Fluid Mechanics Chapter 8. Mass Density The concentration of matter of an object, measured as the mass per unit volume of a substance. Represented by.

Fluid Mechanics

• Chapter 8

Mass Density

The concentration of matter of an object, measured as the mass per unit volume of a substance.Represented by the Greek letter ρ (rho)mass density ( ρ ) = mass/volumeUnits kg/m3

Buoyant Force

Upward force exerted by a liquid on an object immersed in or floating on the liquid.Because the buoyant force acts in an opposite direction as the force of gravity, the net force acting on an object submerged in a fluid, is smaller than the object’s weight.Objects appear to weigh less in water than they do in air so the weight of an object in a fluid is the object’s apparent weight.

Your Turn!

Why does an air mattress float and a brick sink? Think of an answer and make sure you put it in terms of forces.

Eureka!!!Archimedes’ Principle- Any object completely or partially submerged in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object.Does this mean that the buoyant force is just like weight (mg)?

Buoyant Force

FB=Fg(displaced fluid)FB=mfgIn other words

The magnitude of the buoyant force equals the weight of fluid displaced What does Fg equal?Based on Archimedes’ Principle, what would be a good equation for FB?

Fg -FB =apparent weight

Fg-apparent weight= FB

Fg=mg

FB= ρ V g

Where did ρ V come from?

What is V?

Sink or float?

Buoyancy Largest = AscendBuoyancy Largest = Ascend

Forces Balanced = HoverForces Balanced = Hover

Weight Largest = SinkWeight Largest = Sink