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chemical engineering

Questions and Answers of Chemical Engineering

Tube Flow for the Oldroyd 6-Constant Model, find the mass flow rate for the steady flow in a long circular tube 6 using Eq. 8.5-3.
Chain Models with Rigid-Rod connectors read and discuss the following publications: M. Gottlieb, Computers in Chemistry, 1, 155-160 (1977); O. Has sager, J. Chem. Phys., 60, 2111-2124 (1974); X. J.
Prediction of thermal conductivities of gases at tow density, (a) Compute the thermal conductivity of argon at 100°C and atmospheric pressure, using the Chapman-Enskog theory and the
Computation of the Prandtl numbers for gases at low density. (a) By using the Eucken formula and experimental heat capacity data, estimate the Prandtl number at 1atm and 300K for each of the
Estimation of the thermal conductivity of a dense gas, predict the thermal conductivity of methane at 110.4atm and 127°F by the following methods: (a) Use Fig. 9.2-1. Obtain the necessary
Prediction of the thermal conductivity of a gas mixture, calculate the thermal conductivity of a mixture containing 20 mole % CO2 and 80 mole % H2 at 1atm and 300K. Use the data of Problem 9A.2 for
Estimation of the thermal conductivity of a pure the thermal conductivity of liquid H2O at 40°C and 40megabars pressure (1megabar = 106dyn/cm2). The isothermal compressibility, (1/p) (∂p/∂p)τ,
Calculation of the Lorenz number, (a) Application of kinetic theory to the "electron gas" in a metal3 gives for the Lorenz number L = π2/3(K/e)2 in which K is the Boltzmann constant and e is
Corroboration of the Wiedemann-Franz-Lorenz law, given the following experimental data at 20oC for pure metals, compute the corresponding values of the Lorenz number, L, defined in Eq. 9.5-1.
Thermal conductivity and Prandtl number of a polyatomic gas. (a) Estimate the thermal conductivity of CH4 at 1500K and 1.37 atm. The molar heat capacity at constant pressure4 at 1500K is 20.71
Thermal conductivity of gaseous chlorine, use Eq. 9.3-15 to calculate the thermal conductivity of gaseous chlorine. To do this you will need to use Eq. 1.4-14 to estimate the viscosity, and will also
Thermal conductivity of chlorine-air mixtures, Using Eq. 9.3-17, predict thermal conductivities of chlorine-air mixtures at 297K and 1 arm for the following mole fractions of chlorine: 0.25, 0.50,
Calculation of molecular diameters from transport properties(a) Determine the molecular diameter d for argon from Eq. 1.4-9 and the experimental viscosity given in Problem 9A.2. (b) Repeat part
Heat loss from an insulated pipe, a standard schedule 40, 2-in. steel pipe (inside diameter 2.067 in. and wall thickness 0.154 in.) carrying steam is insulated with 2 in. of 85% magnesia covered in
Heat loss from a rectangular fin calculates the heat loss from a rectangular fin (see Fig. 10.7-1) for the following conditions: Air temperature
Maximum temperature in a lubricant, oil is acting as a lubricant for a pair of cylindrical surfaces such as those shown in Fig. 10.4-1. The angular velocity of the outer cylinder is 7908 rpm. The
Current-carrying capacity of wire, a copper wire of 0.040 in. diameter is insulated uniformly with plastic to an outer diameter of 0.12 in. and is exposed to surroundings at 100°F. The heat transfer
Free convection velocity. (a) Verify the expression for the average velocity in the upward-moving stream in Eq. 10.9-16. (b) Evaluate β for the conditions given below. (c) What is the
Insulating power of a wall (Fig. 10A.6), the "insulating power" of a wall can be measured by means of the arrangement shown in the figure One places a plastic panel against the wall. In the panel two
Viscous heating in a ball-point pen, you are asked to decide whether the apparent decrease in viscosity in ball-point pen inks during writing results from "shear thinning" (decrease in viscosity
Temperature rise in an electrical wire. (a) A copper wire, 5 mm in diameter and 15 ft long, has a voltage drop of 0.6 volts. Find the maximum temperature in the wire if the ambient air
Heat conduction from a sphere to a stagnant fluid, a heated sphere of radius R is suspended in a large, motionless body of fluid. It is desired to study the heat conduction in the fluid surrounding
Viscous heating in slit flow, find the temperature profile for the viscous heating problem shown in Fig. 10.4-2, when given the following boundary conditions: at x = 0, T = T0; at x - b, qr = 0.
