**M**

**ECHANICS OF FLUID**

**Pressure :**The force/threat acting per unit area is called pressure

S.I Unit of pressure is N/M

^{2}or pascal (Pa)

Dimensional formula (ML

^{-1}T

^{2})

**Pascal’s law:-**Pressure applied to an enclosed fluid is transmitted to all part of the fluid and to the wall of the container.

**Application of Pascal’s law:-**

(1) Hydraulic lift, presses etc.

(2) Hydraulic brakes

**Pressure exerted by liquid column:-**

P = hρg, where h = depth of liquid,

ρ = density ,

g = acc

_{n}. due to gravity.

**Variation of pressure with depth:-**

P = P

_{a }+ hρg, where P

_{a}= atmospheric pressure

**Atmospheric pressure:-**The pressure exerted by atmosphere is called atmospheric pressure.

At sea level, atmospheric pressure= 0.76m of Hg column

Mathematically 1 atm = 1.013 x 10

^{5}Nm

^{-2}

^{}

^{}

**Archimedes’ principle:-**It states that when a body is immersed completely or partly in a fluid, it loses in weight equal to the weight of the fluidrue weight – Vρg

Where V is volume of fluid displaced displaced by it.

Mathematically: Apparent weight = T, ρ is its density.

**Viscosity:-**It is the property of liquid (or gases) due to which a backward dragging force acts tangentially between two layers of liquid when there is relative motion between them.

**Newton’s formula for Viscous force:-**The viscous force between two liquid layer each of area A and having a velocity gradient dv/dx is

F = ƞA (dv/dx) , where ƞ is coefficient of viscosity

**Coefficient of viscosity:-**It is define as the tangential viscous force which maintains a unit velocity gradient between two parallel layers each of unit area

S.I unit of coefficient of viscosity is poiseuille or pascal-second

**Poiseuille’s equation:-**When a liquid of coefficient of viscosity flows through a tube of length ‘l’ and radius r, then the volume of liquid following out per second is given

Where P is the difference of pressure between the two ends of the tube.

**Stoke’s law:-**The backward dragging force acing on a small sphere of radius r falling with uniform velocity v through a medium of coefficient of viscosity is given by

**Terminal velocity:-**It is the maximum constant velocity acquired by the body while falling freely in a viscous medium

The terminal velocity v of a spherical body of radius r and density ϭ while falling freely in a viscous medium of viscosity ¶ , density is given by

**Stream line:-**It is the path, straight or curved, the tangent at any point to which given the direction of the flow of liquid at that point.

**Tube of flow:-**A tube of flow is a bundle of stream lines having the same velocity of fluid elements over any cross section perpendicular to the direction of flow.

**Stream line flow:-**The flow of the liquid in which each molecule of the liquid passing through a point travels along the same path and with the some velocity as the preceeding molecule passing through the same point.

**Laminar flow:-**The flow of liquid, in which velocity of the layer varies from maximum at the axis to minimum for the layer in contact with the wall of the tube is called laminar flow.

**Turbulent flow:-**It is the flow of liquid in which a liquid moves with a velocity greater than its critical velocity. The motion of the particles of liquid becomes disorderly or irregular.

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