Code No: RR320804
RR
Set No. 2
in
III B.Tech II Semester Examinations,APRIL 2011 MATHEMATICAL METHODS FOR CHEM.ENGINEERS Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Derive the equation of continuity in cylindrical coordinates by mean by a mass balance over a stationary volume element r∆r∆θ∆z. [10+6]
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(b) Give the physical significance of ∂T /∂t and dT /dt .
or
2. A tank is initially filled with 100 gallons of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lb. of salt per gallon runs into the tank at the rate of 5 gallons per minute and the mixture assumed to be kept uniform by stirring, runs out at the same rate. Find the amount of salt in the tank at any time, and determine how long it will take for this amount to reach 150 lb. [16] 3. (a) Find the torque about the point 2i + j - k of a force represented by 4i + k acting through the point i - j + 2k.
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(b) A centrifuge is spinning with angular velocity 27 rad. per second about an axis parallel to 2i + j - 2 k passing through the point i + 3j - k. Find the velocity of the point of the body whose position vector is 4i + 8j + k. [8+8]
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4. A countercurrent packed absorption tower is to be used for carrying out the liquidphase reaction A+B →C This reaction is irreversible, and the reaction rate may be expressed as follows: A − dN = kNA XB dt Components Band C are nonvolatile and never appear in the gas phase. Substance B is introduced into the tower dissolved in a nonvolatile solvent. Compound A is volatile and is introduced into the tower as a vapor carried by an insoluble, inert gas.The rate of transfer of A from the gas phase to the liquid phase is controlled by the gas-phase resistance and is proportional to Kg a(YA − YA∗ ).YA∗ is the equilibrium gas-phase concentration corresponding to the liquid-phase concentration, XA . YA∗ is related to XA by the equation YA∗ = mXA Assuming isothermal conditions, develop the differential equation for the decrease in the concentration of A in the gas phase as a function of the tower height z and the following known quantities: a = area for mass transfer per unit of tower volume, f t2 /f t3 G = inert-gas rate, lb moles/hr H = moles of inert solvent held up by packing per unit of tower volume k = reaction-rate constant, lb moles/- (lb mole/hr) KG = mass-transfer coefficient, lb moles/hr (unit YA -YB ) (f t2 ) L = inert-solvent rate, lb moles/hr 1
Code No: RR320804
RR
Set No. 2
in
m = proportionality constant S = tower cross section, f t2 . Nomenclature for Variables t -time, hr z = distance from bottom of tower, ft N = moles of a component; NA refers to moles of substance A, etc. Y -gas-phase concentration, moles per mole of inert gas; YA refers to sub-stance A X = liquid-phase concentration, moles per mole of inert solvent; XA refers to substance A, etc. [16]
(a) The straight line from (0,0,0) to (2,1,3).
ld .
5. Find the work done in moving a particle in the force field F = 3x2 .i+(2xz-y).j +z.k along
(b) The curve define by x2 = 4y, 3x3 = 8z from x= 0 to x=2. Use the concept of line integral. [6+10]
or
6. Change the following equation in Cartesian coordinate to cylindrical coordinate. ∂ 2 T /∂x2 + ∂ 2 T /∂y 2 + ∂ 2 T /∂Z 2 = 0 Give x = r cos θ y = r sin θ and z = z . [16]
7. Find the Laplace inverse transform of the following functions.
(b)
2s2 −6s+5 s3 −6s2 +11s−6 4s+5 . (s−1)2 (s+2)
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(a)
[8+8]
8. Suppose that a slab (extending indefinitely in the y and z directions) at an initial temperature T1 has its two faces suddenly cooled to T0 . What is the relation between temperature, time after quenching, and position within the slab? [16]
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2
Code No: RR320804
RR
Set No. 4
in
III B.Tech II Semester Examinations,APRIL 2011 MATHEMATICAL METHODS FOR CHEM.ENGINEERS Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) Derive the equation of continuity in cylindrical coordinates by mean by a mass balance over a stationary volume element r∆r∆θ∆z. [10+6]
ld .
(b) Give the physical significance of ∂T /∂t and dT /dt .
or
2. A tank is initially filled with 100 gallons of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lb. of salt per gallon runs into the tank at the rate of 5 gallons per minute and the mixture assumed to be kept uniform by stirring, runs out at the same rate. Find the amount of salt in the tank at any time, and determine how long it will take for this amount to reach 150 lb. [16] 3. Find the work done in moving a particle in the force field F = 3x2 .i+(2xz-y).j +z.k along (a) The straight line from (0,0,0) to (2,1,3).
