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Chapter 6: Viscosity and the Patterns of Flow : (Viscosity (Reynolds…
Chapter 6: Viscosity and the Patterns of Flow :
General Info
Gases are easier to push around quantitatively.
Gases and liquids have widely different compressibility.
The compression difference in a biological manner are virtually identical and of no consequence.
Difference on liquids/gases of gravity and surface tension
Can be ignored with natural flows that don't involve fluid-fluid interactions.
Viscosity
Reynolds Number
Why is it important?
Laminar v. Turbulent Regimes
Examples of Reynolds Numbers
Consequences of the no-slip condition
Viscosities and Densities at 20*C
Air
Viscosity: 18.1x10e-6 (pa*s)
Density: 1.2 (kg*m^-3)
Ratio: 15.00x10e-6 (m^2s^-1)
Water
Viscosity: 1e-3 pa*s
Density: 1e3 kg*m^-3
Ratio: 1e-6 m^3s^-1
Seawater
Viscosity: 1.07e-3 pa*s
Density: 1.02e3 kg*m^-3
Ratio: 1.05e-6 m^2s^-1
Modeling
Streamlines and Appearances of Flows
Solids v. Fluids
Liquids and Gases
Share viscosity
Shear stiffness/elasticity doesn't apply in the same sense
Do not resist being deformed, but still respond to shear stresses
Capable of unlimited distortion
Force depends on the rate of strain of the fluid block
Resistance of fluid depends on how fast it's distorted
shear stress = viscosity x shear strain rate
measure of how rapidly layers of fluid slides in respect to one another
rate of change of velocity with distance (gradient) but velocity varies with a right angle to the flow.
Solids
Shear stiffness/elasticity
Resist being deformed
greater the force, more distortion of object
ratio of stress to strain is shear modulus: shear
stress=shear modulus x shear strain
If a fluid is highly resistant to shearing rates, then velocity gradients are slower to slope and are over long distances
If effects of viscosity are slight, the gradients are steeper over shorter distances
Equations and their Uses
F/S=μv/d
F(force)
S(area)
μ(coefficient of viscosity)
v(velocity)
d(distance between upper/lower bounds)
Modeling quantitatively the no-slip condition of a fluid between two plates
Units are Kg/m
s or Pa
s
St=nl/v
mr^2 ω=mv_t r
Re=F_i/F_v =ρlv/μ
mv⁄t=〖ρSv〗^2=F_i
Vortices
Irrotational Vortices
Ground-Level Vortices
Yay! More Vortices!
