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Mechanical Properties of Fluids

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Physics Part II

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Physics

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Class 10 Class 12
State and prove Pascal's law.

PAscal's law states that, if some pressure is applied at any point of incompressible liquid then the same pressure is transmitted to all the points of liquid and on the walls of the container.

Let us imagine an arbitrary right angled prismatic triangle in the liquid of density ρ. This prismatic element is very small so, every part is considered at the same depth from the liquid surface. Therefore, effect of gravity is the same at all these points. That, the small element is in equilibrium. 


The area of faces ABFE, ABDC and CDFE are ad, bd and cd respectively. Let the pressure of liquid on faces ABFE, ABDC and CDFE be P1, P2 and P3respectively.

The pressure of liquid exerts the force normal to the surface. Let us assume pressure P1exerts the force F1 on the surface ABFE, pressure P2 exerts force F2 on the surface ABDC and pressure P3 exerts force on the surface CDFE. 

So, Force F1 is given by, 

F1 = P1 × Area ABFE = P1ad F2 = P2 × Area ABDC = P2bd F3 = P3 × Area CDFE = P3cd Also, sin θ = ba and sin θ = ca 

Since the prism is in equilibrium, so net force on the prism is zero. 

Thus, 

F1 sin θ = F2 , and F1 cos θ = F3 Therefore, P1 ad (b/a) = P2 bd , and    ... (1)P1 ad (c/a)= P3 cd               ... (2) So, from equations (1) and (2), we haveP1 = P2 , and P1 = P3  P1 = P2 = P3 So, Pascal's law is proved.




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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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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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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 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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