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+acwhere 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 conveyor saline water density qw LIs model 1200 . expertnental data 1150 1100 p=p{c}=Pw+ ac a = 0.64 g solution/g salt 1050 saline solution Jouot LIS C g/L 1000- 0.2 salt concentration, c [g salt/L solution] 0.0 0.1 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 = c(t) in terms of the two inputs qw and w = w(t). qw(t) (a) write a component mass balance on the salt. it will be a differential equation. 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+acwhere 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 conveyor saline water density qw LIs model 1200 . expertnental data 1150 1100 p=p{c}=Pw+ ac a = 0.64 g solution/g salt 1050 saline solution Jouot LIS C g/L 1000- 0.2 salt concentration, c [g salt/L solution] 0.0 0.1 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 = c(t) in terms of the two inputs qw and w = w(t). qw(t) (a) write a component mass balance on the salt. it will be a differential equation. 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
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![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 + gout. 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
model
qw LIs
1200
experinental data
1150
1100
saline solution
p=ptc)=Dpw+ 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.
c(t) in terms of the two inputs qw = qw(t)
your goal is to derive a dynamic model for c =
and w = w(t).
(a) write a component mass balance on the salt. it will be a differential equation.
density of solution, p
[g solution/L solution]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4182e5fe-a12a-4c0b-bb5e-835d4eda4ff6%2F3629bb27-c325-45f3-93e5-ccd0c2c79aad%2Fsox3vd_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 + gout. 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
model
qw LIs
1200
experinental data
1150
1100
saline solution
p=ptc)=Dpw+ 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.
c(t) in terms of the two inputs qw = qw(t)
your goal is to derive a dynamic model for c =
and w = w(t).
(a) write a component mass balance on the salt. it will be a differential equation.
density of solution, p
[g solution/L solution]
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