Fluid Mechanics L2 - Fluid Mechanics and Cardiovascular Terminology

Statics

F = 0

Dynamics

F = ma

Normal Stress

σ (or pressure) = F/A

Shear Stress

τ

Fluid

Any material that deforms continually under the application of shear stress

How does a solid resist applied shear stress?

By deforming

What happens when a constant shear force is applied to solid

Solid eventually stops deforming at some fixed strain angle

What happens when a constant shear force is applied to fluid

Fluid never stops deforming and approaches a constant rate of strain

In a fluid at rest, the normal stress is called what?

Pressure

A fluid at rest is at a state of how much shear stress?

τ = 0

liquid have weaker/stronger cohesive forces than gases

Stronger

liquids form a ___________ indicated by _____________

Free surface; three lines

characteristic of liquid

Incompressible (unable to squeeze or compress)

characteristics of gases

Deformable and compressible

What is on free surface?

Atmospheric pressure

Ideal Gas Law

PV = nRT

Two plate model

The fluid that is in contact with the top plate will move with the same velocity and move to the same displacement as the top plate

Viscosity

Resistance to flow; interaction between molecules

Viscous flow

Frictional effects are significant; consider friction

Inviscid flow

Neglecting viscous terms for simplification (no viscosity); no friction

Example of high viscosity

Honey

Example of low viscosity

Water, air

External flow

Unbounded; flows over a surface or object without being confined by solid boundaries all around it

Internal flow

Bounded by solid; fluid moving through a pipe or duct

Open channel flow

Flow where the fluid is bounded by a solid surface from below and has a free surface exposed to the atmosphere.

Laminar

Layered; lower velocity; highly viscous; modeled and predictable; ex: blood

Turbulent

Chaotic; higher velocity; lower viscosity; hard to model

Transitional

Flow that falls between laminar and turbulent flow

Reynolds number

Re = (density*velocity*diameter)/viscosity

dimensionless number

Forced flow

Pump; ex: heart or fan

Natural flow

Ex: heat dissipating

Is blood steady or unsteady?

Unsteady because heart pumping causes it to flow at changing velocities

Steady flow

Flow where fluid properties at any point in space do not change with time.

Unsteady flow

Flow where fluid properties at any point in space change with time.

Transient flow

Flow where fluid properties are changing over a temporary period of time.

Fully developed flow

When the fluid's speed and direction (velocity) pattern becomes constant and no longer changes as it flows

Period flow

A type of unsteady flow where fluid properties change in a repeating pattern over time.

What is 1, 2, 3-D flow characterized by?

Its velocity distribution and if it varies by one, two, or three dimensions

What are the different coordinates for 1, 2, 3-D flow?

Rectangular V(x,y,z) or cylindrical V(r,θ,z)

Steady flow entering a circular pipe:

• Fluid flow at pipe surface is what and why?

0 due to no-slip condition

Steady flow entering a circular pipe:

• At entrance, flow is what and why?

2-D because velocity changes in both r and z directions, not angular θ

Steady flow entering a circular pipe:

• Fully developed flow is what and why

1-D since the velocity varies in radial (r) direction but not angular (θ) or axial (z) direction - symmetric about the axis of the pipe

Why do we need to study fluid mechanics as BMEs?

• 1/3 deaths in US due to cardiovascular disease (1.5 times cancer)

• Our body is 65% water

Purpose of blood circulation

• Transport

  • O₂ and CO₂

• Communication

  • Growth factor signals

• Heat Exchanger

• Protection

  • Immune system

What does the left side of the heart do?

Takes blood all around the body

List order of blood flow

Left side of heart → oxygenated blood → systemic arteries → capillaries → systemic veins → deoxygenated blood → right side of heart → lungs