Week 06 Fluid Flow Lecture Flashcards
What is volumetric flow rate?
Its equation?
- the amount of volume passing a point per unit time
What is viscocity?
What does it measure?
What does it depend on highly?
- the “internal friction” of a fluid that arises from collisions between neighboring particles moving at different velocities
- measures resistance to deformation due to shear or tensile stress
- highly dependent on temperature … higher temp = lower viscocity
How can viscocity be calculated?
What are the units of viscocity?
Viscocity = Shear Stress / Velocity Gradient
(see equation below)
- Pascals (Pas) … N⋅s/m2
…or poise (p)
- 1 Pas = 10 p
What is a velocity gradient in relation to modeling viscocity?
A fluid can be modeled as layers on top of each other.
The bottom layer moves least due to pressure from the above layers.
The top layer moves most, due to lack of pressure.
All layers in between have a velocity gradient based on the increasing pressure from above as you move down through the layers.
What are the 3 main basic types of fluids and their properties?
- Ideal - frictionless, non-compressible (constant ⍴), non-viscous
- Real Newtonian - constant viscocity (ind. of shear stress)
- Real Non-Newtonian - visc. changes w/ shear stress (AKA anomalous)
How do the (4) different types of real fluids react to variations in shear stress?
This includes the various types of anomalous fluids.
- Newtonian - linear relationship btwn shear stress and velocity gradient starting from origin
- St. Venant - does not flow at all, until a shear stress threshold at which it begins to flow almost perfectly
- Bingham - has a linear relationship once threshold is met
- Casson - has exponential relationship once threshold is met
What are the 3 different types of fluid flow?
- Stationary - constant volumetric flow rate
- Laminar - fluid layers do not mix
- Turbulent - fluid layers mix
What is the continuity equation?
Describe the theory behind it.
A1v1 = A2v2
A = cross-sectional area
v = flow velocity
- a volume of fluid has a higher flow velocity (NOT vol. flow rate) in a tube with a smaller cross-sectional area
What is the engineering model of a viscoelastic body called?
What are its two parts and what do they represent?
Kelvin Body
- spring (rubbery, but solid, non-flowing quality) and dashpot (viscocity) coupled in parallel
What does the Reynolds number of a fluid flow system indicate?
What factors increase Reynolds number?
What is the equation?
- whether a fluid will flow laminarly or turbulently
- __Rc = 2000 is cutoff between flow types
- higher number = more turbulence
- factors increasing R:
- increased radius
- increased flow velocity
- increased fluid density
- decreased fluid viscocity
What is Bernoulli’s Law?
What is its equation?
- the sum of all forms of energy (pressure) in a fluid along a streamline is the same at all points on that streamline (law of conservation of energy)
What are the 3 types of pressures relevant to Bernoulli’s law?
- Static - pressure exerted by fluid on wall of vessel
- Dynamic - pressure difference between inlet/outlet of tube, maintains Ekin of flow
- Hydrostatic - pressure measured at the bottom of fluid column
What effect does Bernouli’s law create in fluid flow systems?
Venturi effect
- the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe
- results because the fluid velocity must increase in accordance with the continuity equation, so the pressure must decrease to keep the sum of all energies within the system constant
What is Stokes Law?
What two kinds of fluid/object situations does it pertain to?
- an equation which relates Stokes Force/Drag to flow rate, radius of object in the flow and viscocity
- affects stationary objects in moving fluid and moving objects in stationary fluid (ie spermatocytes)
What assumptions does Stokes Law make for the behaviour of a particle in fluid?
- Laminar Flow
- Spherical particles
- Homogeneous (uniform in composition) material
- Smooth surfaces
- Particles do not interfere with each other
What is the Hagen-Poiseuille Law?
a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section
What is the medical signifance of the Hagen-Poiseuille Law?
Oxygen delivery changes DRASTICALLY with small changes in vessel diameter (because of fourth-power dependence of flow intensity on vessel radius)
- changes in blood viscocity in fever/anemia also have an effect
How does the continuity equation change in bifurcating vessels?
- when a vessel bifurcates, we must consider the total cross-sectional area of the two new vessels and the average velocity of each of the new branches
How does static pressure changed as we travel from aortic SLV to right atrium?
a steady decrease from about 100 mmHg in aorta
How does flow rate change throughout the vascular system?
Starts very high in aorta
Dips to lowest in arterioles/capillaries
Increases again in veins to just below arterial levels
How does total cross sectional area change throughout the vascular system?
opposite of flow rate
starts out lowest in aorta/arteries (2.5 cm2)
increases to highest in capillaries (2500 cm2)
decreases to just above aortic level in veins (8 cm2)
What is the Young-Laplace equation?
an equation explaining the relationship between pressure on the wall (from the blood within) and tension arising in the wall
