Lecture 3 - Basic Variables and definitions

Question 1

Scalars - ?
Vectors - ?
Tensors - ?

Answer 1

Scalars - Magnitude
Vectors - Magnitude + Direction
Tensors - Magnitude + Direction + Orientation

Question 2

Gradient operation ?

Answer 2

grad f = nabla * f

Question 3

Curl operation ?

Answer 3

curl F_–> = nabla X F_–>

Question 4

Divergence operation ?

Answer 4

div F_–> = nabla . F_–>

Question 5

Laplacian operation ?

Answer 5

delta_f = nabla^2 * F = nabla . nabla * f

Question 6

Curl operator ?

Answer 6

omega_–> = nabla X v_–>

Question 7

Vorticity is related to …

Answer 7

the average angular momentum of a fluid particle and the swirl present in the flow.

Question 8

Two measures of rotation in a fluid?

Answer 8

Vorticity and Circulation

Question 9

Vorticity characteristics

Answer 9

vector field that gives a microscopic measurement of the rotation at any point of the field

Question 10

Circulation characteristics

Answer 10

scalar integral quality, macroscopic measure of rotation for a finite area of the fluid

Question 11

Circulation definition

Answer 11

Circulation, Gamma, about a closed contour in a field - line integral evaluated along the contour of the component of the velocity vector that is locally tangent to the contour

Question 12

Circulation equation

Answer 12

see sheet

Question 13

in XY plane circulation definition represents?

Answer 13

Greens Lemma

Question 14

Role of vortices in cardiac function ?

Answer 14

1. Keep blood in motion inside cardiac chambers
2. Preserve momentum to help avoid excessive dissipation of energy facilitating inflow into the ventricle, and redirecting it towards the aortic valve.

Question 15

Vortical flow patterns in the heart have differences related to … ?

Answer 15

1. Age
2. Gender
3. Blood pressure
4. Ventricular geometry