Density, Pressure, Upthrust and Flows

pressure

Density

Definition: mass/ volume

Unit: ρ

Formula:

ρ(rho - kgm^-3) = m/v

Definition = Force/ Surface Area

Unit for pressure: Nm^-2/ Pa ( 1 Pa is the force of 1N is spread over 1m^2)

1 atm is the pressure due to the air at surface of the Earth (atmosphere) = 1.01 x 10^5 Pa

Velocity of air particle (Room temperature) = 500 ms^-1

Pressure increases with depth = F/A = W/A= mg/A = ρvg/A

=> P = ρgh

If ρL > ρS => it will float

ρL > ρS => it will sink

Force = Pressure x Area => F down = P x A = ρgdA

P = ρgh => F up = P x A = ρg( d + h)A

F up is bigger than F down because pressure increases with depth

=> F up - F down = Upthrust

Upthrust comes from the difference in the forces on the surface

=> U = ρ liquid x g x v

Upthrust equals the weight of the liquid (fluid) which has been displaced

=> U= F up - F down

= ρg (d + h)A -ρgdA

=ρgA (d + h -d)

=ρgAh = ρgV= mg (weight of the liquid which has been displaced)

(*Ah = Volume of the object, ρV= the mass of the liquid which has been displaced)

Flows, floating & sinking

upthrust