Chapter 15 Fluids Dr. Haykel Abdelhamid Elabidi 1 st /2 nd week of December 2013/Saf 1435

Units of Chapter 15 Density Pressure Static Equilibrium in fluids Archimedes' Principle and Buoyancy Fluid Flow and Continuity Bernoulli's Equation

Density Definition of fluid: it is a substance that can readily flow from place to place, and take the shape of a container rather than retain a shape of their own. Examples: gases and liquids

Pressure

The pressure in fluid acts equally in all directions, and acts at right angles to any surface, so we don’t usually notice it.

Pressure

Static equilibrium in fluids: Pressure and depth The increased pressure as an object descends through a fluid is due to the increasing mass of the fluid above it.

Static equilibrium in fluids: Pressure and depth

A barometer compares the pressure due to the atmosphere to the pressure due to a column of fluid, typically mercury (Hg).

Static equilibrium in fluids: Pressure and depth Pascal’s Principle: An external pressure applied to an enclosed fluid is transmitted unchanged to every point within the fluid.

Static equilibrium in fluids: Pressure and depth

Archimedes’ principle and buoyancy A fluid exerts a net upward force on any object it surrounds, called the buoyant force. the buoyant force is due to the increased pressure at the bottom of the object compared to the top.

Archimedes’ principle and buoyancy

Fluid flow and continuity Continuity tells us that whatever the volume of fluid in a pipe passing a particular point per second, the same volume must pass every other point in a second. The fluid is not accumulating or vanishing along the way. This means that where the pipe is narrower, the flow is faster.

Fluid flow and continuity Most gases are easily compressible; most liquids are not. Therefore, the density of a liquid may be treated as constant, but not that of a gas. 3.3.

Bernoulli’s equation The Bernoulli’s Equation is the work – energy theorem applied to fluids. The result is a relation between the pressure of a fluid, its speed, and its height. If there is no change in height, the Bernoulli’s equation becomes:

Bernoulli’s equation

Exercise 15-4 page 520 There is a difference in height, so we apply the Bernoulli’s equation (the subscript (1) for the bottom and (2) for the top:

Bernoulli’s equation Figure 15-19

Thank you for your attention See you next time Inchallah