BME110C BIOMECHANICS III (Requied for BME) Catalog Data: BME110C Biomechanics III (Credit Units: 4) Applications of statics and dynamics to biomedical systems. Cellular biomechanics, hemodynamics, circulatory system, respiratory system, muscles and moveme
April 14, 2016
BME 110C
Arash Kheradvar
Solution Set 3
Due April 21, 2016
In class
1) What is a fully developed flow? Simplify the NavierStokes equations in polar
coordinate for a fully developed in a pipe, and find the steady state solution (Poiseuille
March 31, 2016
BME 110C
Arash Kheradvar
Problem Set 1
Due April 07, 2016
In class
1) Describe varus and valgus deformities, and define how abnormal angulation of
a bone or joint, stand from the midline in each deformity (40 points).
2) Many people with ce
Vector Differential Calculus
Grad, Div, Curl
BME 110 C
Biomechanics III
Vectors in 2D and 3D Space
In engineering and physical quantities are described
with
scalars (e.g. potential energy, pressure, density, etc.)
vectors (e.g. force, velocity, electri
April 21, 2016
BME 110C
Arash Kheradvar
Solution Set 4
Due April 26, 2016
In Class
1) Considering the ratio of inertial to viscous forces in a fluid, show that the
Womersley parameter is analogous to the Reynolds number for unsteady flow (30
points).
Answ
BME 110C: Biomechanics III
(Biofluidics)
Instructor:
Dr. Tibor Juhasz
TTH: 2:003:20PM, SSL 290
Course Objectives
1) Students will learn about the fundamental fluid
dynamics and their applications to human
biomechanics.
2) Students will learn about th
5
Pulsatile Flow in an Elastic Tube
5.1
Introduction
In the case of a rigid tube it is possible to postulate a fully developed
region away from the tube entrance where the flow is independent of x, thus
derivatives of u, v with respect to x are zero. The
1
Preliminary Concepts
1.1
Flow in a Tube
Flow in a tube is the most common fluid dynamic phenomenon in biology.
For two good reasons, the bodies of all living things, from the primitive to
the complex, plant or animal, are permeated with a plethora of fl
2
Equations of Fluid Flow
2 .1
Introduction
Equations governing steady or pulsatile flow in a tube are a highly simplified
form of the equations that govern viscous flow in general. The laws on which
the general equations are based and the assumptions by
3
Steady Flow in 'lUbes
3.1
Introduction
When flow enters a tube, the noslip boundary condition on the tube wall
arrests fluid elements in contact with the wall while elements along the
axis of the tube charge ahead, less influenced by that condition. Be
6
Wave Reflections
6.1
Introduction
Solutions of the equations for pulsatile flow in an elastic tube considered
in Chapter 5 produce a flow field that differs only slightly from the corresponding solutions in a rigid tube. The elastic tube solution is bas
4
Pulsatile Flow in a Rigid Tube
4.1
Introduction
Flow in a tube in which the driving pressure varies in time is governed by
Eq.3.2.9, namely,
pau + ~ ap
at pax
= fl
(a 2u + ~ au)
ar2 r ar
Providing that all the simplifying assumptions on which the equati
Wall Stress and Patterns of Hypertrophy
in the Human Left Ventricle
WILLIAM GROSSMAN, DONALD JONES, and LAMBERT P. MCLAURIN
From the C. V. Richardson Cardiac Catheterization Laboratory and the
Department of Medicine, University of North Carolina School of
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Solution Set 6
May 12, 2016
BME110c
Arash Kheradvar
Due May 17, 2013
In class
1) Considering the cube law for the arterial branching, based on the assumption of
Poiseuille flow, derive the optimum branching angle to minimize the pumping power
required to
Solution Set 5
May 05, 2016
BME 110C
Arash Kheradvar
Due May 12, 2016
In class
1) In an experiment on an exposed abdominal aorta of a dog, the pulse wave speed is
determined to be 1.5m/s. If the density of the EORRG is 1.06 g/cm3, the wall
thickness of th
Problem Set #1  Solutions
1. Describe the most important physical properties of liquids and explain the differences between
liquids and solids.
Fluids deform under the action of a force and continue to do so o
Homework 8
Solutions
1) Show by substitution that separation of variables in equation:
u (r , t ) = U (r )e it
reduces the partial differential equation of
2 u
r 2
+
1 u u Ks it
=
e
r r
t
into an ordinary differential equation.
Solution:
Substituting U
Problem Set 4
1. (25 Points) Consider highspeed turbulent flow through a narrow constriction, as shown below.
Assuming that the velocity profiles are uniform in turbulent flow (i.e., the time averaged velocity
v is a constant and does not vary with di
Problem Set 6  Solutions
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of radius a if !
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April 07, 2016
BME 110C
Arash Kheradvar
Solution Set 2
Due April 14, 2016
In class
1) When density is constant, the law of conservation of mass in a fluid as expressed:
1
0
does not contain either mass or density. Explain how this is possible (30 points).
The NavierStokes Equations in Vector
Representation and in Cylindrical
Coordinates
BME 110 C
Newtons Second Law of Motion Expressed Per
Unit Volume in a Flow Field
v
+ (v )v = p + + g
t
In the absence of fluid motion :
p = g
(The equation of fluid stat
The Circulatory System:
Rheology of Blood
BME 110C: Biomechanics
University of California at Irvine
Outline
1. Blood characterisBcs
2. Viscous behavior
3. Flow eects for small vessels
Blood C
M. Zamir
The Physics of
Pulsatile Flow
Foreword by Erik L. Ritman
With 75 Illustrations
AlP
ffi.~
,
Springer
M. Zamir
Department of Applied Mathematics
University of Westem Ontario
London, Ontario N6A 5B7
Canada
[email protected]
Cover illustration: Pul
M. Zamir
The Physics of
Pulsatile Flow
Foreword by Erik L. Ritman
With 75 Illustrations
AlP
,
Springer
M. Zamir
Department of Applied Mathematics
University of Westem Ontario
London, Ontario N6A 5B7
Canada
[email protected]
Cover illustration: Pulsatile