13 Fluid Mechanics Lectures by James L. Pazun Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley

Goals for Chapter 13 To study density and pressure in a fluid. To apply Archimedes Principle of buoyancy. To describe surface tension and capillary action To study and solve Bernoulli's Equation for fluid flow. To see how real fluids differ from ideal fluids (turbulence and viscosity).

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Density – Example 13.1 Density is a macroscopic measurable that gives us some insight to atomic spacing. Refer to table 13.1 and the example worked out on page 409 in your text. At right, liquids of different densities separate with denser liquids lower in the glass.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Pressure in a fluid – Figure 13.3 P = F/A The pressure is equal to force (in N) per unit area (in m 2 ). A new derived unit N/m 2 = 1 Pascal = 1Pa atmospheric pressure is 1 atmosphere = 760mmHg = 14.7 lb/in2 = 760mmHg = Pa = bars = millibars. Refer to example 13.2.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley The pressure in a fluid – Figure 13.6 The pressure in any fluid at the same elevation will be the same regardless of the shape or size of the container.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Pascal’s law – Figure 13.7 In a closed system, pressures transmitted to a fluid are identical to all parts of the container. Variations in the pressure are due only to the depth of the fluid. This principal in vital to mechanical devices like lifts and brakes.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Determining absolute or gauge pressure – Example 13.4 The gauge pressure in exerted by the system. Absolute pressure includes the local atmospheric pressure. Refer to the worked example on page 414.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Archimedes’s Principle – Figure An object submersed in a fluid experiences buoyant force equal to the mass of any fluid it displaces. An object can experience buoyant force greater than its mass and float. Even if it sinks, it would weigh measurably less. Refer to worked example 13.7.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Surface tension – Figures and Also, refer to worked example 13.8.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Capillary action – Figure Figure Interactions between the fluid and the container walls are significant.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Fluids in motion – Figure Two kinds of flow exist. Laminar flow – regular streamlines may be drawn. The smoke in the figure near the incense stick. Turbulent flow – Irregular and difficult to model. The smoke well away from the incense stick.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Bernoulli’s Equation – Figure A comprehensive work for ideal fluids, Bernoulli accounted for: fluid densities height differences different pipe diameters exterior pressures at the inlet and outlet Refer to problem solving strategy 13.1 and example 13.9.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Bernoulli’s Equation Applied I – Figures Blood flow characteristics are changed dramatically by plaque.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Bernoulli’s Equation Applied II – Figures The venturi tube allows pressure measurement “in line”.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Bernoulli’s Equation Applied III – Figures Sports abounds with good examples but the very best direct application of Bernoulli's Equation is pitching in baseball.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley A viscous fluid flowing in a pipe – Figure Attraction to the walls and drag is maximized at outer radii. As a result there will be higher velocities near the center.

Copyright © 2012 Pearson Education, Inc. publishing as Addison-Wesley Turbulence - Figure Forces a terminal fluid velocity much like air resistance limiting velocity in free fall.