FLUID MECHANICS

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FLUID MECHANICS
How is electricity generated at the bottom of
dams?
When you catch a deep-sea fish, why does its eyes
pop-out?
Why do your ears pop on an airplane or while
climbing up mountains?
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Pressure

• Pressure is equal to the force applied to a
  surface, divided by the area.

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Equations for Pressure

• Pressure Force/surface area

• Pressure Newtons (Kg x m/s/s)

side x side

• Units are in Pascals or N/m²

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Fluid

• A substance that can easily change its shape,
  such as liquids and gases.

• The molecules in a fluid have a certain amount of
  force (mass and acceleration) and exert pressure
  on surfaces they touch.

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FLUID PRESSURE

• All the molecules add up together to make up the
  force exerted by the fluid.

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• Air has a mass of 1Kg/m³

AIR PRESSURE

• Gravity creates an air pressure of 10.13N/m³ at
  sea level.

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1 atmosphere 760 mmHg 29.92 inHg 14.7
lb/in2 101.3 KPa
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Pressure and Elevation

• Air Pressure decreases as elevation increases.

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The whole system is a low pressure, but it
dramatically decreases towards the eye of the
hurricane.
Very Low pressure
Pressure always flows from high to low, which
creates the high velocity winds.
Higher Pressure
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Barometric Pressure

• The barometer is used to forecast weather.
• Decreasing barometer means stormy weather and an
  increasing barometer means warmer weather.

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Measuring Pressure

• A manometer is a U-shaped tube that is partially
  filled with liquid.
• Both ends of the tube are open to the atmosphere.
• A container of gas is connected to one end of the
  U-tube.
• If there is a pressure difference between the gas
  and the atmosphere, a force will be exerted on
  the fluid in the U-tube. This changes the
  equilibrium position of the fluid in the tube.

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From the figure
At point C
Also
The pressure at point B is the pressure of the
gas. Pgauge easily remembered as hot dog
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A Barometer
The atmosphere pushes on the container of mercury
which forces mercury up the closed, inverted
tube. The distance d is called the barometric
pressure.
From the figure
and
Atmospheric pressure is equivalent to a column of
mercury 76.0 cm tall.
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Pressure and Depth
P ?gh where P Pressure ? density of
fluid g gravity h height of fluid

• Water pressure increases with depth.

• When the liquid is pressing against a surface
  there is a net force directed perpendicular to
  the surface.
• If there is a hole in the surface, the liquid
  initially moves perpendicular to the surface.
• At greater depths, the net force is greater and
  the horizontal velocity of the escaping liquid is
  greater.

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• At any point within a liquid, the forces that
  produce pressure are exerted equally in all
  directions.
• Pressure increases vertically downward.
• Pressure constant horizontally.

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Columnar Fluid Pressure(sometimes called gauge
pressure)

• pressure due to a column of fluid of height h and
  mass density D
• The pressure of a liquid at rest depends on the
  density and depth of the liquid.
• Liquids are practically incompressible, so except
  for changes in the temperature, the density of a
  liquid is normally the same at all depths.

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Columnar Fluid Pressure

• At a given depth, a given liquid exerts the same
  pressure against any surface - the bottom or
  sides of its container, or even the surface of an
  object submerged in the liquid to that depth.
• Pressure a liquid exerts depends only on its
  density and depth.
• Total pressure (or absolute pressure) Pabsolute
  on a submerged surface equals the pressure the
  liquid exerts plus the atmospheric pressure Po (1
  atm 1.013 x 105 Pa) .

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Fluid Pressure

• Pressure of a liquid does not depend on the
  amount of liquid.
• Neither the volume or total weight of the liquid
  matters.
• If you sampled water pressure at 1 m beneath a
  large lake surface and 1 m beneath a small pool
  surface, the pressure would be the same.
• The fact that water pressure depends on depth and
  not on volume is illustrated by Pascal vases.
• Water surface in each of the connected vases is
  at the same level.
• Occurs because the pressures at equal depths
  beneath the surface are the same.

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Forces Exerted By a Fluid

• When the liquid is pressing against a surface
  there is a net force directed perpendicular to
  the surface.
• If there is a hole in the surface, the liquid
  initially moves perpendicular to the surface.
• At greater depths, the net force is greater and
  the horizontal velocity of the escaping liquid is
  greater.

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Pascals Principle

• When force is applied to a confined fluid, the
  change in pressure is transmitted equally to all
  parts of the fluid.

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Transmission of Pressure Pascals Principle.

• Pascals Principle A CHANGE IN PRESSURE IN A
  CONFINED FLUID IS TRANSMITTED WITHOUT CHANGE TO
  ALL POINTS IN THE FLUID.
• Ex. Hydraulic lift.
• Hydraulic piston apparatus uses an incompressible
  fluid to transmit pressure from a small cylinder
  to a large cylinder.
• According to Pascals Principle, the pressure in
  the small cylinder resulting from the application
  of F1 to a frictionless piston is transmitted
  undiminished to the larger piston.

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Transmission of pressure Pascals Principle.

• P1 P2
• A2 is larger than A1, so the force exerted by the
  large piston is greater than the force exerted on
  the small piston.
• AMA (actual mechanical advantage) for hydraulic
  lift

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Hydraulic Devices

• By changing the size of the pistons, the force
  can be multiplied.

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3. What is the total force of the right Piston?
4 N
40,000N
FP A 2000 N/m2 x 20m2
20 m2
.002m2
1. What is the pressure of the left piston? 2.
What is the pressure of the right Piston?
P F/A 4 N/.002 m2 2000 Pa
2000Pa
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Hydraulic Brakes

• The hydraulic brake system of a car multiplies
  the force exerted on the brake pedal.