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engineering
chemical engineering
Questions and Answers of
Chemical Engineering
Go to a large supermarket and look at some of the household products. How many of these could you separate?
Arrange a tour of the chemical engineering unit operations laboratory to observe the different types of separation equipment. Although this equipment is often much larger than the equipment in
The following data were obtained for the absorption of a sparingly soluble gas A at 20°C into an aqueous solution of a non-volatile reactant B in a laminar jet apparatus as described in Example
Verify by inputting the various constants that \(R_{\mathrm{G}} T / F\) is equal to \(k_{\mathrm{B}} T / e\).
Find the mobility of \(\mathrm{H}^{+}, \mathrm{OH}^{-}\), and other ions from the diffusivity data given in Table 22.1. Table 22.1. Diffusion coefficients of ions in water at 25 C. H+ Na+ K+ Ca+ OH-
Show from combination of the equation for current and the flux expression that the conductivity of an electrolyte solution is given by\[\kappa=\frac{F^{2}}{R_{\mathrm{G}} T} \sum_{i}^{N} D_{i}
When there is a concentration gradient in the system, show that the potential gradient is composed of two terms, (i) an Ohm's-law contribution and (ii) a diffusional contribution. State the equation
Copper is deposited at a cathode from solution with a bulk concentration of \(0.5 \mathrm{M}\) at the rate of \(3.0 \mathrm{~g} / \mathrm{m}^{2} \cdot \mathrm{s}\). Find the surface concentration of
Consider a system with a "supporting" electrolyte, for example \(\mathrm{CuSO}_{4}\), and a second salt such as a mixture of \(\mathrm{CuSO}_{4}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\). The system
Calculate the diffusion potential for an uncharged membrane with a concentration of 0.5 \(\mathrm{M}\) on one side and \(0.1 \mathrm{M}\) on the other side for solutions of (a) \(\mathrm{CuSO}_{4}\),
Consider an uncharged membrane of thickness \(100 \mu \mathrm{m}\) with concentrations of \(1 \mathrm{M} \mathrm{HCl}\) on one side and \(0.1 \mathrm{M} \mathrm{HCl}\) on the other side. Assume that
Two solutions are separated by a porous sintered disk ( \(1 \mathrm{~mm}\) thick) that permits diffusion across the disk. On one side we have a mixture of \(1 \mathrm{M} \mathrm{HCl}\) and \(1
Diffusion of weakly ionized acids such as acetic acid is an interesting and complex problem in diffusion. The diffusion involves the ionized species \(\mathrm{CH}_{3} \mathrm{COO}^{-}\)as well as the
Consider a charged membrane of thickness \(100 \mu \mathrm{m}\) with concentrations of \(1 \mathrm{M} \mathrm{HCl}\) on one side and \(0.1 \mathrm{M} \mathrm{HCl}\) on the other side. The membrane
Extend the analysis of a system for transport in a charged membrane to the case of a mixture of two electrolyte salts with a common anion (a mixture of \(\mathrm{NaCl}\) and \(\mathrm{KCl}\), for
Calculate the Debye length for a \(0.1-\mathrm{M}\) solution of a univalent \((1,1)\) electrolyte, i.e., one with single-charged cations and single-charged anions, in water.If the surface has a
A solid is in the form of a long cylinder and has a surface charge of \(q_{\mathrm{S}}\). Derive an expression for the potential in the external region. Use the Debye-Hückel approximation and solve
A solid is in the form of a sphere and has a surface charge of \(q_{\mathrm{S}}\). Derive an expression for the potential in the external region.
Solve the non-linear equation for the double-layer potential given by\[\begin{equation*}abla^{2} \phi=-\frac{2 v F C_{\infty}}{\epsilon} \sinh \left[F u \phi /\left(R_{\mathrm{G}} T\right)\right]
Solve the Debye-Hückel equation for circular pipes whose walls carry a surface potential of \(\phi_{0}\). Show that the potential is given by\[\phi=\phi_{\mathrm{s}} \frac{I_{0}(\kappa
Verify that the current carried in electro-osmotic flow can be expressed as\[I=\int_{0}^{R} 2 \pi r v_{z} ho_{\mathrm{c}} d r\]Using this relation, derive an expression for the current in
Analyze the problem of electro-osmotic flow with an additional imposed pressure gradient. Show that the volumetric flow rate can be expressed as\[Q=L_{11} \Delta \phi+L_{12} \Delta P\]where \(\Delta
Find the flow rate for an electro-osmotic flow in a tube of diameter \(5 \mu \mathrm{m}\) and length \(10 \mathrm{~cm}\) filled with an aqueous solution. The applied potential is \(1 \mathrm{kV}\).
