Fluid Resistance

Objectives

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.

Drag – the opposing force of an object in a fluid.

Factors effecting drag

Speed of the object (or fluid) Size and shape of the object The physical properties of the fluid

Speed of Fluid

Laminar (streamlined) - results in frictional drag.

Turbulent – results in pressure drag

Speed of Fluid

Drag forces increase linearly with velocity until turbulence takes place.

Viscosity ( - eta)

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

Viscosity units

Nm2

* slb

ft2 * s

(Pa • s) (psi • s)F y

A v =

Viscosity (cont.)

A Liquid's viscosity decreases with temperature increase

A Gas’ viscosity increases with increases in temperature

Motor oil rated by the Society of Automotive Engineers (SAE) – SAE10 has less viscosity than SAE 40. What does 10W40 mean?

Stokes’ Law

The drag force on an object in fluid flow (or an object moving in a fluid).

Fdrag = 6 r v

Product of a constant (sphere)

RadiusSpeed

Viscosity

Terminal Velocity

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

Poiseuille’s Law

Gives the volume flow rate of a fluid flowing through a tube or pipe.

V = -• r 4 P

8 LVolume flow rate

Pipe radius

Change in pressure for length

‘L’

Viscosity of fluid

Factors effecting flow through a Pipe

Radius (cross-sectional area) of pipe

Length of pipe Viscosity of fluid Bends or “T’s” in the pipeR = - P

V•

Summary 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.) 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.