure required to deliver 13 x 106 standard cubic feet per day (SCFD) of CO to a customer 60 mi. away. By contract the pressure at the customer's site must be at least 300
A partial oxidation is carried out by passing air with 1.2 mole percent (mol %) hydrocarbon through 40-mm tubes packed with 2 m of 3-mm by 3-mm cylindrical catalyst pellets. The air enters at 350°C
A catalyst tower 40 ft high and 18 ft in diameter is packed with 1-in.-diameter spheres. Gas enters the top of the bed at a temperature of 450°F and leaves at the same temperature. The pressure at
The pressure drop for airflow through a column filled with 1-in. ceramic Raschig rings is 0.01 in. water per foot when Go = 80 lb/ft2 - h and 0.9 in./ft water when Go = 800 lb/ft2 . h, all for a mass
The following data are reported for the flow of air through beds of granular activated carbon. Compare the pressure drops with values predicted using the Ergun equation, and predict the pressure
How long will it take for the spherical particles in Table 7.3 to settle, at their terminal velocities under free-settling conditions, through 2 m of water at 20°C?Table 7.3 TABLE 7.3 Data for Prob.
The pressure drop through a particle bed can be used to determine the external sur- face area and the average particle size. Data for a bed of crushed ore particles show Δp/L = 84 (lbƒ/in.2)/ft for
A 150-mm-thick demister pad for removing fine droplets of H2SO4 from a gas stream is made of 50-μm fibers randomly oriented in the plane perpendicular to the gas flow. The average porosity is 0.90.
A cyclone separator is used to remove sand grains from an airstream at 150°C. If the cyclone body is 0.6 m in diameter and the average tangential velocity is 16 m/s, what is the radial velocity near
Urea pellets are made by spraying drops of molten urea into cold gas at the top of a tall tower and allowing the material to solidify as it falls. Pellets 6 mm in diameter are to be made in a tower
Catalyst pellets 5 mm in diameter are to be fluidized with 45,000 kg/h of air at 1 atm and 80°C in a vertical cylindrical vessel. The density of the catalyst particles is 960 kg/m3; their sphericity
According to a brochure from Dow Chemical Company, the pressure drop for water flowing through a bed of 20-mesh to 50-mesh Dowex 50-X8 resin is said to be proportional to the flow rate and has a
In backwashing a bed of 20-mesh to 50-mesh Dowex 50-X8 resin, the bed starts to expand when the flow rate reaches 0.4 gal/min · ft2 and has expanded 45 percent at 6 gal/min · ft2. Are these values
In a process for removing SO2 from flue gas, gas at 410°C and 1.2 atm is passed upward through a fluidized bed containing 1.5-mm spherical particles of Al2O3 impregnated with copper. The particle
Make a preliminary estimate of the approximate pipe size required for the following services: (a) A transcontinental pipeline to carry 250,000 std m3/h of natural gas at 20 atm abs and 20°C;(b)
It is proposed to pump 10,000 kg/h of toluene at 114°C and 1.1 atm abs pressure from the reboiler of a distillation tower to a second distillation unit without cooling the toluene before it enters
Calculate the power required to drive the pump in Prob. 8.2 if the pump is to elevate the toluene 10 m, the pressure in the second unit is atmospheric, and the friction loss in the discharge line is
Air entering at 70°F and atmospheric pressure is to be compressed to 4,000 lbƒ/in.2 gauge in a reciprocating compressor at the rate of 125 std ft3/min. If the compression ratio is the same in each
What is the discharge temperature of the air from the first stage in Prob. 8.4?Problem 8.4Air entering at 70°F and atmospheric pressure is to be compressed to 4,000 lbƒ/in.2 gauge in a
After the installation of the orifice meter of Example 8.4, the manometer reading at a definite constant flow rate is 45 mm. Calculate the flow through the line in m3/h measured at 15°C.Exercise
Natural gas having a specific gravity relative to air of 0.60 and a viscosity of 0.011 cP is flowing through a 6-in. Schedule 40 pipe in which is installed a standard sharp-edged orifice equipped
A horizontal venturi meter having a throat diameter of 20 mm is set in a 75-mm-ID pipeline. Water at 15°C is flowing through the line. A manometer containing mercury under water measures the
A V-element meter is used to measure the flow of a 15 percent slurry of ion-exchange beads in water. The slurry is carried in a 3-in. Schedule 40 pipe, and the expected range of flows is 30 to 150
The mass flow rate of flue gas in a 1.2-m by 2-m rectangular duct is to be measured using a thermal meter. The normal gas composition is 76 percent N2. 3 percent O2. 14 percent CO2, and 7 percent
Ammonia at 10°C and 1 atm is compressed to 5 atm in a single-stage adiabatic compressor. The flow rate is 50 kg/h. (a) Calculate the exit temperature and the power required for an ideal compressor.
