Archimede’s Principle An object immersed in a fluid has an upward (buoyant) force equal to the weight of the fluid it displaces. F B =  gV F B = buoyant force  = mass density of the fluid g = acc. due to gravity V = volume of the fluid displaced

Floating Since apparent weight = 0, the weight of the object = weight of the fluid displaced (or buoyant force). W app = 0 so W obj = F B = W fd Volume of the fluid displaced = volume of the submerged part of the object. V fd = V submerged density of the object < density of the fluid

Sinking The object can’t displace enough fluid to equal its own weight. W obj > F B The volume of the fluid displaced = the volume of the object. V fd = V obj W app = W air - F B W app = apparent weight W air = weight of object in air (= mg) F B = buoyant force (= W fd =  f Vg)

Pressure Force per unit area Units: Pa (N/m 2 ) P = pressure F=force A= area

Pascal’s Principle Pressure applied to a fluid is transmitted throughout that fluid unchanged in all directions. Pressure increases in a fluid with depth  P =  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 the each is the same.

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. P 1 =P 2 so… F 1 /A 1 = F 2 /A 2 Pressure is constant MA = F 2 / F 1 = A 2 / A 1

Bernouilli’s Principle As the velocity of a fluid increases, the pressure exerted by that fluid decreases. (not valid for turbulent flow)

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. Spoilers on a race car - opposite of the airplane wing.