Heat conduction in a nuclear fuel rod assembly (Fig. 10B.3) considers a long cylindrical nuclear fuel rod, surrounded by an annular layer of aluminum cladding. Within the fuel rod heat is produced by
Heat conduction in an annulus (Fig. 10B.4), (a) Heat is flowing through an annular wall of inside radius r0 and outside radius r1. The thermal conductivity varies linearly with temperature from
Viscous heat generation in a polymer melt rework the problem discussed in S10.4 for a molten polymer, whose viscosity can be adequately described by the power law model (see Chapter 8). Show that the
Insulation thickness for a furnace wall (Fig. 10B.6) a furnace wall consists of three layers: (i) a layer of heat-resistant or refractory brick, (ii) a layer of insulating brick, and (iii) a steel
Forced-convection heat transfer in flow between parallel plates (Fig. 10B.7), a viscous fluid with temperature-independent physical properties is in fully developed laminar flow between two flat
Electrical heating of a pipe (Fig. 10B.8), in the manufacture of glass-coated steel pipes, it is common practice first to heat the pipe to the melting range of glass and then to contact the hot pipe
Plug flow with forced-convection heat transfer. Very thick slurries and pastes sometimes move in channels almost as a solid plug. Thus, one can approximate the velocity by a constant value v0 over
Heat conduction with temperature-dependent thermal conductivity (Fig. 10B.12) the curved surfaces and the end surfaces (both shaded in the figure) of the solid in the shape of a half-cylindrical
Flow reactor with exponentially temperature-dependent source, formulate the function F(Θ) of Eq. 10.5-1 for a zero-order reaction with the temperature dependence Sc = ke-E/RT in which K and E are
Evaporation loss from an oxygen tank(a) Liquefied gases are sometimes stored in well-insulated spherical containers vented to the atmosphere. Develop an expression for the steady-state heat transfer
Radial temperature gradients in an annular chemical reactor a catalytic reaction is being carried out at constant pressure in a packed bed between coaxial cylindrical walls with inner radius r0 and
Temperature distribution in a hot-wire anemometer, a hot-wire anemometer is essentially a fine wire, usually made of platinum, which is heated electrically and exposed to a flowing fluid. Its
Temperature in a friction bearing, calculate the maximum temperature in the friction bearing of Problem 3Aol, assuming the thermal conductivity of the lubricant to be 4.0 x 10-4 cal/s ∙ cm ∙ C,
Viscosity variation and velocity gradients in a non isothermal film, water is falling down a vertical wall in a film 0.1 mm thick. The water temperature is 100°C at the free liquid surface and 80°C
Transpiration cooling (a) Calculate the temperature distribution between the two shells of Example 11.4-4 for radial mass flow rates of zero and 10 -5 g/s for the following conditions:(b)
Free-convection heat loss from a vertical surface, a small heating panel consists essentially of a flat, vertical, rectangular surface 30 cm high and 50 cm wide. Estimate the total rate of heat loss
Velocity, temperature, and pressure changes in a shock wave, air at 1 arm and 70°F is flowing at an upstream Mach number of 2 across a stationary shock wave. Calculate the following quantities,
Adiabatic frictionless compression of an ideal gas, calculate the temperature attained by compressing air, initially at 100°F and 1atm, to 0.1 of its initial volume. It is assumed that γ = 1.40 and
Effect of free convection on the insulating value of a horizontal air space, two large parallel horizontal metal plates are separated by a 2.5 cm air gap, with the air at an average temperature of
Adiabatic frictionless processes in an ideal gas (a) A gas that obeys the ideal gas law may deviate appreciably from Cp = constant. Hence rework Example 11.4-6 using a molar heat capacity
Heat conduction in a spherical shell (Fig. 11B.4), a spherical shell has inner and outer radii R1 and R2. A hole is made in the shell at the North Pole by cutting out the conical segment in the
Transpiration cooling in a planar system, two large flat porous horizontal plates is separated by a relatively small distance L. The upper plate at y = L is at temperature TL, and the lower one at y
Reduction of evaporation losses by transpiration (Fig. 11B.7), it is proposed to reduce the rate of evaporation of liquefied oxygen in small containers by taking advantage of transpiration. To do
Temperature distribution in an embedded sphere, a sphere of radius R and thermal conductivity k1 is embedded in an infinite solid of thermal conductivity k0. The center of the sphere is located at
Heat flow in a solid bounded by two conical surfaces (Fig. 11B.9). A solid object has the shape depicted in the figure. The conical surfaces θ1 = constant and θ2 = constant are held at temperatures
Freezing of a spherical drop (Figure 11B.10) to evaluate the performance of an atomizing nozzle, it is proposed to atomize a nonvolatile liquid wax into a stream of cool air. The atomized wax
Temperature rise in a spherical catalyst pellet (Fig. 11B.11) a catalyst pellet has a radius R and a thermal conductivity k (which may be assumed constant). Because of the chemical reaction occurring
Laminar annular flow with constant wall heat flux, repeat the development of S10.8 for flow in an annulus of inner and outer radii kR and R, respectively, starting with the equations of change. Heat
Dimensionless variables for free convection, the dimensionless variables in Eqs 11.4-39 to 43 can be obtained by simple arguments. The form of Θ is dictated by the boundary conditions and that of ζ
Free convection in a slot, a fluid of constant viscosity, with density given by Eq. 1 1.3-1, is confined in a rectangular slot. The slot has vertical walls at x = + B, y = + W, and a top and bottom
Tangential annular flow of a highly viscous liquid, show that Eq. 11.4-13 for flow in an annular region reduces to Eq. 10.4-9 for plane slit flow in the limit as ,c approaches unity. Comparisons of
Heat conduction with variable thermal conductivity (a) For steady-state heat conduction in solids, Eq. 11.2-5 becomes (∆ ∙ q) = 0, and insertion of Fourier's law gives (∆ ∙ k∆ T) = 0.