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(b) The curve define by x2 = 4y, 3x3 = 8z from x= 0 to x=2. Use the concept of line integral. [6+10]
4. Find the Laplace inverse transform of the following functions. (a) (b)
2s2 −6s+5 s3 −6s2 +11s−6 4s+5 . (s−1)2 (s+2)
[8+8]
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5. Suppose that a slab (extending indefinitely in the y and z directions) at an initial temperature T1 has its two faces suddenly cooled to T0 . What is the relation between temperature, time after quenching, and position within the slab? [16]
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6. Change the following equation in Cartesian coordinate to cylindrical coordinate. ∂ 2 T /∂x2 + ∂ 2 T /∂y 2 + ∂ 2 T /∂Z 2 = 0 Give x = r cos θ y = r sin θ and z = z . [16]
7. A countercurrent packed absorption tower is to be used for carrying out the liquidphase reaction A+B →C This reaction is irreversible, and the reaction rate may be expressed as follows: A = kNA XB − dN dt Components Band C are nonvolatile and never appear in the gas phase. Substance B is introduced into the tower dissolved in a nonvolatile solvent. Compound A is volatile and is introduced into the tower as a vapor carried by an insoluble, inert gas.The rate of transfer of A from the gas phase to the liquid phase is controlled by 3
Code No: RR320804
RR
Set No. 4
uW
or
ld .
in
the gas-phase resistance and is proportional to Kg a(YA − YA∗ ).YA∗ is the equilibrium gas-phase concentration corresponding to the liquid-phase concentration, XA . YA∗ is related to XA by the equation YA∗ = mXA Assuming isothermal conditions, develop the differential equation for the decrease in the concentration of A in the gas phase as a function of the tower height z and the following known quantities: a = area for mass transfer per unit of tower volume, f t2 /f t3 G = inert-gas rate, lb moles/hr H = moles of inert solvent held up by packing per unit of tower volume k = reaction-rate constant, lb moles/- (lb mole/hr) KG = mass-transfer coefficient, lb moles/hr (unit YA -YB ) (f t2 ) L = inert-solvent rate, lb moles/hr m = proportionality constant S = tower cross section, f t2 . Nomenclature for Variables t -time, hr z = distance from bottom of tower, ft N = moles of a component; NA refers to moles of substance A, etc. Y -gas-phase concentration, moles per mole of inert gas; YA refers to sub-stance A X = liquid-phase concentration, moles per mole of inert solvent; XA refers to substance A, etc. [16] 8. (a) Find the torque about the point 2i + j - k of a force represented by 4i + k acting through the point i - j + 2k.
(b) A centrifuge is spinning with angular velocity 27 rad. per second about an axis parallel to 2i + j - 2 k passing through the point i + 3j - k. Find the velocity of the point of the body whose position vector is 4i + 8j + k. [8+8]
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nt
?????
4
Code No: RR320804
RR
Set No. 1
in
III B.Tech II Semester Examinations,APRIL 2011 MATHEMATICAL METHODS FOR CHEM.ENGINEERS Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
ld .
1. Suppose that a slab (extending indefinitely in the y and z directions) at an initial temperature T1 has its two faces suddenly cooled to T0 . What is the relation between temperature, time after quenching, and position within the slab? [16]
or
2. A tank is initially filled with 100 gallons of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lb. of salt per gallon runs into the tank at the rate of 5 gallons per minute and the mixture assumed to be kept uniform by stirring, runs out at the same rate. Find the amount of salt in the tank at any time, and determine how long it will take for this amount to reach 150 lb. [16]
3. Change the following equation in Cartesian coordinate to cylindrical coordinate. ∂ 2 T /∂x2 + ∂ 2 T /∂y 2 + ∂ 2 T /∂Z 2 = 0 Give x = r cos θ y = r sin θ and z = z . [16]
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4. (a) Find the torque about the point 2i + j - k of a force represented by 4i + k acting through the point i - j + 2k. (b) A centrifuge is spinning with angular velocity 27 rad. per second about an axis parallel to 2i + j - 2 k passing through the point i + 3j - k. Find the velocity of the point of the body whose position vector is 4i + 8j + k. [8+8]
5. (a) Derive the equation of continuity in cylindrical coordinates by mean by a mass balance over a stationary volume element r∆r∆θ∆z. [10+6]
nt
(b) Give the physical significance of ∂T /∂t and dT /dt .
6. Find the work done in moving a particle in the force field F = 3x2 .i+(2xz-y).j +z.k along (a) The straight line from (0,0,0) to (2,1,3).
Aj
(b) The curve define by x2 = 4y, 3x3 = 8z from x= 0 to x=2. Use the concept of line integral. [6+10]
7. Find the Laplace inverse transform of the following functions. (a)
(b)
2s2 −6s+5 s3 −6s2 +11s−6 4s+5 . (s−1)2 (s+2)
[8+8]
8. A countercurrent packed absorption tower is to be used for carrying out the liquidphase reaction A+B →C
5
Code No: RR320804
RR
Set No. 1
uW
or
ld .
