2. pure water and salt granules are continuously fed into a well-mixed tank at a rate qw(t) [L/s] and w(t) [g/s], respectively, to produce saline solution. let c(t) [g salt/L solution] be the concentration of salt in the saline solution in the well-mixed tank and qout (t) [L/s] be the volumetric flow rate of saline solution out of the tank. in contrast to the lecture notes, here qw + qout- to relate qw to qout, we model the density p [g/L] of the saline solution as a function of the salt content, via p(c) = Pw+ac where pw [g/L] is the density of pure water and a [g/g] is a constant identified from experimental data as in the plot below. Salt solids w gls water saline water density conveyor que qw LIs model 1200- experinental data 1150 1100 saline solution p=p{c)= Pw + ac a = 0.64 g solution/g salt 1050 Jout LIS C g/L 1000 - 0.0 salt concentration, c [g salt/L solution] 0.1 0.2 0.3 (a) (b) Figure 2: (a) our familiar saline solution process except qw 7 qout• the volume V of liquid in the tank is constant because of the overflow line. (b) density of saline solution versus concentration of salt. the line shows the model p(c) = Pw+ac. your goal is to derive a dynamic model for c = and w = w(t). c(t) in terms of the two inputs qw = qw(t) density of solution, p (g solution/L solution]
2. pure water and salt granules are continuously fed into a well-mixed tank at a rate qw(t) [L/s] and w(t) [g/s], respectively, to produce saline solution. let c(t) [g salt/L solution] be the concentration of salt in the saline solution in the well-mixed tank and qout (t) [L/s] be the volumetric flow rate of saline solution out of the tank. in contrast to the lecture notes, here qw + qout- to relate qw to qout, we model the density p [g/L] of the saline solution as a function of the salt content, via p(c) = Pw+ac where pw [g/L] is the density of pure water and a [g/g] is a constant identified from experimental data as in the plot below. Salt solids w gls water saline water density conveyor que qw LIs model 1200- experinental data 1150 1100 saline solution p=p{c)= Pw + ac a = 0.64 g solution/g salt 1050 Jout LIS C g/L 1000 - 0.0 salt concentration, c [g salt/L solution] 0.1 0.2 0.3 (a) (b) Figure 2: (a) our familiar saline solution process except qw 7 qout• the volume V of liquid in the tank is constant because of the overflow line. (b) density of saline solution versus concentration of salt. the line shows the model p(c) = Pw+ac. your goal is to derive a dynamic model for c = and w = w(t). c(t) in terms of the two inputs qw = qw(t) density of solution, p (g solution/L solution]
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
Help
![2. pure water and salt granules are continuously fed into a well-mixed tank at a rate qw(t)
[L/s] and w(t) [g/s], respectively, to produce saline solution. let c(t) [g salt/L solution] be
the concentration of salt in the saline solution in the well-mixed tank and qout (t) [L/s] be
the volumetric flow rate of saline solution out of the tank. in contrast to the lecture notes,
here qw # qout. to relate qw to qout, we model the density p [g/L] of the saline solution as a
function of the salt content, via p(c) = Pw+ac where pw [g/L] is the density of pure water
and a [g/g] is a constant identified from experimental data as in the plot below.
Salt solids
w gls
water
saline water density
conveyor
qw LIs
model
1200-
experimental data
1150
1100 -
saline solution
p=p(c) = pw+ ac-
a = 0.64 g solution/g salt
1050
Jout LIS
C g/L
1000
0.0
0.1
0.2
0.3
salt concentration, c [g salt/L solution]
(a)
(b)
Figure 2: (a) our familiar saline solution process except qw # qout. the volume V of liquid in the
tank is constant because of the overflow line. (b) density of saline solution versus concentration
of salt. the line shows the model p(c) = Pw + ac.
qw(t)
your goal is to derive a dynamic model for c = c(t) in terms of the two inputs qw =
and w = w(t).
density of solution, p
Ig solution/L solution]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4182e5fe-a12a-4c0b-bb5e-835d4eda4ff6%2F72aff38e-935a-498f-a2e0-098aba8c5e4e%2Fjb4ex3_processed.png&w=3840&q=75)
Transcribed Image Text:2. pure water and salt granules are continuously fed into a well-mixed tank at a rate qw(t)
[L/s] and w(t) [g/s], respectively, to produce saline solution. let c(t) [g salt/L solution] be
the concentration of salt in the saline solution in the well-mixed tank and qout (t) [L/s] be
the volumetric flow rate of saline solution out of the tank. in contrast to the lecture notes,
here qw # qout. to relate qw to qout, we model the density p [g/L] of the saline solution as a
function of the salt content, via p(c) = Pw+ac where pw [g/L] is the density of pure water
and a [g/g] is a constant identified from experimental data as in the plot below.
Salt solids
w gls
water
saline water density
conveyor
qw LIs
model
1200-
experimental data
1150
1100 -
saline solution
p=p(c) = pw+ ac-
a = 0.64 g solution/g salt
1050
Jout LIS
C g/L
1000
0.0
0.1
0.2
0.3
salt concentration, c [g salt/L solution]
(a)
(b)
Figure 2: (a) our familiar saline solution process except qw # qout. the volume V of liquid in the
tank is constant because of the overflow line. (b) density of saline solution versus concentration
of salt. the line shows the model p(c) = Pw + ac.
qw(t)
your goal is to derive a dynamic model for c = c(t) in terms of the two inputs qw =
and w = w(t).
density of solution, p
Ig solution/L solution]
Transcribed Image Text:(b) write an overall (salt + water) mass balance. it will be a differential equation.
(c) use the overall mass balance to eliminate qout from the salt balance, so that the input
qw appears in the salt balance. also, use p(c) = Pw + ac to eliminate p from your
dynamic model. write the final dynamic model as
dc
(..
:).
dt
with .. representing algebraic (not differential) expressions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 16 images
Recommended textbooks for you
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
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