Ch. 9Fluid

Mechanicspgs. 317 - 342

Examine the motion of a fluid using the continuity equation.

Recognize the effects of Bernoulli’s Principle on fluid motion.

Objectives

When a fluid is in motion, the flow can be described in two ways

◦ Laminar (Streamline) – every particle moves along the same smooth path traveled by earlier particles

◦ Turbulent – the flow of the fluid becomes irregular. These irregular motions are called eddy currents.

Fluid Flow

The ideal fluid model simplifies fluid-flow analysis

Ideal Fluid◦ Incompressible◦ Nonviscous – lose no kinetic energy due to

friction as they flow◦ Steady Flow – velocity, density, and pressure at

each point are constant◦ Nonturbulent – no eddy currents in the moving

liquid

Fluid Flow

The continuity equation results from mass conservation; in other words when a fluid flows,mass is conserved.

Flow rate = Avt

The speed of fluid flow depends on cross-sectional area

The pressure in a fluid is related to the speed of flow

Fluid Flow

The volume per unit time of a liquid flowing in a pipe is constant throughout the pipe.

We can say this because liquids are not compressible, so mass conservation is also volume conservation for a liquid.

Fluid Flow

Bernoulli’s Principle

http://library.thinkquest.org/27948/bernoulli.html

The sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow.

All other considerations being equal, when fluid moves faster, the pressure drops.

Bernoulli’s Theorem

Relates pressure to energy in a moving fluid

The expression for the conservation of energy in fluids is called Bernoulli’s Equation

Bernoulli’s Equation

To compare the energy in a given volume of fluid at two different points, Bernoulli’s equation takes the following equivalent form

Bernoulli’s Equation

In a hurricane or tornado, the high winds traveling across the roof of a building can actually lift the roof off the building.

http://video.google.com/videoplay?docid=6649024923387081294&q=Hurricane+Roof&hl=en

Bernoulli’s Principle and Hurricanes

A water tank has a spigot near its bottom. If the top of the tank is open to the atmosphere, determine the speed at which the water leaves the spigot when the water level is 0.500 m above the spigot.