ECH 141
Problem Set #4
1. Eulers First Law (or the Linear Momentum Principle, or Conservation of Linear Momentum) is
sometimes written in words as
The rate of change of
The sum of the forces
=
.
momentum of a fluid particle acting on the particle
In
ECH 141
Problem Set #5
1. The generalized Newtonian fluid model provides a simple way to describe non-Newtonian fluids in
steady unidirectional flow. Here you will derive a generalized form of the Hagen-Poiseuille equation
for fully developed flow of a po
ECH 141
Problem Set #7
Due 3/8/2017
1. Text 7-15
Solution
This problem is very similar to the tank-draining problem discussed in the text and in class. It is a
rounded orifice, so the discharge coefficient can be taken to be unity. The complication has be
ECH 141
Problem Set #3
1. Whitaker problem 2-8. Substitute y=6m for y=6ft, and use =1m1/2.
Solution
If L=6m, then the pressure in the water is, from derivations in class,
p = p atm + g ( L y ) .
To calculate the force on the curved gate in the figure, we
ECH 152B, Winter 2016, Roland Faller & Adam Moule
Solution for Homework 8, March 3, 2016.
Problem 1
Assume you have a system with two compartments each holding 10 liters of
water separated by a semipermeable membrane which can pass water but not
sugar. On
ECH 141
Problem Set #6
1. Text 7-3
(Use only the macroscopic momentum balance, not the mechanical energy balance. Your result will not
be the same as that obtained from the energy balance, because different assumptions are involved.
Assume quasi-steady co
ECH 152B, Winter 2016, Roland Faller & Adam Moule
Solutions for Homework 9, March 14, 2016
Problem 1
Chain length determination by osmometry
Assume you have two identical vessels of water (10 l in each) connected by a
semipermeable membrane (waterpermeabl
Here dAZ is the surface area projected to the xy plane. The transition from dA to dAZ requires a
negative sign when the angle between n and eZ is greater than 90, as discussed below. Otherwise,
projection of the upper part of the dome and the lower part i
ECH 141
Problem Set #8
1. Two immiscible liquids A and B of specific gravities 0.8 and 1.0, respectively, flow into a closed
tank in which they separate into two layers. Pure A and pure B are taken off by pipes which discharge
to atmosphere at a point 5 f
ECH 152B, Winter 2016, Roland Faller and Adam Moule
Solution for Homework 7, February 17, 2016
Problem 1
(a) Determine the number of independent reactions if the system contains
C2 H5 OH, H2 O, O2 and CH4 .
(b) Write the mole fractions of all constituents
Fluid Mechanics (ECH 141)
Problem Set #1
Due Wednesday 1/18/2017
1. a) Evaluate the dot product of a and b if
a = xe x + (1 xy ) e y + e t e z
and
b = 2e x + 3e y + e z .
b) Find the magnitude of the vector a if
a = cose x + sine y + e z .
Solution
a) The
WHAT HAVE WE LEARNED?
When I complete this review, I want to be
able to recall the following.
Build a feedback control loop
Design and tune PID controllers
Analyze closed-loop stability
Evaluate the control performance
Design feed-forward control sys
DYNAMICS OF MORE COMPLEX
PROCESS SYSTEMS
When I complete this chapter, I want to be
able to do the following.
Predict output for typical inputs for
common dynamic systems
Derive the dynamics for important
structures of simple dynamic systems
Recognize
University of California, Davis
Department of Chemical Engineering
ECH 157 - Process Dynamics and Control
Fall 2016
Practice Problem Set # 1
Note: The following selection of problems are intended to provide you with
additional practice in your preparation
University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 - Process Dynamics and Control
Fall 2016
Homework Problem Set # 5
Group Assignment
Assigned: Monday, Oct. 31.
Due: Monday, Nov. 7 (at the beginning of class).
R
University of California, Davis
Department of Chemical Engineering
ECH 157 - Process Dynamics and Control
Fall 2016
Practice Problem Set # 3
Problem 1: A cascade control configuration is sometimes used to separate
different objectives of feedback control.
University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 - Process Dynamics and Control
Fall 2016
Practice Problem Set # 2
Note: The following selection of problems are intended to provide you with
additional practice
11/14/2016
MID-TERM EXAM II: CHECKLIST
Understand concepts of controlled
variable, measured variable, manipulated
variable, and disturbance.
Derive first-principle dynamic models
using mass and energy balances.
Be able to linearize nonlinear models and
University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 - Process Dynamics and Control
Fall 2016
Homework Problem Set # 2
Assigned: Monday, Oct. 3.
Due: Wednesday, Oct. 10 (at the beginning of class).
Reading Materia
University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 - Process Dynamics and Control
Fall 2016
Homework Problem Set # 3
Assigned: Monday, Oct. 10.
Due: Monday, Oct. 17 (at the beginning of class).
Reading Material:
University of California, Davis
Department of Chemical Engineering
ECH 157 - Process Dynamics and Control
Fall 2016
Homework Problem Set # 1
Assigned: Monday, Sept. 26.
Due: Monday, Oct. 3 (at the beginning of class).
Reading Material: Lecture notes, Chap
University of California, Davis
Department of Chemical Engineering & Materials Science
ECH 157 - Process Dynamics and Control
Fall 2016
Homework Problem Set # 4
Group Assignment
Assigned: Saturday, Oct. 15.
Due: Friday, Oct. 21 (before 5:00 pm).
Reading M
ECH 141
Problem Set #6
1. Text 7-3
(Use only the macroscopic momentum balance, not the mechanical energy balance. Your result will not
be the same as that obtained from the energy balance, because different assumptions are involved.
Assume quasi-steady co
Exam 1 Solution
ECH 140: Mathematical Methods in Biochemical and Chemical Engineering
Closed book, no notes
October 23, 2015
1. Solve the following:
a.
b.
df
+ f = 0 where f(0)=1
dt
df
= t 2 f + e 2t where f(0)=1
dt
Solution
a. Multiply by the integrating
ECH 140
Problem Set #8
1. Use the method of characteristics to solve the first-order problem
u u
+
=0 ,
x t
with the initial condition
u ( x,0 ) = cos x .
Consider the unbounded domain < x < and 0 < t < . Sketch your solution at different times,
and expla
ECH 140
Problem Set #7
1. Solve Laplaces equation inside a semi-infinite strip defined by 0 x < and 0 y H with the
boundary conditions
u
u
( x,0 ) = 0, ( x,H ) = 0 and u(0,y)=f(y)
y
y
Assume that u(x,y) is finite as x gets arbitrarily large.
Solution
We h
ECH 140: Mathematical Methods
Exam 2 Solution
Closed book, no notes, no calculators
November 20, 2015
1. The function u(r,z) is the solution to Laplaces equation in cylindrical coordinates,
1 u 2 u
=0 .
r +
r r r z 2
The boundary conditions are
and
u = 0
1. Solve the followuig:
dzf d1 25
a. 2+3+?f=
h dzff+sinui Wh: 0H5)?
hr 4 '
Solution
3. Since this is a lirear, secondorder, ordinary diEferentisl equation with oonstant
coefcients, assume the solution has the form of an exponential and substitute to obtai
100
Chapter
3
Fourier Series
mclre and
extrapolate to guess what happens for 1000 tenns. Tire series sliorrld beli:orne
to r'anish
more accurate as the nurlber of terms increases. We rnight expect the ovelrsltoot
just
does not
It
as n + oo, but put a, str