in
This reaction is irreversible, and the reaction rate may be expressed as follows: A = kNA XB − dN dt Components Band C are nonvolatile and never appear in the gas phase. Substance B is introduced into the tower dissolved in a nonvolatile solvent. Compound A is volatile and is introduced into the tower as a vapor carried by an insoluble, inert gas.The rate of transfer of A from the gas phase to the liquid phase is controlled by the gas-phase resistance and is proportional to Kg a(YA − YA∗ ).YA∗ is the equilibrium gas-phase concentration corresponding to the liquid-phase concentration, XA . YA∗ is related to XA by the equation YA∗ = mXA Assuming isothermal conditions, develop the differential equation for the decrease in the concentration of A in the gas phase as a function of the tower height z and the following known quantities: a = area for mass transfer per unit of tower volume, f t2 /f t3 G = inert-gas rate, lb moles/hr H = moles of inert solvent held up by packing per unit of tower volume k = reaction-rate constant, lb moles/- (lb mole/hr) KG = mass-transfer coefficient, lb moles/hr (unit YA -YB ) (f t2 ) L = inert-solvent rate, lb moles/hr m = proportionality constant S = tower cross section, f t2 . Nomenclature for Variables t -time, hr z = distance from bottom of tower, ft N = moles of a component; NA refers to moles of substance A, etc. Y -gas-phase concentration, moles per mole of inert gas; YA refers to sub-stance A X = liquid-phase concentration, moles per mole of inert solvent; XA refers to substance A, etc. [16]
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nt
?????
6
Code No: RR320804
RR
Set No. 3
in
III B.Tech II Semester Examinations,APRIL 2011 MATHEMATICAL METHODS FOR CHEM.ENGINEERS Chemical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????
Aj
nt
uW
or
ld .
1. A countercurrent packed absorption tower is to be used for carrying out the liquidphase reaction A+B →C This reaction is irreversible, and the reaction rate may be expressed as follows: A = kNA XB − dN dt Components Band C are nonvolatile and never appear in the gas phase. Substance B is introduced into the tower dissolved in a nonvolatile solvent. Compound A is volatile and is introduced into the tower as a vapor carried by an insoluble, inert gas.The rate of transfer of A from the gas phase to the liquid phase is controlled by the gas-phase resistance and is proportional to Kg a(YA − YA∗ ).YA∗ is the equilibrium gas-phase concentration corresponding to the liquid-phase concentration, XA . YA∗ is related to XA by the equation YA∗ = mXA Assuming isothermal conditions, develop the differential equation for the decrease in the concentration of A in the gas phase as a function of the tower height z and the following known quantities: a = area for mass transfer per unit of tower volume, f t2 /f t3 G = inert-gas rate, lb moles/hr H = moles of inert solvent held up by packing per unit of tower volume k = reaction-rate constant, lb moles/- (lb mole/hr) KG = mass-transfer coefficient, lb moles/hr (unit YA -YB ) (f t2 ) L = inert-solvent rate, lb moles/hr m = proportionality constant S = tower cross section, f t2 . Nomenclature for Variables t -time, hr z = distance from bottom of tower, ft N = moles of a component; NA refers to moles of substance A, etc. Y -gas-phase concentration, moles per mole of inert gas; YA refers to sub-stance A X = liquid-phase concentration, moles per mole of inert solvent; XA refers to substance A, etc. [16] 2. A tank is initially filled with 100 gallons of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lb. of salt per gallon runs into the tank at the rate of 5 gallons per minute and the mixture assumed to be kept uniform by stirring, runs out at the same rate. Find the amount of salt in the tank at any time, and determine how long it will take for this amount to reach 150 lb. [16] 7
Code No: RR320804
RR
Set No. 3
3. Find the work done in moving a particle in the force field F = 3x2 .i+(2xz-y).j +z.k along (a) The straight line from (0,0,0) to (2,1,3). (b) The curve define by x2 = 4y, 3x3 = 8z from x= 0 to x=2. Use the concept of line integral. [6+10]
in
4. (a) Find the torque about the point 2i + j - k of a force represented by 4i + k acting through the point i - j + 2k.
ld .
(b) A centrifuge is spinning with angular velocity 27 rad. per second about an axis parallel to 2i + j - 2 k passing through the point i + 3j - k. Find the velocity of the point of the body whose position vector is 4i + 8j + k. [8+8] 5. Suppose that a slab (extending indefinitely in the y and z directions) at an initial temperature T1 has its two faces suddenly cooled to T0 . What is the relation between temperature, time after quenching, and position within the slab? [16]
or
6. Change the following equation in Cartesian coordinate to cylindrical coordinate. ∂ 2 T /∂x2 + ∂ 2 T /∂y 2 + ∂ 2 T /∂Z 2 = 0 Give x = r cos θ y = r sin θ and z = z . [16]
7. Find the Laplace inverse transform of the following functions.
(b)
2s2 −6s+5 s3 −6s2 +11s−6 4s+5 . (s−1)2 (s+2)
uW
(a)
[8+8]
8. (a) Derive the equation of continuity in cylindrical coordinates by mean by a mass balance over a stationary volume element r∆r∆θ∆z. (b) Give the physical significance of ∂T /∂t and dT /dt .
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nt
?????
8
[10+6]