Effect of surface-tension gradients on a failing film (a) Repeat the determination of the shear-stress and velocity distributions of Example 2.1-1 in the presence of a small temperature gradient
Viscous heating in laminar tube flow (a) Continue the analysis begun in Problem 11B.2--namely, that of finding the temperature profiles in a NewtonJan fluid flowing in a circular tube at a speed
Derivation of the energy equation using integral theorems, in S11.1 the energy equation is derived by accounting for the energy changes occurring in a small rectangular volume element ∆x ∆y
Equation of change for entropy this problem is an introduction to the thermodynamics of irreversible processes. A treatment of multi component mixtures is given in SS24.1 and 2. (a) Write an
Unsteady-state heat conduction in an iron sphere, an iron sphere of 1-in. diameter has the following physical properties: k = 30 Btu/hr ∙ ft ∙ F, Cp = 0.12 Btu/lbm ∙ F. and p = 436lbm/ft3,
Comparison of the two slab solutions for short times, what error is made by using Eq. 12.1-8 (based on the semi-infinite slab) instead of Eq. 12.1-31 (based on the slab of finite thickness), when
Bonding with a thermo setting adhesive (Fig. 12A.3). it is desired to bond together two sheets of a solid material, each of thickness 0.77 cm. This is done by using a thin layer of thermosetting
Quenching of a steel billet, a cylindrical steel billet 1 ft in diameter and 3 ft long, initially at 1000°F, is quenched in oil. Assume that the surface of the billet is at 200°F during the
Measurement of thermal diffusivity from amplitude of temperature oscillations(a) It is desired to use the results of Example 12.1-3 to measure the thermal diffusivity a = k/pCp of a solid material.
Forced convection from a sphere in creeping flow, a sphere of diameter D, whose surface is maintained at a temperature T0, is located in a fluid stream approaching with a velocity v∞ and
Measurement of thermal diffusivity in an unsteady=state experiment. A solid slab, 1.90 cm thick, is brought to thermal equilibrium in a constant-temperature bath at 20.0°C. At a given °instant (t =
Heating of a wall {constant wall heat flux, A very thick solid wall is initially at the temperature T0. At time t = 0, a constant heat flux q0 is applied to one surface of the wall (at y = 0), and
Temperature in a slab with heat production, the slab of thermal conductivity k in Example 12.1-2 is initially at a temperature T0. For time t > 0 there is a uniform volume production of heat S0
Non-Newtonian heat transfers with constant wall heat flux (asymptotic solution for small axial distances), rework Example 12.2-2 for a fluid whose non-Newtonian behavior is described adequately by
Product solutions for unsteady heat conduction in solids (a) In Example 12.1-2 the unsteady state heat conduction equation is solved for a slab of thickness 2b. Show that the solution to Eq.
Heat transfer in a falling non-Newtonian film, repeat Problem 12B.4 for a polymeric fluid that is reasonably well described by the power law model of Eq. 8.3-3.
Unsteady-state heating of a slab (Laplace transform method) (a) Re-solve the problem in Example 12.1-2 by using the Laplace transform, and obtain the result in Eq. 12.1-31. (b) Note that
The Graetz problem for flow between parallel plates, work through ProNems 12D.2, 3, and 4 for flow between parallel plates (or flow in a thin rectangular duct)
The constant wall heat flux problem for parallel plates, apply the methods used in S10.8, Example 12.2-1, and Ex. 12.2-2 to the flow between parallel plates.
Forced conduction heat transfer from a flat plate (thermal boundary layer extends beyond the momentum boundary layer), show that the result analogous to Eq. 12.4-14 for ∆ > 1 is
Wall heat flux for turbulent flow in tubes (approximate), work through Example 13.3-1, and fill in the missing steps. In particular, verify the integration in going from Eq. 13.3-6 to Eq. 13.3-7.
