**Critical velocity:-**It is that velocity of liquid flow, upto which the flow of liquid is streamlined and above which its flow becomes turbulent. Critical velocity of a liquid (V

_{c}) flowing through a tube is given by

Where ρ is the density of liquid following through a tube of radius r and ƞ the coefficient of viscosity of liquid

**Reynold’s number:-**It is a pure number which determines the nature of flow of liquid through a pipe.

Quantitatiively Renold’s number

Where ƞ is coefficient of viscosity of liquid , ρ is density of liquid D is the diameter of the tube, Vc is critical velocity

For stream line flow, Reynold’s number < 2000

For turbulent flow, Reynold’s number > 3000

For uncertain flow, 2000 < Reynold’s number < 3000

**Theorem of continuity:-**If there is no source or sink of the fluid along the length of the pipe, the mass of the fluid crossing any section of the pipe per second is always constant

Mathematically

It is called the equation of continuity

For in compressible liquid

**ρ1 = ρ2**

**Bernoulli’s theorem:-**It states that for an in compressible non-viscous liquid in steady flow, the total energy i.e. pressure energy, potential energy and kinetic energy remains constant its flow.

Mathematically

are called pressure head, gravitational head and velocity head respectively.

**Application of Bernoull’s theorem**

(i) Working of Bunsen burner

(ii) Lift of an air foil

(iii) Spinning of ball (Magnus effect)

(iv) Sprayer

(v) Ping pong ball in air jet.

**Toricelli’s theorem/speed of efflux:-**It states that the velocity of efflux i.e. the velocity with which the liquid flows out of an orifice (i.e. a narrow hole) is equal to that which is freely falling body would acquire in falling through a vertical distance equal to the depth of orifice below the free surface of liquid.

Quantitatively velocity of efflus

**Venturimeter:-**It is a device use to measure the rate of flow of liquid. Venturimeter consists of a wide tube having a constriction in the middle. If a1 and a2 are the areas of cross section of the wide end and the threat, p1 and p2 are the pressure of liquid, then velocity of the liquid entering at the wide end is given by

**Surface tension (T):-**It is the property of a liquid by virtue of which, it behaves like an elastic stretched membrane with a tendency to contract so as to occupy a minimum surface area

Mathematically T = F/l

S.I Unit is : Nm

^{-1}

^{}

^{0}T

^{-2}

^{}

Surface tension is numerally equal to surface energy

**Excess of pressure inside a drop and double:-**

There is excess of pressure on concave side of a curved surface

1. Excess of pressure inside a liquid drop = 2T/R

2. Excess of pressure inside a liquid bubble = 4T/R

3. Excess of pressure inside an air bubble = 2T/R, Where T is the surface tension , R = radius of liquid drop

**Angle of contact:-**The angle which the tangent to the free surface of the liquid at the point of contact makes with the wall of the containing vessel, is called the angle of contact

For liquid having convex meniscus, the angle of contact is obtuse and for having concave meniscus, the angle of contact is acute.

**Capillary tube:-**A tube of very fine bore is called capillary tube

**Capillarity:-**The rise or fall of liquid inside a capillary tube when it is dipped in it is called capillarity

**Ascent formula:-**when a capillary tube of radius ‘r’ is dipped in a liquid of density s and surface tension T, the liquid rises or depresses through a height,

There will be rise a liquid when angle of contact θ is acute. There will be fall in liquid when angle of contact θ is obtuse.

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