Fluid Mechanics

hordesalmonΜηχανική

24 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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Newtonian Fluids




Gases are considered
compressible fluids





Liquids are considered
incompressible fluids


Another thing we pretend is true because the
compression is usually a negligible amount


Non
-
Newtonian fluids do not always act predictably


Pascal's Principles


External pressure applied to a fluid will be applied
uniformly throughout the fluid




F₁/A₁ = F₂/A₂


F₁/A₁ = F₂/A



50
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 Depth


F=mg and the mass =
ρ
V


ρ

= density


V=area of the cross section x height


So F=
ρ
gV
=

ρ
g
Ah



P

= F/A=
ρ
gh



*for a uniform shape

Explain this phenomenon:


Relating KE, GPE, and existing P


From conservation of energy we can derive Bernoulli’s
equation:


P₁ +
ρ
gh
₁ + 1/2

ρ
v₁² = P₂ +
ρ
gh
₂ + 1/2

ρ
v₂²

Vocabulary


Conditions


Isobaric


constant pressure


Isothermic



constant temperature


Adiabatic


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 collisions


Forces between molecules have no effect except during
a collision


The gas is a pure substance


The gas and the walls of the container are not
exchanging thermal energy

Ideal Gas Law



P₁V₁/T



= P₂V₂/T




or


PV=
nRT


Pressure x Volume =

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



0⁰ Kelvin =
-
273

⁰ Celsius



Pressure 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 Sponsor

m

a


=
m

a


The 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.