A gas with a specific heat of 9.2 cal/mol · °C is compressed from 25°C and 1 atm to 8 atm in a single-stage adiabatic compressor that is 75 percent efficient. (a) What is the work done per mole
Show that the equation for the power needed for adiabatic compression reduces to the equation for isothermal compression as the pressure ratio pb/pa approaches 1.0.
A pitot tube is installed at the center of a large duct to measure the flow rate of a gas containing about 20 percent CO2 and 80 percent air at 250°C and 1.1 atm. (a) What is the gas velocity at
A rotameter has a linearly tapered tube with a diameter at the bottom about equal to the float diameter. Assume a constant drag coefficient and derive the relationship that shows why the flow is
A tank 1.2 m in diameter and 2 m high is filled to a depth of 1.2 m with a latex having a viscosity of 10 P and a density of 800 kg/m3. The tank is not baffled. A three-blade 360-mm-diameter
What is the maximum speed at which the agitator of the tank described in Prob. 9.1 day be driven if the liquid is replaced by one having a viscosity of 1 P and the same density?Prob. 9.1A tank 1.2 m
What power is required for the mixing operation of Prob. 9.1 if a propeller 360 mm in diameter turning at 15 r/s is used and if four baffles, each 120 mm wide, are installed?Prob. 9.1A tank 1.2 m in
The propeller in Prob. 9.1 is replaced with a six-blade turbine 400 mm in diameter, and the fluid to be agitated is a pseudoplastic power law liquid having an apparent viscosity of 15 P when the
A mixing time of 29 s was measured for a 4.5-ft baffled tank with a 1.5-ft six-blade turbine and a liquid depth of 4.8 ft. The turbine speed was 75 r/min, and the fluid has a viscosity of 3 cP and a
A pilot-plant reactor, a scale model of a production unit, is of such size that I g charged to the pilot-plant reactor is equivalent to 500 g of the same material charged to the production unit. The
A stirred tank reactor 3 ft in diameter with a 12-in. flat-blade turbine has been used for a batch reaction in which the blending time of added reagents is considered critical. Satisfactory results
A six-blade disk turbine (Da = 3 ft) is used to disperse hydrogen gas into a slurry reactor containing methyl linoleate at 90°C and 60 lbƒ/in.2 gauge with 1 percent suspended catalyst particles
For the conditions of Prob. 9.8, estimate the power required for complete suspension of the catalyst.Prob. 9.8A six-blade disk turbine (Da = 3 ft) is used to disperse hydrogen gas into a slurry
A reaction in which the product forms a crystalline solid has been studied in a 1-ft-diameter pilot-plant reactor equipped with a 4-in. six-blade turbine with curved blades. At stirrer speeds less
Gaseous ethylene (C2H4) is to be dispersed in water in a turbine-agitated vessel at 110°C and an absolute pressure of 3 atm. The vessel is 3 m in diameter with a maximum liquid depth of 3 m. For a
In the scaleup of a stirred-tank process involving a shear-sensitive suspension, it is important to keep the maximum shear rate below a critical value. (a) If scaleup requires a 10-fold increase in
For a helical-element static mixer with flow at a low Reynolds number, (a) How much of an increase in pressure drop would be expected over that for a straight pipe because of the decrease in
Repeat Problem 9.15 for Re> 2,000.Prob. 9.15For a helical-element static mixer with flow at a low Reynolds number, (a) How much of an increase in pressure drop would be expected over that for a
A cylindrical tank 2.4 m in diameter with a normal liquid depth of 3.5 m is equipped with a 0.8-m HE-3 impeller. The liquid density is 980 kg/m3 and the viscosity is 25 P. When the impeller speed is
Estimate the blending time in a 2-L reactor with a six-blade turbine operating at 2,000 r/min, when the liquid in the reactor is chlorobenzene at 50°C. The turbine parameters are Da/Dt = 1/3 and
What might be the form of a correlation for the critical stirrer speed for particle suspension if the impeller speed is assumed to be a multiple of, or an exponential function of, the terminal
The Beattie-Bridgman equation, a famous equation of state for real gases, may be writtenEq. 1.61where a, A0, b, B0 and c are experimental constants and ν is the molar volume, 1/g mol. (a) Show that
A mixture of 25 percent ammonia gas and 75 percent air (dry basis) is passed upward through a vertical scrubbing tower, to the top of which water is pumped. Scrubbed gas containing 0.5 percent

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