Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 4, Problem 4.9E
Interpretation Introduction
(a)
Interpretation:
The transfer function which relates tank temperature to the inlet liquid temperature is to be determined.
Concept introduction:
For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.
The process models generally include algebraic relationships which commence from
The difference in the actual variable
In steady-state process, the accumulation in the process is taken as zero.
Interpretation Introduction
(b)
Interpretation:
The steady-state gain for the transfer function determined in part (a) is to be calculated.
Concept introduction:
In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by
Interpretation Introduction
(c)
Interpretation:
It is to be determined if the steady-state gain calculated in part (b) can be unity based on the physical arguments only.
Concept introduction:
In any steady state, the ratio of the amplitude of input signal to the amplitude of the amplifier output is known as steady-state gain. This gain will be same for the entire input range if the amplifier output is linear. For a transfer function, steady-state gain occurs as times tends to infinity which means that in s-domain, this infinite time is represented by
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Provide steps
Example A continuous fractionating column is to be design to separate 30 Ib/h of a mixture of 40 percent benzene and 60 percent toluene into an overhead product containing 97 percent benzene and a bottom product containing 98 percent toluene. These percentages are by weight. A reflux ratio of 3.5 mol to 1 mol of product is to be used. The molal latent heats of benzene and toluene are 7,360 and 7,960 cal/mol, respectively. Benzene and toluene form an ideal system with a relative volatility of about 2.5; the equilibrium curve is shown in Figure below. The feed has a boiling point of 95 °C at a pressure of 1 atm.
(a) Calculate the moles of overhead product and bottom product per hour.
(b) Determine the number of ideal plate and the position of the feed plate:
(i) if the feed is liquid and at its boiling point.
(ii)if the feed is liquid and at 20 °C (specific heat 0.44 cal/ g.°C) (iii) if the feed is a mixture of two-thirds vapor and one-third liquid.
(c) If steam at 20 Ib/in? (1.36 atm)…
Hydrogen, important for numerous processes, can be produced by the shift reaction:
CO+H2O-CO2 +H2
In the reactor system shown in the Figure, the conditions of conversion have been adjusted so
that the H2 content of the effluent from the reactor is 3 mol %. Based on the data in following
figure:
a. Calculate the composition of the fresh feed.
b. Calculate the moles of recycle per mole of hydrogen produced.
Recycle
CO, H2O
Feed
CO
H₂O
Reactor
%
3 mol %
H₂
Separator
%
CO₂ 48
H₂ 48
CO 4
Knowledge Booster
Similar questions
- heat and mass transferarrow_forwardheat and mass transferarrow_forwardA biodiesel mixture consisting of 60 mol% methyl oleate (MO), 25 mol% methyl linoleate (ML), and 15 mol% methyl palmitate (MP) is held at 373.15 K and 200 MPa. Given PC-SAFT parameters: segment number \( m_i = [5.7, 6.3, 4.8] \), segment diameter \( \sigma_i = [3.95, 3.98, 3.91] \) Å, dispersion energy \( \epsilon_i/k = [260, 270, 250] \) K, and binary interaction parameters \( k_{ij} = 0.01 \), determine the isentropic speed of sound (m/s) using the PC-SAFT Helmholtz energy formulation and the thermodynamic identity\[c^2 = \left( \frac{\partial P}{\partial \rho} \right)_T + \frac{T \left( \frac{\partial P}{\partial T} \right)_\rho^2 }{ \rho^2 c_v },\]assuming the density is precomputed at 200 MPa and \( c_v \) is obtained from ideal mixing of pure-component values.arrow_forward
- A steady Williamson nanofluid containing Cu nanoparticles flows over a permeable wedge with wall suction \( V_w = 0.015 \, \text{m/s} \), under a transverse magnetic field \( B_0 = 0.6 \, \text{T} \). The flow obeys the Buongiorno model, with \( D_B = 9 \times 10^{-10} \), \( D_T = 3.5 \times 10^{-8} \), and activation energy \( E_a = 65 \times 10^3 \). Hall and ion-slip effects are included with \( m_e = 0.4 \), \( \beta = 0.15 \). Thermal conductivity varies as \( k(T) = 0.6 (1 + 0.002 (T - 305)) \). Apply velocity and thermal jump conditions with \( \alpha_u = 0.9 \), \( \alpha_T = 0.8 \), \( \lambda = 2 \times 10^{-7} \). Using Keller’s method and similarity variables for wedge parameter \( m = 0.4 \), determine the entropy generation number \( N_s \) at \( x = 0.03 \), where \[N_s = \frac{k(T)}{T_\infty^2} \left( \frac{\partial T}{\partial y} \right)^2 + \frac{\mu}{T_\infty} \left( \frac{\partial u}{\partial y} \right)^2.\]arrow_forwardE. coli was continuously cultured in a continuous stirred tank fermenter with a working volume of 1 L by chemostat. A medium containing 4.0 g/L of glucose as a carbon source was fed to the fermenter at a constant flow rate of 0.5 L/hr, and the glucose concentration in the output stream was 0.20 g/L. The cell yield with respect to glucose was 0.42 g dry cells per gram glucose.arrow_forwardPlease do not use any AI tools to solve this question. I need a fully manual, step-by-step solution with clear explanations, as if it were done by a human tutor. No AI-generated responses, please.arrow_forward
