Boundary Conditions at a Solid-Fluid Interface
One of the boundary conditions that must be
satisfied at a solid-fluid interface is that the fluid must
not penetrate the solid if it is impermeable to t
Stokes Number and Womersly Number
Recall Navier-Stokes equations:
ui
ui
2 ui
p
+ u j
= X i
+
t
x j
xi
xk xk
represents the balance of four kinds of forces. Term by term, they are
transient
inertial
52 2 The Meaning of the Constitutive Equation
we question of Choosing the right model to t the experimental ata is an
1 curves of
lex modulus)
imp rtant one. Usually the rst step is to compare the
Principal Stresses and Axes
We have seen that 9 components of stress, of which 6 are independent,
are necessary to specify the state of material interaction at any given
point in a body:
11 12 13
=
Red Blood Cells
Erythrocytes (Red Blood Cells, RBC):
RBC is an important cell whose prime function is
to transport O2 from the lungs to the cells of the body
and return CO2 to the lungs to be exhaled
Field Equations in Fluid Mechanics
We have acquired enough basic equations to deal with a
broad range of problems. Most objects on a scale that we
can see are continua. Their motion follows the laws o
Navier-Stokes Equation
Let us recall the Navier-Stokes equation. For simplicity, we
shall consider a homogeneous incompressible fluid:
Du
1 p 2
=X
+ u
Dt
x
Dv
1 p 2
=Y
+ v
Dt
y
Dw
1 p 2
=Z
+ w
Dt
Linear Differential Equations
A first-order differential equation is said to be linear if it
can be written:
'
y + p ( x) y = r ( x)
The characteristic feature of this equation is that it is
linear
Transport Equations and Material Derivatives
The Equation of Continuity
The law of conservation of mass was discussed in the previous sections.
With the results of material derivatives and transport e
- - . .i . . Maaw A; J5. Prim 4.3%; hed-9E. 9:24;.5; mesa-4.x A
gure 64! Substitution Reactions in the Mechanism oi Action of
Some Enzymes. (a) Nucleophilic substitution. with N- as the nucleophilic
understanding AG
tmr nal task in this chapter will be to understand how AG is
calculated and how it can then be used to assess the thermo-
dynamic feasibility of reactions under specied condi-
tions.
12W. 1.
. E MCH 213
1) _'_ Strength of Materials
2) m .
3>_ ' EXAMI
.4)
Summer 2017
Total
Score out of 100%
INSTRUCTIONS:
1. Read the problems carefully H!
2. Your exam should contain 3 problems
Penn State University
Abington College
Spring 2017
MATH 251 Ordinary and Partial Differential Equations
Instructor: Dr. Matthew Fury, Assistant Professor of Mathematics
333 Sutherland, phone: 215-881-
PENN STATE UNIVERSITY
ABINGTON COLLEGE
Division of Science and Engineering
COURSE SYLLABUS
MATH 141, CALCULUS WITH ANALYTIC GEOMETRY II
Spring 2017
Credits: 4
Section: 006
Class Days &Time: M, W, F: 2
Math 141 Final 6:50pm-8:40pm, Monday, December 12, 2016
Exam Day
1. KNOW your instructors name
2. KNOW your section number
3. KNOW your exam location
Questions? Read the syllabus and/or ask your instr
BME 301 Analysis of Physiological Systems Fall 2017
August 27, 2017
Homework #1
Due: Tuesday September 5, 2017 at the beginning of class, please write your last name and initials,
and section number o
BME 301 Analysis of Physiological Systems Fall 2017
September 12, 2017
Homework #3
Due: Tuesday September 19, 2017 at the beginning of class, please write your last name and initials,
and section numb
BME 301 Analysis of Physiological Systems Fall 2017
September 28, 2017
Homework #4
Due: Thursday October 5, 2017 at the beginning of class, please write your first name, last name and
initials, and se
BME 301 Analysis of Physiological Systems Fall 2017
September 5, 2017
Homework #2
Due: Tuesday September 12, 2017 at the beginning of class, please write your last name and initials,
and section numbe
Homework #3 (assigned on 9/8/17; due on 9/15/17 by 5pm)
1. Consider a transformation of stress components.
(a) Label all those missing stress components ij in the coordinate system xi (i = 1, 2, 3)
an
Homework #6 (assigned on 10/9/17; due on 10/18/17 by 5pm)
1. If the mass contained in a compressible domain V at a given t is m = dV
V
where = (x1, x2, x3, t) is the density within V at location x = x
Homework #5 (assigned on 9/22/17; due on 9/29/17 by 5:00 pm)
1.
A unit square OABC is changed to OABC in three ways, as shown: (a)
Extension in x2 but compression in x1 direction (1 and 2 are infinite
Homework #4 (assigned on 9/15/17; due on 9/22/17 by 5 pm)
1. Consider the plane stress element shown in figure representing the state of stress at a
material point in the xy-plane. If the magnitudes o
Homework #2 (assigned on 9/1/17; due on 9/8/17 by 5pm)
!
!
!
!
1. For any two vectors: u = u i ei and v = v j e j (i, j = 1, 2, 3), the cross product of these
two vectors is given by c = u v = rst u