An effectiveness factor of electro-osmotic flow is often used. This factor is defined as the volumetric flow rate due to electo-osmosis divided by that due to an applied pressure gradient.Derive an
Derive expressions for the velocity profile and the volumetric flow rate for a circular channel. Examine the limiting cases of this equation for small \(R\) and large \(R\) (in comparison with the
A circular capillary has a diameter of \(10 \mu \mathrm{m}\) and a length of \(3 \mathrm{~cm}\). The surface carries a zeta potential of \(-0.5 \mathrm{~V}\). The flowing fluid is an aqueous solution
Find the streaming potential when a pressure drop of \(0.1 \mathrm{MPa}\) is applied to a liquid with a specific conductivity of \(0.0014 \mathrm{~S} / \mathrm{m}\). The surface charge is \(100
Consider the settling of charged spherical particles with a zeta potential of \(50 \mathrm{mV}\) in a solution of \(0.05 \mathrm{M} \mathrm{NaCl}\). The particle density is \(2060 \mathrm{~kg} /
It is required to separate two proteins with the mobilities of \(\mu_{1}=8 \times 10^{-5} \mathrm{~m} \cdot \mathrm{C} /(\mathrm{N} \cdot \mathrm{s})\) and \(\mu_{2}=6 \times 10^{-5} \mathrm{~m}
Various methods have been developed in order to increase the throughput in electrophoresis. Most of these designs vary in the flow arrangement and the changes in the direction of the electric field.
In the text we considered only the zone electrophoresis where a zone of a solute-rich layer is created by the action of an electric field. Other techniques are isotochorphoresis and iso-electric
A hydrogen fuel cell using a PEM consists of a gas-diffusion backing layer with a Pt on \(\mathrm{C}\) supported catalyst as anode and cathode. The two electrodes are separated by a membrane, which
The classical Fick or Einstein model for diffusion is based on the assumption that the diffusing molecule is exposed to a random force field arising from molecular motion. The assumption is
The phenomenon of electroosmosis can be used for dewatering and consolidation of soils and mine tailing and waste sludges. The idea is that by appropriate placement of electrodes the flow can be
A simplified relation for heat transfer in natural convection from a vertical wall is of the form\[h=A(\Delta T / x)^{B}\]where \(A\) and \(B\) are fitting constants. Determine the values of these
Repeat the calculations for the previous problem if the fluid were water instead of air. In which case do you expect the maximum velocity to be higher?Previous Problem:A vertical plate \(3
Use BVP4C to simulate the Blasius flow with non-zero velocity in the y-direction at the plate. Use the assumption that a true similarity exists. Examine the effect of the parameter K (the blowing or
Consider again the problem of flow past a cylinder with rotation considered in Example 15.4. Calculate and plot the location of the stagnation point on the cylinder surface for \(0)\). Plot typical
Reaction in the catalyst pellet with external transport resistances is another classic problem in chemical reaction engineering. This system needs to be modeled as a set of two second-order
For the above problem find the eddy viscosity as a function of position (based on the universal velocity profile) and plot the eddy viscosity as a function of the distance from the wall.Above
Natural convection: air. Show that \(\beta=1 / T\) for an ideal gas.Repeat the example above for air instead of water.Which fluid generates more circulation? Suggest a reason for this.Example above:
Examine the sensitivity of the results of Problem 1 to changes in the transport parameters by \(\pm 20 \%\) on either side and tabulate the results for the predicted values of the condensation rate,
The following problem arises in gas absorption with fast reaction. The notations have been slightly changed from Eq. (10.5) earlier:\[\begin{equation*}\epsilon^{2} \frac{d^{2} c_{\mathrm{A}}}{d
A more general scenario for the lubrication approximation is the problem where the fluid is contained in a gap of height \(h\), which is assumed to be a general function of \(x\), i.e.,
Show all the steps leading to the integral balance equation (18.6) in the text.Use the following boundary conditions and verify Eq. (18.7). (i) At \(y=0, T=T_{\mathrm{S}}\). (ii) At
For fluids with \(\operatorname{Pr}
Consider the flat-plate heat transfer to be solved by the similarity approach. Show all the details leading to Eq. (18.15). What are the boundary conditions on \(\theta\) ? Extend your MATLAB code to
For the similarity solution, what are the boundary conditions for the constant-wall-flux case? Show that a complete similarity does not exist for this case. Also show the condition for the case where
