Solids & Fluids Relating Pressure to Solid & Fluid systems 01/30

What is a “FLUID”? A fluid is a nonsolid state of matter in which the atoms or molecules are free to move past each other, as in a gas or a liquid. Both liquids and gases are considered fluids because they can flow and change shape. Liquids have a definite volume; gases do not. 02/30

Recall the definition of Density “How much matter there is in an amount of space.” In other words… Density = Mass / Volume or… ρ=m/V (Greek letter “rho” is given for density) 03/30

Buoyancy…what is it and how is it applied? The buoyant force is the upward force exerted by a liquid on an object immersed in or floating on the liquid. Buoyant forces can keep objects afloat if they are great enough. It really depends on the density of the object and the density of the fluid it is in. – Ex’s: ice in liquid water, helium balloon in air, brick in air, stone in pool water, etc. 04/30

Archimedes’ Principle Archimedes’ principle describes the magnitude of a buoyant force. Archimedes’ principle: Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. F B = F g (displaced fluid) = m f g magnitude of buoyant force = weight of fluid displaced 05/30

For example… The Brick, when added, will cause the water to be displaced and fill the smaller container. What will the volume be inside the smaller container? The same volume as the brick! 06/30

Another example… The raft and cargo are floating because their weight and buoyant force are balanced. 07/30

Another example… Now imagine a small hole is put in the raft. The raft and cargo sink because their overall density is now greater than the density of the water. 08/30

More about Buoyancy… For a floating object, the buoyant force equals the object’s weight (they would be BALANCED). The apparent weight (actual weight minus buoyant force experienced) of a submerged object depends on the density of the object. 09/30

More about Buoyancy… For an object with density ρ o which is submerged in a fluid ρ f, the following relationship is true: Weight / Buoyant Force = Object’s Density / Fluid’s Density Or… 10/30

Example: 11/30

Example: 12/30

Example: 13/30

Pressure The SI unit for pressure is the pascal, Pa. It is the same as a N/m 2. The pressure at sea level is about 101,000 Pa. This gives us another unit for pressure, the atmosphere, where 1 atm = 101,000 N/m 2 14/30

A woman’s high heels sink into the soft ground, but the larger shoes of the much bigger man do not. Pressure = force / area Definition of Pressure 15/30

Solid Applications We often relate this Force-to-Area ratio to the idea of “stress” felt by an object. In 1-Dimension, the change in Length due to stress is determined by Young’s Modulus. In 2-Dimensions, the change in Area due to stress is determined by the Shear Modulus. In 3-Dimensions, the change in Volume due to stress is determined by the Bulk Modulus. 16/30

Solid Applications “strain” is defined as the measure of the amount of deformation (the EFFECT of the STRESS on the material) – Examples: tension on a suspension bridge cable, applying a horizontal force to the top of a textbook, submerging a block of plastic in a tank of water. 17/30

NOW for some FLUID applications… Pascal’s Principle: Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid. 18/30

Some visuals… 19/30

Here’s a common application: 20/30

Here’s a common application: 21/30

Here’s a common application: 22/30

A small force F 1 applied to a piston with a small area produces a much larger force F 2 on the larger piston. This allows a hydraulic jack to lift heavy objects. 23/30

Example: 24/30

Example: 25/30

More on Pressure… Pressure varies with depth in a fluid. The pressure in a fluid increases with depth. It is also important to know that “Absolute Pressure” takes fluid Atmospheric Pressure into account ALONG with Fluid Pressure. 26/30

Fluid FLOW Viscosity is related to the “thickness” (internal resistance) of a fluid. The higher the viscosity, the slower a fluid will flow. There is a Continuity Equation which is important for ideal fluids: Think: Pinching a water-hose 27/30

Bernoulli’s Principle The speed of fluid flow depends on cross- sectional area. Bernoulli’s principle states that the pressure in a fluid decreases as the fluid’s velocity increases. Think: “Is this true”? What’s happening inside of a DRINKING STRAW, for instance? Think: “How does this relate to Lift”? 28/30

To Sum it all Up “TOTAL ENERGY is ________” – Because of this, we can show that the following is valid for these fluid-flow systems: “The sum of the Pressure, Kinetic Energy per unit Volume, and the Potential Energy per unit Volume has the same value at all points along a streamline.” Think: “Can you tell from where each term comes”? 29/30

The END! 30/30