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### Sub Unit 1.2 – Fluid Force

Pressure in Fluid Systems

Objectives

- 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.

mass

Density =

(rho)

volume

m

r =

v

Example

- The mass of 1 cm3 of water has a mass of 1g; therefore the density is 1g/1cm3.

Weight Density

- Weight Density is the comparison of an object’s weight to it’s volume

weight

Weight Density =

volume

weight

lb

N

r =

w

3

V

ft

3

m

Units

Weight Density of Water

- Water has a weight density of 62.4 lb/ft3.

Pressure Units

- N/m2 = 1 Pascal (Pa)
- 1000 Pa = 1kilopascal (kPa)
- lb/in2 = psi (pounds per square inch)

Pressure and Depth

- Pressure increase with depth because of the additional weight of the fluid above.

Pressure =

weight density

x

height

P =

r

h

x

w

Buoyancy and Archimedes’ Principle

- Ptop = rw x h
- Pbottom = rw x (h + d)
- F = P x A
- Ftop = Ptop x A = (rw x h) x A
- Fbottom = Pbottom x A = [rw x (h+d)] x A
- Fbuoyant = Fbottom – Ftop = rw Ad
- Ad = Vbrick
- Fbuoyant = rw x Vbrick = 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

F = P x A

A = p r2

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 1m2, encloses about 10,000 kg of air.
- This air weighs about 1 x 105 N
- Therefore, atmospheric pressure is about 105 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/ft2

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.

Summary

- Matter can exist in four states: solid, liquid, gas, and plasma.
- Liquids and gases are called fluids.
- The density of a substance is its mass per unit volume.
- The density ofwater is 1g/cm3.
- 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.

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.

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