Air at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\) flows along a flat plate at \(3 \mathrm{~m} / \mathrm{s}\). At a location of \(0.3 \mathrm{~m}\) from the leading edge, find the thickness of the
Extend the analysis of heat transfer over a wedge flow. Derive the following equation for the temperature profile:\[\begin{equation*}\theta^{\prime \prime}+(m+1) \operatorname{Prf} \theta^{\prime}=0
Consider heat transfer over a flat plate again but now include an additional term due to viscous heating. Show that the similarity method is applicable to this problem as well, and derive the
Integral balances can also be used for heat transfer in a turbulent-flow boundary layer if a form for the velocity profile is assumed. A common form is the 1/7th-power
A vertical plate \(3 \mathrm{~m}\) long is at a temperature of \(400 \mathrm{~K}\) and exposed to air at \(300 \mathrm{~K}\). Calculate the thickness of the boundary layer and the value of the local
An immersion heater operating at \(1000 \mathrm{~W}\) is in the form of a rectangular solid with dimensions of \(16 \mathrm{~cm}\) by \(10 \mathrm{~cm}\) by \(1 \mathrm{~cm}\). Determine the heat
Water is boiled in a polished stainless steel pot with a \(3 \mathrm{~kW}\) heater. The efficiency of the heater is \(60 \%\), i.e., only \(60 \%\) of the heat is transferred to the water. Find the
Consider boiling of water under sea-level conditions in a copper vessel. Calculate and plot the heat flux vs. \(\Delta T\) diagram for water at three different pressures. Show the temperature at the
Consider a film of vapor in contact with a liquid. From a heat balance show that the mass flow rate in the vapor, \(\dot{m}\), per unit transfer area changes as\[\hat{h}_{\lg } \frac{d \dot{m}}{d
Find the temperature at which the surface tension of water becomes zero. What is the physical significance of this temperature?
Consider a vapor condensing on a wall and forming a liquid film. Assume that locally the film thickness is related to the flow rate per unit transfer area by momentum-transfer considerations.Then
Saturated steam at \(356 \mathrm{~K}\) condenses on a vertical tube of diameter \(5 \mathrm{~cm}\) whose surface is maintained at \(340 \mathrm{~K}\).Find the height at which the flow becomes wavy.
Saturated steam at \(55^{\circ} \mathrm{C}\) is to be condensed at a rate of \(10 \mathrm{~kg} / \mathrm{h}\) on the outside of a vertical tube of diameter \(3 \mathrm{~cm}\) by maintaining the
What are the key dimensionless parameters? Integrate the equation to find an expression for \(\lambda / L\) as a function of dimensionless time. Is a steady state reached in this system?
A deep pool of water is initially at \(4^{\circ} \mathrm{C}\) and suddenly the surface is exposed to a freezing front at \(-4{ }^{\circ} \mathrm{C}\) and remains so exposed for a long time.Find the
A common procedure in metallurgy is solidification from a melt in a cylindrical mold. If the Jacob number is small we can use the pseudo-steady-state model, which should now include the conduction in
A stainless-steel component is exposed to laser heating at an initial temperature of \(300 \mathrm{~K}\). After a short transient the surface reaches its melting point, and the surface recedes at a
A schematic diagram of crystal growth by directional solidification is shown in Fig. 18.8. Analyze the various flow mechanisms and indicate how they affect the heat transfer, the movement of the
A heat pipe is an evaporator-condenser system in which the liquid is returned to the evaporator by capillary action. In the simplest form it consists of a wire-mesh region that serves to act as a
Using the basic physical constants, show that \(C_{1}=3.742 \times 10^{8} \mathrm{~W} \mu \mathrm{m}^{4} / \mathrm{m}^{2}\) and \(C_{2}=\) \(1.4389 \times 10^{4} \mu \mathrm{m} / \mathrm{K}\) in the
The solar constant is defined as the average flux of solar energy incident on the outer fringes of the Earth's atmosphere and a commonly used value is \(1.353 \mathrm{~kW} / \mathrm{m}^{2}\). If the
Verify the algebra leading to Eq. (19.22) for radiation exchange between two plates facing each other. 1 21 -(Eb1 - Eb2) (19.22) 1/1 + 1/62-1
Consider a shield with an emissivity of \(\epsilon_{\mathrm{s}}\) separating two parallel plates as shown in Fig. 19.11. Assume that the shield is adiabatic and that there is no net loss of heat.
Consider radiation exchange between two annular cylinders of radii \(R_{\mathrm{i}}\), and \(R_{\mathrm{o}}\) facing each other. This is similar to the radiation between flat plates considered in the
Two parallel disks each of radius \(R\) are facing each other and separated by a distance \(H\). Derive an expression for the view factor between these disks.
