1.12 - Fluids
● ***Fluids: liquids/gases; in a fluid particles can move relative to one another (unlike a
solid, in which atoms occupy fixed positions)
Density (𝝆)
m(mass)
● *** ρ( density)=
V (volume)
● Density of a substance is reduced when heated from liquid to gas state
● Liquids - generally incompressible, gases - readily squeezed
Pressure (P)
F( force [N ])
● *** P( pressure)=
A(area)
● Eg if you dive to the bottom of a swimming pool, you will feel the water pressure
pushing into your ears, in which this pressure is created by the weight of the water
above you
F( weight of water above you) mg
○ Ie P( pressure)= =
A ( surface area of your body ) A
∵ m=V ρ , V = Ah, ∴ *** P= ρ gh
● Atmospheric pressure ≈ 1.01 x 105 Pa (“weight of gases above you head”)
● For larger values for h, gases compress in the lower regions, ∴ Earth’s
atmosphere has a lower density at higher altitudes (its pressure is ∴ NOT
directly proportional to height above Earth)
Upthrust (U)
● Eg if you are in a swimming pool, you will experience a buoyancy force which
enables you to float or swim - this force is called an upthrust (a consequence of the
water pressure being greater below an immersed object than above it)
● F 1( pressure at top of object , downward force)=P 1 A=h1 ρ gA
F 2( pressure at bottom of object , upward force)=P 2 A=h2 ρ gA
***U (upthrust )=F2−F 1=(h2−h1) ρ gA=V ρ g=mg/¿ {Archimedes’ principle}
Flotation
● ***An object will float in a fluid if the upthrust (weight of displaced fluid) = its weight
○ Ie if U > W, it means object is underwater, will return to surface of water due
to upward resultant force
Moving fluids — streamlines and laminar flow
● ***Streamline: represents the velocity of a fluid at each point within it
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● ***Fluids: liquids/gases; in a fluid particles can move relative to one another (unlike a
solid, in which atoms occupy fixed positions)
Density (𝝆)
m(mass)
● *** ρ( density)=
V (volume)
● Density of a substance is reduced when heated from liquid to gas state
● Liquids - generally incompressible, gases - readily squeezed
Pressure (P)
F( force [N ])
● *** P( pressure)=
A(area)
● Eg if you dive to the bottom of a swimming pool, you will feel the water pressure
pushing into your ears, in which this pressure is created by the weight of the water
above you
F( weight of water above you) mg
○ Ie P( pressure)= =
A ( surface area of your body ) A
∵ m=V ρ , V = Ah, ∴ *** P= ρ gh
● Atmospheric pressure ≈ 1.01 x 105 Pa (“weight of gases above you head”)
● For larger values for h, gases compress in the lower regions, ∴ Earth’s
atmosphere has a lower density at higher altitudes (its pressure is ∴ NOT
directly proportional to height above Earth)
Upthrust (U)
● Eg if you are in a swimming pool, you will experience a buoyancy force which
enables you to float or swim - this force is called an upthrust (a consequence of the
water pressure being greater below an immersed object than above it)
● F 1( pressure at top of object , downward force)=P 1 A=h1 ρ gA
F 2( pressure at bottom of object , upward force)=P 2 A=h2 ρ gA
***U (upthrust )=F2−F 1=(h2−h1) ρ gA=V ρ g=mg/¿ {Archimedes’ principle}
Flotation
● ***An object will float in a fluid if the upthrust (weight of displaced fluid) = its weight
○ Ie if U > W, it means object is underwater, will return to surface of water due
to upward resultant force
Moving fluids — streamlines and laminar flow
● ***Streamline: represents the velocity of a fluid at each point within it
1
