1. Pressure Force per unit area Units: Pa (N/m2), lb/in2, atm, torr, mmHg
P = pressure, N (psi)
F=force, N (lb)
A= area, m2 (in2)

2. Pascal’s Principle
Pressure applied to a fluid is transmitted throughout that fluid unchanged in all directions.
Pressure acts perpendicular to the walls of the container.

3. Hydraulics Machines using hydraulics use fluids to multiply forces.
These machines have a small piston and a large piston connected by a chamber filled with hydraulic fluid.
P1=P2 so… F1/A1 = F2/A Pressure is constant
MA = F2 / F1 = A2 / A1

4. Pressure at a Depth Pressure increases in a fluid with depth
P = f g h, where  = density of fluid, g= acc. due to gravity, and h = height of the fluid column
The shape of the container has no effect on pressure. Only Depth!
The pressure at the bottom of each is the same.

5. Archimedes’ Principle
An object immersed in a fluid has an upward (buoyant) force equal to the weight of the fluid it displaces FB = mfd g so FB = f Vfd g
FB = buoyant force, N
f = mass density of the fluid, kg/m3
g = acc. due to gravity, m/s2
Vfd = volume of the fluid displaced, m3

6. Floating
Since apparent weight = 0, the weight of the object = weight of the fluid displaced (or buoyant force).
Fnet = Fapp = 0 so Fg = FB = Ffd
Volume of the fluid displaced = volume of the submerged part of the object.
Vfd = Vsubmerged (< Vo )
density of the object < density of the fluid
ρo < ρf

7. Sinking
The object can’t displace enough fluid to equal its own weight. Fg > FB
The volume of the fluid displaced = the volume of the object. Vfd = Vobj
Fapp = Fair - FB
Fapp = apparent weight or weight in fluid (=Fnet), N
Fg = weight of object in air (= mo g = o Vo g), N
FB = buoyant force (= Ffd = mfd g = f Vfd g), N
density of the object > density of the fluid
ρo > ρf

8. Suspended in a Fluid – Neutral Buoyancy
Fg = FB so Fapp = Fnet = 0
Volume of the fluid displaced is equal to the volume of the object.
(Vfd = Vobject)
density of the object = density of the fluid (ρo = ρf )
A submarine or a fish can float, sink, or suspend by changing its density.

9. Bernouilli’s Principle
As the velocity of a fluid increases, the pressure exerted by that fluid decreases.
(not valid for turbulent flow)
Note: Pressure goes from high to low pressure.

10. Applications of Bernouilli’s Principle
Lift on an airplane wing - air has to travel farther over the top of the wing, so velocity is greater and pressure is less on top of the wing than underneath. As a result the higher pressure underneath causes lift.
Spoilers on a race car - opposite of the airplane wing; pressure is greater above, pushing the car down for more traction.