Wall heat flux for turbulent flow in tubes(a) Summarize the assumptions in S13.4.(b) Work through the mathematical details of that section, taking particular care with the steps connecting Eq.
Constant Wall heat flux for turbulent flow between two parallel plates (a) Work through the development in S13.4, and then perform a similar derivation for turbulent flow in a thin slit shown in
The temperature profile for turbulent flow in tubes, to calculate the temperature distribution for turbulent flow in circular tubes from Eq. 13.4-12, it is necessary to know C2. (a) Show how to
Average heat transfer coefficients (Fig. 14A.1), Ten thousand pounds per hour of an oil with a heat capacity of 0.6 Btu/lbm F is being heated from 100°F to 200°F in the simple heat exchanger shown
Heat transfer in laminar tube flow, One hundred pounds per hour of oil at 100°F is flowing through a 1-in.i.d. Copper tube, 20ft long the inside surface of the tube is maintained at 215°F by
Effect of flow rate on exit temperature from a heat exchanger (a) Repeat parts (b) And (c) Of Problem 14A.2 for oil flow rates of 200, 400, 800, 1600, and 3200 lbm/hr.(b) Calculate the total
Local heat transfer coefficient for turbulent forced convection in a tube. Water is flowing in a 2-in.i.d tube at a mass flow rate w = 15,000 lbm/hr. The inner wall temperature at some point along
Heat transfer from condensing vapors. (a) The outer surface of a vertical tube I in. in outside diameter and 1 ft long is maintained at 190°F. If this tube is surrounded by saturated steam at I
Forced-convection heat transfer from an isolated sphere (a) A solid sphere 1 in. in diameter is placed in an otherwise undisturbed air stream, which approaches at a velocity of 100 ft/s, a
Free convection heat transfer from an isolated sphere. If the sphere of Problem 14A.6 is suspended in still air at 1atm pressure and 100°F ambient air temperature, and if the sphere surface is again
Heat loss by free convection from a horizontal pipe immersed in a liquid, estimate the rate of heat loss by free convection from a unit length of a long horizontal pipe, 6 in. in outside diameter, if
Local overall heat transfer coefficient. In Problem 14A.1 the thermal resistances of the condensed steam film and wall were neglected. Justify this neglect by calculating the actual inner-surface
Limiting local Nusselt number for plug flow with constant heat flux(a) Equation 10B.9-1 gives the asymptotic temperature distribution for cooling a fluid of constant physical properties in plug flow
The hotwire anemometer) A hot-wire anemometer is essentially a fine wire, usually made of platinum, which is heated electrically and inserted into a flowing fluid. The wire temperature, which is a
Dimensional analysis, consider the flow system described in the first paragraph of S14.3, for which dimensional analysis has already given the dimensionless velocity profile (Eq. 6.2-7) and
Heat loss by free convection from a pipe, in Example 14.6-1, would the heat loss be higher or lower if the pipe-surface temperature were 200°F and the air temperature were 180°F?
Rates of heat transfer in a double-pipe heat exchanger, (a) Hot oil entering the heat exchanger in Example 15.4-1 at surface 2 is to be cooled by water entering at surface 1. That is, the
Adiabatic flow of natural gas in a pipeline, recalculate the power requirement wW in Example 15.4-2 if the flow in the pipeline were adiabatic rather than isothermal. (a) Use the result of
Mixing of two ideal-gas streams, (a) Calculate the resulting velocity, temperature, and pressure when the following two air streams are mixed in an apparatus such as that described in Example
Flow through a Venturi tube, a Venturi tube, with a throat 3 in. in diameter, is placed in a circular pipe I ft in diameter carrying dry air. The discharge coefficient Cd of the meter is 0.98.
Free batch expansion of a compressible fluid, a tank with volume V = 10 ft3 (see Fig. 15.5-6) is filled with air (γ = 1.4) at T0 = 300K and P0 = 100 atm. At time t = 0 the valve is opened, allowing
Heating of air in a tube, a horizontal tube of 20 ft length is heated by means of an electrical heating element wrapped uniformly around it, Dry air enters at 5°F and 40 psia at a velocity 75 ft/s
The Mach number in the mixing of two fluid streams(a) Show that when the radicand in Eq. 15.3-13 is zero, the Mach number of the final stream is unity. Note that the Mach number, Ma, which is the
Limiting discharge rates for Venturi meters. (a) Starting with Eq. 15.5-34 (for adiabatic flow), show that as the throat pressure in a Venturi meter is reduced, the mass rate of flow reaches a

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