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) 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.

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.

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.

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

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

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

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) ·

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 ·