Two rectangular plates of sizes \(L\) and \(W\) are facing each other and separated by a distance \(H\). Derive an expression for the view factor between these disks. Find the limit if \(W\) is
Consider two plates at temperatures of \(600 \mathrm{~K}\) and \(500 \mathrm{~K}\) with emissivities of 0.8 and 0.4 , respectively. The plates are separated by a gray gas that has an absorption
A solid at an initial temperature of \(T_{0}\) is exposed to colder surroundings at \(T_{\mathrm{a}}\) and is cooling down by radiation heat loss. Develop a model based on the lumping approximation
A gray gas with an absorption coefficient of \(\kappa\) is contained between two plates separated by a distance \(L\). Using the diffusion approximation for radiation, derive the
Two plates are at temperatures of \(T_{1}\) and \(T_{2}\) and a chemical reaction is producing heat at a constant rate within the system. Derive a model to predict the temperature distribution within
The common methods for the computational solution of radiative transport equations are summarized briefly below:1. The discrete ordinate method 2. The Monte-Carlo method 3. Hottel's zonal
The calculation of solar radiation impinging on a surface is of importance in many applications, for example, design of solar collectors, temperature control of buildings, etc.Your goal is to review
Radiation interactions are of importance in crystal pullers for growing crystals from melts since these operate at very high temperatures. The radiation view factors change at various stages of
Although radiation is important in heat transfer, an analogous model can be used in the design of photochemical reactors. The modeling of these reactors requires that the radiation intensity be
Develop an expression for the average mass transfer coefficient for a plate of length \(L\), where part of the flow is turbulent for part of the plate. Assume that there is no transition and that the
The factor \(j_{\mathrm{D}}\) is also used in the correlation. This is defined as\[j_{\mathrm{D}}=S t(S c)^{2 / 3}=\frac{k_{\mathrm{m}}}{v_{\text {ref }}}(S c)^{2 / 3}\]where \(S t\) is the Stanton
Verify that the \(j\)-factor is related to the drag coefficient by the relation\[j_{\mathrm{D}}=\frac{c_{\mathrm{D}}}{2}\]for mass transfer for flow over a flat plate.
A silicon substrate \(10 \mathrm{~cm}\) long is exposed to a gas stream containing an arsenic precursor so that a GaAs film can be deposited on the surface. Estimate the mass-transfer coefficient,
The scaling analysis for the mass-transfer boundary-layer thickness is parallel to that for heat transfer analysis. Use the same method to show that \(\Delta\) is proportional to \(S c^{-1 / 3}\) for
An indirect way of measuring of secondary emission from ponds or large bodies of water used in waste treatment is to measure the concentration and velocity over the surface. The data can then be
Chemical vapor deposition (CVD) on an inclined susceptor: a case-study problem. An important application of convective mass transfer theory is in CVD processes employed to coat surfaces with thin
Mass transfer from a bubble. Calculate the mass transfer coefficient for the air-water system for bubbles rising at a gas velocity of \(5 \mathrm{~cm} / \mathrm{s}\) in a pool of stagnant liquid. Use
Axial dispersion in channel flow. Consider the pressure-driven laminar flow in a channel of height \(2 h\). Derive the following formula for the axial dispersion coefficient:\[D_{\mathrm{E}}=\frac{2
Axial dispersion in turbulent flow. Taylor showed that the following expression is suitable for the calculation of the axial dispersion coefficient for turbulent flow in a pipe:\[D_{\mathrm{E}}=10 R
A model for a hemodialyser with simulation of the patient-artificial-kidney system: a case-study problem. A useful case study is the paper by Ramachandran and Mashelkar (1980), where a mesoscopic
A model for chromatographic separation: a case-study problem. An important application of Taylor dispersion is in chromatography. Here pulses of a mixture of solutes are introduced into one end of a
Show that the two representations of the Stefan-Maxwell model given by Eqs. (21.4) and (21.5) are equivalent. ns -VA = j=1 y;Ni-yiNj CDij (21.4)
Show that the Stefan-Maxwell model can be rearranged to define a pseudo-binary diffusivity, \(D_{i \mathrm{~m}}\), for species \(i\) in the mixture:\[\frac{1}{D_{i
Support for the form of the generalized version of Fick's law introduced in this chapter can be found in the thermodynamics of irreversible processes. Here we introduce a brief description of this
Acetone is evaporating in a mixture of nitrogen and helium. Find the rate of evaporation and compare it with the rates in pure nitrogen and pure helium. Also compare it with the model using a
Catalytic oxidation of \(\mathrm{CO}\) is an important reaction in pollution prevention. The reaction scheme is\[\mathrm{O}_{2}(\mathrm{~A})+2 \mathrm{CO}(\mathrm{B}) \rightarrow 2
Examine how the rank of the stoichiometric matrix can be used to reduce the number of equations to be solved. For example, if there are \(n_{\mathrm{s}}\) components and \(n_{\mathrm{r}}\) equations
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