Sub Unit 1.2 – Fluid Force

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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

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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

Units

mass

Density =

• English

volume

SI

(slugs)

kg

lb

g

or

3

3

ft

3

m

cm

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
• A force applied over a surface is pressure.

force

Pressure =

area

Units

F

lb

N

P =

2

2

A

ft

m

English

SI

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
• 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.