Fluid Resistance Objectives n n n Define drag

Fluid Resistance

Objectives n n n Define drag Explain the difference between laminar and turbulent flow. Explain the difference between frictional drag and pressure drag. Define viscosity and explain how it can be measured. Use Stoke’s law and Poiseuille’s Law to solve problems involving fluid resistance.

Review Frictional force – the opposing force resulting when one solid slides against another. n Drag – the opposing force of an object in a fluid. n

Factors effecting drag Speed of the object (or fluid) n Size and shape of the object n The physical properties of the fluid n

Speed of Fluid n Laminar (streamlined) - results in frictional drag. n Turbulent – results in pressure drag

Speed of Fluid n Drag forces increase linearly with velocity until turbulence takes place.

Viscosity ( - eta) n The property of fluid that describes its internal frictional forces (like the density of a fluid). Syrup and tar have high viscosity whereas air and water have less viscosity lb N s * n Viscosity units 2 ft m 2 n = F y Av (Pa • s) (psi • s)

Viscosity (cont. ) A Liquid's viscosity decreases with temperature increase n A Gas’ viscosity increases with increases in temperature n Motor oil rated by the Society of Automotive Engineers (SAE) – SAE 10 has less viscosity than SAE 40. What does 10 W 40 mean? n

Stokes’ Law n The drag force on an object in fluid flow (or an object moving in a fluid). Fdrag = 6 r v Viscosity Product of a constant (sphere) Radius Speed

Terminal Velocity n The constant speed that occurs when the drag force equals the gravitational force acting on an object.

Poiseuille’s Law n Gives the volume flow rate of a fluid flowing through a tube or pipe. Pipe radius • V= Volume flow rate r 4 P 8 L Viscosity of fluid Change in pressure for length ‘L’

Factors effecting flow through a Pipe Radius (cross-sectional area) of pipe n Length of pipe n Viscosity of fluid n Bends or “T’s” in the pipe P R= n • V

Summary n n n Drag is the force that opposes the motion of an object moving through a fluid or the force a moving fluid exerts on a stationary object. Laminar flow is slow, smooth flow over a surface, where particles follow streamlines. The streamlines define theoretical layers of fluid that do not mix. The friction between the successive layers of fluid is called frictional drag. Turbulent flow is irregular flow with eddies and whorls that mix the fluid. Turbulence causes a wake behind a moving object. The pressure difference between the fluid outside the wake and the fluid inside the wake causes pressure drag.

Summary (cont. ) n n n Drag increases with speed. When turbulence is created, pressure drag increases more rapidly than friction drag. Viscosity is the property of a fluid that describes its internal friction. The SI units of viscosity are Pa • s. Stokes’ law can be used to calculate the drag force on a sphere moving at constant speed in a viscous fluid. When drag equals the gravitational force acting on a falling body, the body falls at a constant speed, called the terminal speed of the body. Poiseuille’s law can be used to calculate the volume flow rate of pressure drop of viscous fluid flowing through a tube or pipe.