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Mechanical Properties of Fluids

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Physics Part II

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State and prove Archimedes principle.

Archimedes principle: When a body is immersed partially or wholly in a liquid, its weight appears to be reduced and loss of weight is equal to the weight of liquid displaced by the body.

                  

Proof: Consider a body of height h and area of cross-section A placed in liquid of density σ at a depth x below the free surface.

Let ρ be density of the body.

Now the pressure at the upper face of the body is,
                     straight P subscript 1 equals straight P subscript 0 plus xσg 

where,  Pis atmospheric pressure.

Pressure at the lower face of the body is, 

                  straight P subscript 2 equals straight P subscript 0 plus left parenthesis straight h plus straight x right parenthesis σg

Therefore downward thrust on  upper face of the body is,
                  straight F subscript 1 equals straight P subscript 1 straight A

and upward thrust on lower face of body is,

                  straight F subscript 2 equals straight P subscript 2 straight A

Since P> P1  therefore F> F

Body will experience the net force F- Fin upward direction known as upward thrust.


therefore space space space space space straight U equals straight F subscript 2 minus straight F subscript 1 equals left parenthesis straight P subscript 2 minus straight P subscript 1 right parenthesis straight A space

space space space space space space space space space space space equals straight A open square brackets open parentheses straight h plus straight x close parentheses σg minus xσg close square brackets equals Ahσg
italic space italic space italic space italic space italic space italic space italic space italic space italic space italic space

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where, V is volume of body

        = Weight of liquid displaced by body.


Now, the  body experiences two forces: weight of the body itself and upward thrust.

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i.e. Apparent weight is less than the actual weight by amount equal to weight of liquid displaced by body.

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What is hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids. 
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Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law. 
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What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.


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Why solids have definite shape while liquids do not have definite shape?

Solids: Intermolecular forces are very strong and thermal agitations are not sufficiently strong to separate the molecules from their mean position. Solids are rigid and hence they have definite shapes.
Liquids: In liquids intermolecular forces are not sufficiently strong to hold the molecules at definite sites, as a result they move freely within the bulk of liquid, therefore, do not possess definite shapes. Liquids take the same shape as that of the container. 
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What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.
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