Ch 9 Fluid Mechanics pgs 317 342 Objectives

Ch. 9 Fluid Mechanics pgs. 317 - 342

Objectives Examine the motion of a fluid using the continuity equation. Recognize the effects of Bernoulli’s Principle on fluid motion.

Fluid Flow 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 called eddy currents. are

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

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

Fluid Flow The speed of fluid flow depends on crosssectional 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.

Bernoulli’s Principle http: //library. thinkquest. org/27948/bernoulli. html

Bernoulli’s Theorem 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 Equation 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 Principle and Hurricanes 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=66 49024923387081294&q=Hurricane+Roof&hl =en

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.