Fluid DynamicsFluid Dynamics

What is a fluid?

Does a gas differ from other fluids?

What is mass density?

What is apparent weight?

What is a buoyant force?

What is Archimedes’ Principle?

What is a fluidfluid? A fluid fluid is a nonsolid state of matter in which the atoms or molecules are free

to move past one another. –P. 985

How does a gasgas differ from other fluidsfluids?

Although both liquids and gases do not have a definite shape, a liquid is not compressible, while a gas is.

Liquids thus have a fixed volume, while gases do not.

Both liquids and gases are fluids.

The mass density,ρ,represents,represents the the

density of a liquid.density of a liquid.

mathematically:mathematically: ρ = Mass / Volume

What is the apparent weight?

What is the buoyant force?

What is the buoyant force?Fgravity – Fbuoyant = apparent weightFbuoyant = Fgravity – apparent weight

What relationship exists between the submerged volume of the object

and the volume of the displaced liquid?

Let’s try an experiment…

So, The volume of the displaced liquid is equal to the submerged

volume of the object.

Archimedes’ Principle may be stated as follows: 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.

Mathematically: Fbuoyant = Fgravitygravity(displaced fluid) = m(displaced fluid) = mffgg

The buoyant force = weight of fluid displaced The buoyant force = weight of fluid displaced

How may we determine if an object will sink or float?.. Consider…

The apparent weight of a submerged object depends on

density. Fnet = (ρf – ρo) g V

W / FB = ρo / ρf

Let the volume of the object be Vo

Let the density of the object be ρo

Let the volume of the liquid be Vf

Let the density of the liquid be ρf

• ρo Vo = ρf Vf

So,

ρo / ρf = Vf / Vo = r

“r” is the ratio of the density of the object to that of the liquid.

What happens if r < 1 ?

What happens if r > 1 ?

Let the volume of the object be Vo

Let the density of the object be ρo

Let the volume of the liquid be Vf

Let the density of the liquid be ρf

• ρo Vo = ρf Vf

So,

ρo / ρf = Vf / Vo = r

“r” is the ratio of the density of the object to that of the liquid.

What happens if r < 1 ? The object floats.

What happens if r > 1 ?

Let the volume of the object be Vo

Let the density of the object be ρo

Let the volume of the liquid be Vf

Let the density of the liquid be ρf

• ρo Vo = ρf Vf

So,

ρo / ρf = Vf / Vo = r

“r” is the ratio of the density of the object to that of the liquid.

What happens if r < 1 ? The object floats.

What happens if r > 1 ? The object sinks.

1 a) If a stone is thrown overboard from a boat floating in a pool, does the water level on the pool rise, fall, or remain

unchanged?

1. b) If a hole is made in the bottom of the boat so that the

boat sinks, does the water level in the pool change?

If so, when does the change begin? (When water first enters

the boat or later)?

2. a) A boat floating in a pool carries a mass M that can be

placed on the raft or hung below in the raft.

i) How does the water level in the pool compare in the two

cases?ii) In which case does the raft

float higher in the water?