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
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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 a
Problem Set 6
(Due by 5/21/15 in class)
1. The perimeter of an ellipse of semiminor and semimajor axes b and c is equal to that of a circle
2
of radius a if
2 + 2
2
. The flow rate for the ellipse
Problem Set 5
(Due by 5/14/15 in class)
1.
2
2
+
1
2 represents the power dissipated by a thin cylindrical shell of fluid
moving with the same velocity. Show that integrating the above express
Problem Set #3
1. Explain the difference between surface forces and body forces that may act on a fluid
element in a flow field. Give an example of each and discuss their physical meaning.
(30 points)
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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, th
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 comple
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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
Departm
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 t
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 solu
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 t
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
Problem Set #1
1. Describe the most important physical properties of liquids and explain the differences between
liquids and solids.
2. Swordfish is known to feed in
BME 110C: Biomechanics III
(Biouidics)
Instructor:
Dr. Tibor Juhasz
TTH: 2:003:20PM, SSL 290
Course ObjecKves
1) Students will learn about the fundamental uid
dynamic
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Problem Set 6  Solutions
1. The perimeter of an ellipse of semiminor and semimajor axes b and c is equal to that of a circle
of radius a if !
! ! ! !
!
. The flow rate for the ellipse is !" =
The