Fluid Speed in a Pipev2

An incompressible fluid, like water, flowing through a pipe will slow down if the pipe gets wider.

blue volume= purple volume A1 x1 = A2 x2

A1 (v1 t) = A2 (v2 t) A1 v1 = A2 v2

A v = constant The bigger the area, the slower the fluid speed.

A1 A2x1 x2

v1

Bernoulli’s PrincipleBernoulli’s principle says that the faster a fluid is moving the less pressure it exerts.

v1 v2

Bernoulli Example 2

Because air flows faster in the thin section of the top pipe, the pressure is lower there, and the water level beneath it rises more than in the other two. The difference in pressure between the thick section of the top pipe and the thin section is given by: P = g h.

w a t e r

air flow

h

Airplanes

Air on top must travel farther, so it moves faster, and the pressure there is lower, creating lift. Also, because of the wing’s upward tilt, air is pushed downward. So, the air pushes back on the wing in the direction of F.

F

Curve Ball

Whiffle Ball

Stream Lined FlowStream line flow occurs in non-viscous fluids moving over smooth objects.

The Bernoulli principle only applies to stream lined flow.

Viscous fluids, or blunt objects can create turbulent flow

Types of Solids• Solids are of two types:• Crystalline solids- consist of crystals which are

substances which are organized in symmetric, geometric ways.

• Amorphous solids-non crystalline solid where the particles are arranged randomly.

Amorphous and Crystalline Solids

Crystalline SolidsExist either as single crystals or group of crystals fused together. The total three dimensional arrangement of particles is called as crystal structure.

Ex: diamond, salt, ice

Amorphous SolidsUnlike crystalline solids, amorphous solids do not

have a regular shape. Amorphous solids are formed when liquids are cooled gradually, so particles are not arranged in any particular order.

Ex: Plastic, Glasses

Crystalline SolidsThe cohesive forces that hold a substance together depend on the distance between molecules

When an liquid cools down sufficiently, the cohesive forces become greater, and the particles become fixed in their arrangement.

The molecules form a crystal lattice if they arrange themselves in a fixed pattern,

Amorphous Solids• If a substance does not have a fixed crystal

structure, it is hard to distinguish between its solid and its liquid state

• These substances are classified asto as amorphous solids, orhighly viscous liquids

• When an amorphous solid cools sufficiently, the molecules have a random arrangement(glass, plastic)

Thermal Expansion• As an object heats up, its molecules gain energy,

and the distances between particles increases

• This increase in distance increases the volume of the object.

• This effect is called thermal expansion

• This is the reason for many phenomena

What Happened Here?

Why does it help to run a jar lid under hot water to get it open?

The hot water makes the lid expand and loosen. This reduces the friction between the lid and the threads

Why doesn’t the jar expand with the lid?Different materials have a different rate at which they expand due to temperature changes

Coefficient Expansion• Every material experiences a different change in

size from temperature change.

• This difference is reflected in the coefficient of expansion.

• There are three different values that represent this expansion, but they are essentially the same

Coefficient of Expansion

• Linear Expansiono The change in length divided by the original length and

the change in Temperature

• Volume Expansiono The change in volume divided by the original volume,

and the change in Temperature

Example• Find the change in volume of an

aluminum cube with side lengths of 2m after the temperature increases from 20⁰C to 90⁰C.

• What is the new volume?

Volume Expansion

• .042m3

• Final Volume = 8.042m3

Linear Expansion• -6

• L1=2m

• ∆L = L*α*∆T = .0035m

• Final Length = 2.0035m

• Final Volume = 8.042

Volume and Linear Expansion

• The relationship between the linear and spatial dimensions of objects is fixed, the relationship between the coefficients of linear and volume expansion is fixed

• The coefficient of Volume expansion is always 3 times the coefficient of linear expansion.