- In the published paper, "Exergy-based Greenhouse gas metric of buildings", use the value of the Exergy Loss of Emission of carbon dioxide to evaluate the index value for 1000 occupants for 50 years building life span in kilogram per person per yeararrow_forwardA CO₂-saturated brine (ionic strength = 2.5 mol/kg, pH = 3, a_H⁺ = 0.01) flows at 2 cm/s through a horizontal tubular reactor (L = 1 m, D = 0.05 m) packed with 5 kg of olivine (Zhuravlev-BET surface area = 30 m²/g). The system operates at 90 °C and 40 bar, and external mass transfer resistance is negligible. The rate-limiting step is electron transfer at the mineral surface, governed by Marcus theory, with λ = 0.75 eV, ΔG° = –0.30 eV, and k₀ = 10⁶ s⁻¹. The Mg²⁺ activity coefficient is γ = 0.76 (from PHREEQC with Pitzer model). For Mg₂SiO₄ + 4 H⁺ → 2 Mg²⁺ + SiO₂(aq) + 2 H₂O, determine the total moles of Mg²⁺ released after 10 minutes at steady state.arrow_forwardIn baseball, batters frequently attempt to hit a ball as far as possible. However, baseballs are inelastic with an officially required "coefficient of restitution" CR ≈ 0.55 on ash wood. The coefficient of restitution of a dropped ball iswhere H is the initial drop height, h is the max. height on the rebound, and h ≈ 2πH tan δ for a homogeneous material. Assuming that a baseball is homogeneous and has a storage modulus approximately the same as that of cork (E' = 18.6 MPa), what must the value of the loss modulus E'' be so that the ball is regulation?arrow_forward
- The creep strain rate of a polymer (in “Hz”) is given by where T is the temperature and Q = 100. kJ/mol is the activation energy. How long t will it take for a rod of this polymer to extend from 10. mm to 15 mm at 100. °C?arrow_forwardCreep compliance J(t) An amorphous polymer has Tg = 100 °C. A creep modulus of 1/J = 1 GPa was measured after t₁ = 1 h at T₁ = 90 °C. Suppose that log 10 a (T) = 17.5(T-Tg) 52+(T-Tg) 1 for this material. What is the shift factor a at T = T₁ relative to the reference Tg? What is the time t₂ required to reach a modulus of 1 GPa at T2 = 80 °C? TR = T = 100 °C |J(t) = 1 GPa-1 + log a(T₁) T₁ = 75 °C T₂ = 50 °C log tr log t₁ log t log t₂ = ?arrow_forwardA 0.45 mol/kg aqueous solution of 3-(methylamino)propylamine and 1-methylpiperazine (1:1 molar) flows at 0.5 g/s through a 2.5 m horizontal stainless steel coil (inner diameter 1.2 mm), entering at 358.15 K and 22 MPa and exiting at 20 MPa. A constant wall heat flux of 28 W is applied. Local density and isobaric heat capacity are obtained through from the Benedict–Webb–Rubin equation of state, with a 3% increase in heat capacity to account for wall sorption. Dynamic viscosity is obtained using the Green-Kubo relation with a given integral value of 2.1 × 10⁻¹⁰ Pa².s, and thermal conductivity is assumed constant. The local Nusselt number is corrected for thermal development using Nu(x) = 3.66 + (0.065 · Gz(x)^0.7) / (1 + 0.04 · Gz(x)^0.7), where Gz(x) = D · Re(x) · Pr(x) / x. Through a spatially resolved numerical integration of the 1D steady-state energy equation and determine the outlet temperature (K).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami...Chemical EngineeringISBN:9781259696527Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark SwihartPublisher:McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind...Chemical EngineeringISBN:9781118431221Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. BullardPublisher:WILEY
Elements of Chemical Reaction Engineering (5th Ed...Chemical EngineeringISBN:9780133887518Author:H. Scott FoglerPublisher:Prentice Hall
Industrial Plastics: Theory and ApplicationsChemical EngineeringISBN:9781285061238Author:Lokensgard, ErikPublisher:Delmar Cengage Learning
Unit Operations of Chemical EngineeringChemical EngineeringISBN:9780072848236Author:Warren McCabe, Julian C. Smith, Peter HarriottPublisher:McGraw-Hill Companies, The
Introduction to Chemical Engineering Thermodynami...
Chemical Engineering
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind...
Chemical Engineering
ISBN:9781118431221
Author:Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:WILEY
Elements of Chemical Reaction Engineering (5th Ed...
Chemical Engineering
ISBN:9780133887518
Author:H. Scott Fogler
Publisher:Prentice Hall
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:9781285061238
Author:Lokensgard, Erik
Publisher:Delmar Cengage Learning
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:9780072848236
Author:Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:McGraw-Hill Companies, The