Fluid Mechanics

Newtonian Fluids

Gases are considered compressible fluids

Liquids are considered incompressible fluidsAnother thing we pretend is true because the

compression is usually a negligible amount Non-Newtonian fluids do not always act predictably

Pascal's PrinciplesExternal pressure applied to a fluid will be

applied uniformly throughout the fluid

F₁/A₁ = F₂/A₂

F₁/A₁ = F₂/A₂50 Newtons is applied to

pump a squirt gun with a cylinder surface area of .01 square meters. How much force does it take to plug the barrel of the squirt gun if the area of the opening is 0.001 square meters?

Does this obey the law of conservation of energy?

Explain your answer!

Static Pressure and DepthF=mg and the mass = ρVρ = densityV=area of the cross section x heightSo F=ρgV= ρgAh

P = F/A= ρgh *for a uniform shape

Explain this phenomenon:

Relating KE, GPE, and existing PFrom conservation of energy we can derive

Bernoulli’s equation:

P₁ + ρgh₁ + 1/2 ρv₁² = P₂ + ρgh₂ + 1/2 ρv₂²

VocabularyConditions

Isobaric – constant pressureIsothermic – constant temperatureAdiabatic – no heat is added or removed from

the system; this is an important distinction from isothermic

Laminar Flow – smooth movement of fluid without turbulence (this is an important assumption of Bernoulli’s equation)

Turbulent Flow – irregular movement of fluid where the fluid may be working against parts of its own movement

Assumptions about an “ideal gas”

The gas is composed of many molecules that are relatively far apart

As a whole the molecules act according to the laws of motion but individually their motion is random

Molecules undergo elastic collisionsForces between molecules have no effect except

during a collisionThe gas is a pure substanceThe gas and the walls of the container are not

exchanging thermal energy

Ideal Gas LawP₁V₁/T ₁ = P₂V₂/T ₂

orPV=nRT

Pressure x Volume = number of Moles of the substance x Universal Gas Constant x Temperature in Kelvin

0⁰ Kelvin = -273 ⁰ CelsiusPressure is in Pascals (Pa) or Nm² (1

Pa= 1 Nm²)R= 8.31 joules per mole kelvin

Relating P₁V₁/T ₁ = P₂V₂/T ₂ to your experiences: What happens when you heat up a closed

container?

What happens to temperature when you decrease the pressure in a spray can?

How might an air conditioner work?

Does opening the refrigerator door cool off the kitchen?

How does the steamboat toy work?

What does an increase in temperature do to the pressure?

How is pressure related to force?

Example of Algebraic Sponsorm₁a₁ = m₂a₂The mass of the boat is accelerated according to Newton’s third law. The force created by the pressure in the steam chamber results in equal and opposite forces acting on the boat and the water.

Rudder Madness

m₁a₁ = -m₂a₂