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Resistance in Fluid Systems

Resistance in Fluid Systems. 4.2. Drag. The force that opposes the motion when a solid object moves through a fluid Occurs only when there is relative movement between an object and a fluid. Laminar Flow (Streamlined).

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Resistance in Fluid Systems

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  1. Resistance in Fluid Systems 4.2

  2. Drag • The force that opposes the motion when a solid object moves through a fluid • Occurs only when there is relative movement between an object and a fluid

  3. Laminar Flow (Streamlined) • Slow, smooth flow over a surface in which the paths of individual particles do not cross • Fluid speed at the surface is zero. • Fluid moves in theoretical layers, or laminates, with increasing speed away from the surface. • Frictional drag is produced by the friction between successive layers of fluid.

  4. Turbulent Flow • irregular flow with eddies and whorls causing fluid to move in different directions • produced by high speeds, by shapes that are not streamlined, and by sharp bends in the path of a fluid • produces wakes • Pressure drag is produced because the pressure difference in the wake is less than the fluid pressure in the streamlined flow and causes a force to act on the object in the direction opposite its relative velocity. • Frictional drag and pressure drag both increase as speed increases. • Frictional drag is directly proportional to the increase in speed. Pressure drag (and turbulence) increases as the square of the speed.

  5. Viscosity • property of a fluid that describes internal friction • normally how slowly a fluid moves because of internal bonds • Greek letter η (eta) represents viscosity. • Syrup and ketchup have relatively high viscosities; water and air have relatively low viscosities.

  6. Viscosity • Fdrag = F = η (Av/Δy) (Drag force = viscosity X area · velocity divided by the change in the thickness of the fluid layer) • SI Units—N/m2·s or Pa·s—English Units—lb/ft2·s or psi·s • ηwater = 0.001002 N/m2·s = .01002 poise = 1.002 centipoise • Viscosity for Common Fluids—p. 188 • Viscosity of most liquids decreases as temperature increases—ex: honey • Viscosity of most gases increases as temperature increases—more collisions per second as temp increases

  7. Stokes Law • Predicts the drag force on a sphere moving through a fluid • Low speeds, so only laminar flows—no turbulence, just frictional drag. • Drag force acts in the direction opposite the object’s velocity. • Fdrag = 6πrvη-Drag force = 6 X pi X radius X velocity X viscosity

  8. Terminal Speed • When drag equals the weight of the object. • Speed becomes constant. • Terminal speed of baseball—about 40 m/s • Terminal speed of basketball—about 20 m/s

  9. Poiseuille’s Law • A. gives the volume flow rate of a fluid flowing through a tube or pipe • B. V = -(π/8)(r4ΔP/ηL)—Volume flow rate (change in volume with respect to time) = (pi divided by 8) X ({radius4 X change in Pressure} divided by viscosity X length) ·

  10. Factors Affecting Flow Through a Pipe (pp. 193-195) • radius of pipe • length of the pipe • viscosity of the fluid • R = -ΔP/V—Fluid Resistance = -change in pressure divided by the Volume Flow Rate ·

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