Sub Unit 1.2 – Fluid Force
Pressure in Fluid Systems

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Describe the four states of matter.
Define density and pressure
Explain why pressure in a fluid depends on depth in the fluid
 Explain why an object submerged in a fluid experiences a buoyant force
 Predict whether an object will sink or float in a given fluid.
 Explain how a force can be multiplied in a hydraulic lift.
 Explain where atmospheric pressure comes from.
 Describe how a barometer measures atmospheric pressure
 Explain the difference between absolute and gage pressure.

States of Matter
 Matter can exist in four states:
– Solid (ice)
– Liquid (water)
– Gas (steam vapor)
– Plasma (Extremely hot ionized atoms)

Fluids
 Fluids are materials that can flow, has no definite shape of its own, and conforms to the shape of its container.
 Liquids
 Gasses
 Fluid systems use both liquids (hydraulic) and gasses (pneumatic) to operate mechanical devices.

City Water System
Hydraulic system under pressure

Density and Pressure
 Density is how much mass is contained in a given amount of space.
 Amount of matter per unit of volume.
(rho)

Units
 English
 SI

 The mass of 1 cm 3 of water has a mass of
1g; therefore the density is 1g/1cm 3 .
Example

Weight Density
 Weight Density is the comparison of an object’s weight to it’s volume w
Units

Weight Density of Water
 Water has a weight density of
62.4 lb/ft 3 .

Pressure
 A force applied over a surface is pressure.
Units
English SI

Pressure Units
 N/m 2 = 1 Pascal (Pa)
 1000 Pa = 1kilopascal (kPa)
 lb/in 2 = psi (pounds per square inch)

Pressure and Depth
 Pressure increase with depth because of the additional weight of the fluid above. w

Buoyancy and Archimedes’
Principle
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P top
= r
P bottom
= w r x h w x (h + d)
F = P x A
– F top
= P top x A = ( r w x h) x A
– F bottom
= P bottom x A = [ r w x (h+d)] x A
F buoyant
= F bottom
– F top
= r w
Ad
Ad = V brick
F buoyant
= r w x V brick
= weight of water displaced

Archimedes’ Principle
 An object immersed in a fluid has an upward force exerted on it equal to the weight of the fluid displaced by the object.
 Note: the buoyant force is based on the weight of the fluid displaced not on the weight of the object.

Pascal’s Principle
 A change in pressure at any point in a confined fluid is transmitted undiminished throughout the fluid.
 P = F / A or
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F = P x A
A = p r 2

Atmospheric Pressure
 The weight of the air above an area.
 At sea level, a column of air extending up through the atmosphere, with a cross sectional area of 1m 2 , encloses about 10,000 kg of air.
 This air weighs about 1 x 10 5 N
 Therefore, atmospheric pressure is about 10 5
Pa or 100kPa at sea level.
 Decreases with altitude
 This is why your ears pop (equalization)

Atmospheric Pressure
 Barometer – instrument used for measuring atmospheric pressure.
 At sea level the average atmospheric pressure is 101.3 kPa = 760mm of mercury
= one atmosphere = 14.7 psi = 2117 lb/ft 2

Absolute and Gage Pressure
 Absolute pressure is the total pressure measured above zero (perfect vacuum).
 Gage pressure is the pressure measured above atmospheric pressure.
 Absolute pressure = gage pressure + atmospheric pressure
 Suppose a tire gage measures the pressure of a tire to be 30 psi;
 Absolute pressure = 30 psi + 14.7 psi = 44.7 psi
 The air inside the tire pushes out with a pressure of
44.7 psi. The atmosphere pushes in with a pressure of 14.7 psi. The difference is 30 psi – the gage pressure.

Pressure is a Prime Mover
 Pressure acts like a force to cause movement.

Equilibrium

Summary
 Matter can exist in four states: solid, liquid, gas, and plasma.
 Liquids and gases are called fluids.
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The density of a substance is its mass per unit volume.
The density of water is 1g/cm 3 .
 Weight density is weight per unit volume.
 Pressure is force divided by the area over which the force acts.
 We treat pressure as a scalar.
 In SI units, pressure is measured in pascals, where 1 Pa= 1
N/m
 Pressure increases with depth in a fluid.

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Summary
For a given fluid, the pressure does not depend on the size or shape of the container.
 When an object is submerged in a fluid, an upward force is exerted on the object caused by the pressure difference between the top and the bottom of the object. This force is called a buoyant force.
 The buoyant force exerted on a submerged object equals the weight of the fluid displaced by the object.
 A pressure applied to a confined fluid is transmitted throughout the fluid.
 Atmospheric pressure is caused by the weight of the air above a given area.
 Atmospheric pressure can be measured with a barometer.
 Absolute pressure is the sum of the gage pressure and atmospheric pressure.