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### FLUIDS

What is a fluid? A substance that can flow. A fluid is a substance that cannot maintain its own shape but takes the shape of its container. Gases and liquids are called fluids because neither have an orderly arrangement.

In rigid bodies we expressed Newton's laws in terms of mass and force. We describe fluids in terms of density and pressure

Pressure
force per surface area; symbol is P; SI unit is Pa (Pascal)
P = F / A
where F is force or weight in Newtons
A is cross-sectional area in m2

The pressure at any point in a fluid acts equally in all directions.

Atmospheric pressure= 1.013 x 105 Pa

Density
the ratio of mass to volume; density is a characteristic of a substance.
r = m / V
where r is density in kg/m3
m is mass in kilograms
V is volume in m3

r(H2O) = 1000 kg/m3

Hydrostatics
the study of fluids at rest

1. Pascal’s principle - any change in pressure at any point in a fluid is transmitted unchanged throughout the fluid
F1/A1 = F2/A2
This is the basis for squeezing a tube of toothpaste and for the Heimlich maneuver.
2. Hydrostatic pressure - pressure due to a fluid’s depth
P = r g h
where r is density of fluid in kg/m3
h is the height (depth) of fluid
Pressure increases with depth. The pressure at any depth depends only upon that depth and not upon any horizontal dimension. For example, Hoover Dam holds back Lake Mead which is 700 ft deep. The bottom of Hoover Dam must withstand the same pressure if it were only holding bakc a few thousand gallons of water 700 ft deep.
3. Archimede’s principle - an object immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. A fluid provides some support for any object placed in it. The upward force on an object placed in a fluid is called the buoyant force.
FB = r g V
where r is the density of the fluid in kg/m3
V is the volume of the displace fluid
FB is the buoyant force

If an solid floats partially submerged in a liquid, the volume of liquid displaced is less than the volume of the object. According to Archimedes Principle, the weights of the object and its displaced fluid are the same. The fractional part of an object that is submerged is equal to the ratio of the density of the solid to the density of the liquid in which is floats (for example, about 90% of an iceberg is submerged because the density of the ice is about 90% that of sea water). An object floats when the buoyant force is equal to its weight

Hydrodynamics
study of fluids in motion

Equation of Continuity
the volume of fluid passing two points per second is equal
A1 V1 = A2 V2
In a narrow tube, the velocity of the liquid is high; in a wide tube, the velocity of the liquid is low.

Bernoulli’s principle
as the velocity of a fluid increases, the pressure exerted by that fluid decreases
on top of an airfoil there is low pressure due to high velocity airflow
on the bottom of an airfoil there is high pressure due to low velocity airflow