Week 6 Flashcards
What are the four classical solutions of the continuity and momentum equations for incompressible viscous flows?
- Couette flow between a fixed and a moving plate
- Flow due to pressure gradient between two fixed plates
- Fully developed laminar pipe flow
- Flow between long concentric cylinders
These solutions are fundamental in the study of fluid mechanics.
What is the Reynolds number used for in fluid mechanics?
It quantifies the relative importance of inertial forces to viscous forces for given flow conditions.
The Reynolds number is a dimensionless parameter that helps predict flow regimes.
Define Couette flow.
Flow between parallel plates due to a moving upper wall.
In this case, one plate is stationary while the other moves, creating a shear flow.
What is Poiseuille flow?
Fully developed laminar pipe flow.
It describes the flow of a viscous fluid in a straight circular pipe.
What are the assumptions made for Couette flow?
- Plates are very wide and long
- Flow is essentially axial
- Incompressible and steady flow
- No pressure gradient
- Neglect gravity effects
These assumptions simplify the analysis of the fluid motion.
What are the assumptions for flow between long concentric cylinders?
*no axial moon (vz = 0) or end effect (the velocity does not vary
with z)
*Steady flow
*circular symmetry
What does the continuity equation in cylindrical coordinates reduce to for fully developed flow?
The equation reduces to r = R, indicating axial symmetry.
This means that the velocity profile is only a function of the radial position.
What is the significance of the no-slip condition in fluid flow?
It states that the fluid velocity at the boundary (wall) is equal to the velocity of the wall itself.
This condition is crucial for determining shear stress in viscous flows.
Why is the reynolds number the most important quantity in fluid dynamics?
It quantifies the relative importance of inertial forces/dynamic pressure (ρU2) to
viscous forces/shearing stress (μ U/L) for given flow conditions.
What is the Reynolds number (Re) for laminar and turbulent flow?
*Laminar, Re < 2,000
*Turbulent, Re > 2,000
Turbulent flow typically occurs when Re > 2,000.
What happens to flow characteristics as the Reynolds number increases?
High Re indicates turbulent flow dominated by inertial forces, leading to chaotic eddies and vortices.
This transition is vital for understanding fluid behavior in various applications.
What happens to flow characteristics as the Reynolds number decreases? What is this flow often called?
Very low Re indicates viscous creeping motion, where inertia effects are
negligible. Stokes flow.
True or False: Turbulence rarely occurs in healthy blood vessels.
True
When turbulence does occur, it can produce noise, which is used in blood pressure measurement.
What is the condition for very low Reynolds number flow?
Viscous creeping motion, where inertia effects are negligible.
This type of flow is also known as Stokes flow.
List the three basic approaches to the analysis of arbitrary flow problems.
- Control volume analysis
- Differential analysis
- Experimental analysis
Each approach provides different insights into fluid behavior.
What does the z-momentum equation for fully developed laminar flow simplify to?
p = p(z) only, indicating pressure is a function of z-direction only.
This simplification is critical for analyzing flow in cylindrical coordinates.
What Reynolds number are eddies possible?
Re > 200
How are eddies found in blood vessels?
When it occurs it produces noise
(used to measure BP with cuff)
