Ch. 9 Fluid Mechanics

Ch. 9Fluid

Mechanicspgs. 317 - 342

Define a fluid. Distinguish a gas from a liquid. Determine the magnitude of the buoyant

force exerted on an object. Explain how Archimede’s principle applies

to buoyancy.

Objectives

A non solid state of matter

Have the ability to flow◦ Atoms or molecules are free to move past each

other

Can alter their shape

Fluids

Liquids have a definite volume

Gases do not have a definite volume

Fluids

When describing fluids, the mass density is the mass per unit volume of a substance

Units are kg/m3

Mass density is often just called density

Should remember this from Chemistry

Mass Density ()

Volume (V) has units of m3

Mass Density ()

Liquids are almost incompressible, so their densities change very little with pressure

Gases are compressible and can have densities over a wide range of values

Mass Density

Fluids exert an upward force on objects that are partially or completely submerged in it

Keeps objects afloat Acts in the opposite direction of the force of

gravity Which means floating is a type of

equilibriumAn upward force counteracts the force

of gravity for these objects. This upward

force is called the buoyant force.

Buoyant Force (FB)

The density of an object determines the depth of submersion

For an object to float, the object’s density can never be greater than the density of the fluid

Objects can still sink if the buoyant force is not enough to keep it afloat

Floating Objects

Buoyant force = Weight of floating object When an object floats in a fluid, the net

force is zero If the object’s density is less than the fluid density, the net force is positive (upward) and the object floats.

Floating Objects

Apparent Weight◦ Objects submerged in a fluid have a net force on

them that is smaller than their weight.

Whether an object floats or sinks depends on the net force

Submerged Objects

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.

Archimedes’ Principle

The apparent weight of a submerged object depends on density.

When submerged, the volumes are equal.

The net force is the apparent weight of the object◦Fnet = Fg (object) – FB

Archimedes’ Principle

Archimedes’ Principle is applied to the net force (remember that m = ρV), so◦Fnet = Fg – FB

◦Fnet = mog – mfg

◦Fnet = (ρoVo – ρfVf)g

Archimedes’ Principle

If the object floats on the surface, we know for a fact Fbuoy = mg! The volume ofdisplaced water equals the volume of thesubmerged portion of the ship.

Archimedes’ Principle

The apparent weight of a submerged object depends on density

When submerged, the volumes are equal. Using Archimedes’ Principle:◦ Fnet = ρoVog – ρfVfg

◦ Fnet = ρog – ρfg

Submerged Objects

Buoyancy can be changed by changing average density

◦ A fish can adjust its average density by inflating or deflatingan organ called a swim bladder

◦ The ballast tank of a submarine works in the same way as the swim bladder of a fish

Buoyant Force

If the object and fluid densities are the same, the object floats suspended underwater.

If the object’s density is greater than the fluid density, the net force is negative (downward) and the object sinks

Buoyant Force

A bargain hunter purchases a “gold” crown at a flea market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N. Is the crown made of pure gold? (Density of fresh water is 1x103 kg/m3 and density of gold is 19.3 x 103 kg/m3)