handout_on_fluid_friction_and_surface_tension

# handout_on_fluid_friction_and_surface_tension - Fluid...

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Fluid Friction and Surface Tension Fluid Friction Fluid-Solid Friction Far from the solid, the liquid flows without any influence of the solid. The velocity of a fluid relative to a solid surface must go to zero at the fluid-solid interface. Evidence: dust on fan blades; raindrops on your windshield don't blow off when driving at high speeds. Consequently, the fluid velocity tends to vary rapidly near the surface of a solid. For air near the Earth’s surface, the velocity increases from zero at the surface, and reaches a nearly constant value about 30 ft above the surface. Fluid-Fluid Friction Recall – in solid-on-solid friction, the static and kinetic frictional forces oppose relative motion of the surfaces in contact. S i m i l a r l y i n f l u i d s , t h e r e i s f r i c t i o n t h a t o p p o s e s the relative motion of different layers of the fluid. Fluid friction or drag opposes relative motion of layers of fluid.

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Consider this specific geometry: If we want the top plate to move at a speed v top , we have to overcome fluid drag by applying a force equal and opposite to it, of magnitude F D . The velocity of the fluid is 0 at the bottom (no motion relative to the bottom plate) and v top at the top (no motion relative to the top plate.) The velocity profile is linear between these two points. Note that the slope dv/dy of the profile is just v top /L. The drag force should get bigger if we make the plate areas bigger; it should get bigger if we move the top plate faster, and it should get bigger if we put the plates closer together (where the velocity difference between adjacent fluid layers gets bigger). So top D Av F L But top vL is just the slope of the velocity profile and equals dv dy . So, dy dv A F D η = η is called the viscosity. It characterizes the amount of energy lost to friction when a fluid is sheared, i.e., when layers of fluid move past each other. The larger η is, the more viscous the fluid is. [ η ] = kg / ms = Pa s = 10 Poise η water = 1 x 10 -3 Pa s at 20 ° C = 1 centipoise η air = 1.8 x 10 -5 Pa s at 20 ° C
Viscous/Laminar Flow through Tubes The fluid velocity must be zero at the walls, and have a maximum in the middle. The profile is parabolic. Detailed calculations give: ( ) 2 2 ' 1 4 1 )' ( r r L p r v Δ = η Note that if there were no friction, as we assumed in deriving Bernoulli's equation, the flow velocity would be constant across the diameter, there wouldn’t be a pressure difference between the two ends of the tube, and the fluid could flow at constant height without any energy loss or input. Since there is friction (viscosity), there has to be a pressure difference to provide the energy lost to friction and maintain constant flow. W e w a n t t o k n o w t h e v o l u m e f l o w r a t e R . W e k n o w t h at R = Area × v avg = r 2 v avg The average of velocity is taken over the cross-sectional area of the flow. The result is: 22 4 1 8 8 p Rr r L p L π Δ = × Δ = This is called Poiseuille’s Equation. It requires laminar, viscous flow. It is approximately obeyed by the human circulatory

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handout_on_fluid_friction_and_surface_tension - Fluid...

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