Resistance in Fluid Systems

Objectives

Define dragExplain 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 Laws 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…. or

Drag

Drag is defined as the force found when a solid object moves through a fluid, and there is a force that opposes the motion.

Example: When an airplane moves through air.What is another example of drag?

Understanding Drag

Thrust = Drag

Drag is an aerodynamic force that resists the motion of an object moving through a fluid.

Laminar Flow

Laminar or streamlined flow is a slow, smooth flow over a surface, in which the paths of individual particles do not cross. These particle follow theoretical layers of fluid.

Laminar Flow creates frictional dragWhat is an example of Laminar Flow on an object?

Turbulent Flow

Turbulent flow is an irregular flow that is disrupted causing fluid to move in different directions.Turbulence causes a wake behind a moving object.

Turbulent flow creates pressure dragWhat is an example of Turbulent Flow on an object?

Frictional Drag

Frictional Drag is produced by the friction between successive or laminated layers of fluid, with increasing speed away from the surface.

When does Frictional Drag take place?

Pressure Drag

The pressure difference found in turbulent flow causes a force to act on the object in the direction opposite its relative velocity.

When does Pressure Drag take place?

Understanding Drag

Both Frictional and Pressure Drag increase as the speed of an object increases.When turbulence is created, pressure drag increases more rapidly than friction drag.

Stokes’ Law

Irishmen George Stokes used viscosity and the equations of fluid flow to predict the drag force on a sphere moving through a fluid.Stokes’ Law applies to objects moving at low enough speeds that the flow of fluid is streamlined or laminar.

Stokes’ Law

Fdrag = 6rv

6 =Constant for sphereR = Radius of objectV = Speed of object = Fluid’s Viscosity

Stokes’ Law

Fdrag = 6rv

Example:

Poiseuille’s Law

Poiseuille was a physician, who experimented with flowing water, and learned that the rate at which fluid flows through a tube increases proportionately to the pressure applied the fourth power of the radius of the tube.Poiseuille’s Law gives the volume flow rate of a fluid flowing through a tube or pipe.

3 Factors of Resistance

In fluid flow resistance decreases the flow rate though a pipe. Poiseuille’s Law shows how this resistance depends on three factors:

Dependence on RadiusDependence on LengthDependence on Viscosity

Dependence on Radius

The larger the radius of a pipe, the greater volume of fluid per secondFluid resistance decreases as pipe radius and cross-sectional area increase.

Dependence on Length

Longer pipes have higher fluid resistanceVolume flow rate is inversely proportional to length

Dependence on Viscosity

Abrupt changes in the direction of fluid flow can cause turbulence and increase resistanceFluid resistance increases as viscosity increases.

Poiseuille’s Law

V = - r4 8 L

R = Radius of Pipe or Tube = P2 – P1 = ViscosityL = Length of Pipe or Tube

Poiseuille’s Law

V = - r4 8 L

Example:

Viscosity

What is Viscosity??

Viscosity

Friction between two solid surfaces causes a resistance to movement between the surfaces.

Viscosity is the property of a fluid that describes its internal friction.

Viscosity

What are some items that might have a higher viscosity? A lower viscosity?

Viscosity

Different fluids resist motion differently, and therefore have different viscosities.

Gum and Molten Lava have high viscositiesAir and Water have a much lower viscosity

Viscosities of Common Fluids

Physics in Context textbook

Pg. 188 Chapter 4, Table 4.2

Viscosity of most liquids decreases as temperature increases.

Viscosity of most gases increase with temperature

Example:Cold honey is thick

with a high viscosityHot honey is watery

with a low viscosity

Review Questions

What are the two types of drag and give an example of each?What is the main difference between laminar and turbulent flow? Explain viscosity and give an example.Textbook pages 196 – 198, questions 1 - 15

Credits

Basic presentation from Mr. Andrackehttp://www.uhigh.ilstu.edu/tech/PT/