Bulk Materials - Fluid dynamics Viscous

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Defintions

Streamline: Curve whose tangent, at every point is direction of fluid velocity at that point. Where streamlines converge = velocity increases

Tangent: Touches at one point

When shear stress applied to a fluid, it causes it to flow, therefore deform continuously.

Viscosity (n) - resistance of the fluid to flow = 1 Nsm-2 = 10 poise

-velocity depends on distance of fluid from wall of pipe

-high velocity fluid do not flow readily (high n)

-n low for water

- for many fluids Strain rate PROPORTIONAL Shear stress

Poiseulle's Law (viscous volume flow rate equivalent) used for blood flow

-requires higher pressure at inlet to the pipe than the outlet.

EXTRA PRESSURE required to overcome internal friction of the fluid

This is gives the equation (combining volume flow rate and resistance to flow)

Q = FANCY F = volume flow rate

for a laminar, incompressible flow of viscous fluid.

High Viscosity - Laminar flow. Velocity at the ends is lower than centre

Low Viscosity - Constant velocity throughout pipe

Turbulence

-When velocity of fluid exceeds critical value, flow becomes highly complex.

- A SINGLE number which indicates whether flow is laminar or turbulent.

For pipe- Re

Re>about 3000 = Turbulent - v chaotic