Fluid 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 fluid? A 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 gas differ from other fluids?

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 the density of a liquid The mass density,ρ,represents the density of a liquid. mathematically: ρ = Mass / Volume

What is the apparent weight?

What is the buoyant force?

What is the buoyant force What is the buoyant force? Fgravity – Fbuoyant = apparent weight Fbuoyant = 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 = Fgravity(displaced fluid) = mfg 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 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?