Fluid statics
Fluid
The substance which can flow from one point to another point is called fluid.
Example:- liquid and gas
Hydrostatics (fluid statics)
The study of fluid at rest is called hydrostatics.
Density
Mass per unit volume is called density. Its unit is kgm-3
Relative density (specific gravity)
The relative density of a substance is the ratio of its density to the density of water at 4°C
Pressure
Force per unit area is called pressure. Its unit is N/m2 or Pascal(pa)
In fluid pressure (p) = hdg
Derivation of Pressure in a liquid
Let us consider a liquid of density ‘ρ' Contained in a vessel of cross Sectional area ‘A’ up to height ‘h’ as shown in the figure.
Now,
Total mass of Liquid
(m) = volume (v) x density (ρ)
= Area(A) x height(h) x density(ρ)
= Ahρ
>Weight of Liquid is given by ;
W = mg
= Ahρg
So, The normal force on the bottom of the vessel is,
F = W
= Ahρθ
Finally,
The pressure by liquid at the bottom of the vessel is given by P=F/A
Ahρg / A
P= hρg
This is a required relation for pressure due to liquid and this relation shows that pressure due to liquid is directly proportional to
i)density of liquid
ii)height of liquid in the vessel
iii)Acceleration due to gravity at that place.
Principle of flotation
The principle of flotation states, "The weight of a floating body is equal to the weight of the liquid displaced". OR It states," A body is said to be floating in liquid if upthrust acting on the body is greater or equal to the weight of the body".
When a body is immersed in a liquid there are three cases
i ) When the weight of the body is greater than upthrust
Here, W > V
Vρg > Vρ1g
∴ ρ >ρ1
In this case, the body sinks and is set up at the bottom.
ii ) When the weight of the body is equal upthrust
Here, W = V
Vρg = Vρ1g
∴ρ = ρ1
In this case, the body lies inside a liquid with the upper surface on the surface of the liquid.
iii ) When the weight of the body is less than upthrust
Here, W < V
Vρg < Vρ1g
∴ρ <ρ1
In this case, a part of the body lies inside the liquid and the remaining part outside the liquid surface
The principle of floatation states that " A body is said to be in floating in liquid in upthrust acting on the body in greater or equal to the weight of the body.
Upthrust
The upward force by a fluid on an object which is completely or partially immersed in a fluid is called upthrust or buoyancy
Archimedes Principle
It states " When a body is fully or partially immersed in a fluid it expense an upthrust which is equal to the weight of the fluid displaced by the body."
i.e upthrust = weight of the fluid displaced
Pascals law
It states that " When pressure is applied to an enclosed liquid then the pressure is equally transmitted to every portion of it".
Centre of buoyancy
The center of gravity is the displaced liquid is called the center of buoyancy.
A floating body is said to be in equilibrium if the center of gravity and center of buoyancy of the body lies in the same vertical line
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