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**Definition of Fluid:-** A fluid is a substance which flows continuously under the action of shear force (however small the force may be), as long as shear force is there the fluid moves or deforms.

E.g: - Liquids, gases, vapour etc.

For a static fluid shear force = 0

**Density or mass density (ρ):- **

-Density or mass density of fluid is defined as the ratio of the mass of the fluid to its volume.

-The unit of mass density is kg per cubic meter i.e. kg/m^{3}

-Density of water is maximum at 4ºC.

-Density of water at 4ºC = 1000 kg/m^{3}

**Specific Weight or Weight Density:**

-Specific weight or weight density of a fluid is defined as the ratio of weight of a fluid to its volume.

-Thus, weight per unit volume of a fluid is called weight density.

-It is denoted by the symbol ‘w’.

-Mathematically,

-The value of specific weight of water is 9.81 X 1000 N/m^{3} in SI unit.

**Specific Gravity or Relative Density:****-**Specific gravity is defined as the ratio of the density (or weight density) of a fluid to the density (or weight density) of a standard fluid.

-For liquids, standard fluid is taken water and for gases, standard fluid is taken air.

-Specific gravity is also called relative density.

-It is dimensionless quantity and is denoted by symbol S.

-Mathematically,

-Specific gravity of mercury is 13.6.

**Viscosity**:

-Viscosity is defined as the property of fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of fluid.

-When two layers of a fluid distance ‘dy’ apart, move one over the another at different velocities, say u and u + du as shown in fig., the viscosity together with relative velocity causes a shear stress acting between the fluid layers.

-The top layer causes a shear stress on the adjacent lower layer while the lower layer causes shear stress on the adjacent top layer.

-This shear stress is proportional to the rate of change of velocity with respect to

y.

It is denoted by symbol Τ (Tau).

-Where μ (called mu) is the constant of proportionality and is known as the co-efficient of dynamic viscosity or only viscosity

- represents the rate of shear strain or rate of shear deformation or velocity gradient.

-Viscosity is also defined as the shear stress required to produce unit rate of shear strain.**Unit:**

**Newton’s Law of Viscosity::**

-Its states that the shear stress (Τ) on a fluid element layer is directly proportional to the rate of shear strain.

-The constant of proportionality is called the co-efficient of viscosity.

-Mathematically,

**Types of fluids:**

**1. Ideal Fluid (Perfect Fluid)**

-A fluid, which is incompressible and is having no viscosity, is known as ideal fluid.

-Ideal fluid is only an imaginary fluid because all the fluids, which exit, have some viscosity.

-Used in mathematical analysis and flow problems.

-Ideal fluid has no surface tension

**2. Real Fluid**

-Possess the properties such as viscosity, surface tension and compressibility.

-Offers resistance against flow.

-All the fluids in practice are real fluids.

**3.****Newtonian fluid**

-A real fluid,in which the shear stress is directly proportional to the rate of shear strain(or velocity gradient), is known as the Newtonian fluid.

-Example:Water, Air, Thin motor oil

**4. Non-Newtonian Fluid**:

-A real fluid, in which the shear stress is not proportional to the rate of shear strain(or velocity gradient), is known as the non-Newtonian fluid.

-Example : Tooth Paste

**5.Ideal-Plastic Fluid:**

-A fluid, in which shear stress is more than the yield value and shear stress is proportional to the rate of shear strain(or velocity gradient), is known as ideal plastic fluid.

-Example : Sewage sludge

**Surface Tension (s or σ):**

-Surface tensions is due to cohesion only.

-Surface tension decrease with increase in temperature and it also act when fluid is at rest

-It is a surface phenomenon

-At critical point liquid and vapour are at same state thus surface tension is zero

s_{water }= 0.0736 N/m at 20ºC

s_{mercury} = 4.51 N/m

**(i) Pressure inside a liquid drop in excess of atmospheric pressure****-p=4s/d**

p = Pressure intensity inside the droplet (in excess of the outside pressure)

d = Dia. of droplet

s = Surface tension of the liquid

-Equation shows that with increase of diameter of the droplet, pressure intensity inside the droplet decreases.

**(ii) Soap bubble****-p=8s/d**

**(iii) Pressure inside a water droplet****-p=2s/d**

**Capillary Action:**

-Capillarity is defined as a phenomenon of rise or fall of a liquid surface in a small tube relative to the adjacent general level of liquid when tube is held vertically in the liquid.

-The rise of the liquid surface is known as capillarity rise while the fall of liquid surface is known as capillarity depression or fall.

-It is expressed in terms of cm or mm of liquid.

-Its value depends upon the specific weight of the liquid, diameter of the tube and surface tension of the liquid.**Expression for Capillarity Rise:**

h = rise in capillary

σ = surface tension of water & glass

d = diameter of tube

θ = angle of contact between the liquid and the material

-The value of θ between water and clean glass tube is approximately equal to zero and hence cosθ is equal to unity.**Compressibility :**

It refers to change in volume/density due to change in pressure.

The compressibility is reciprocal of bulk modulus of elasticity (K).**Compressibility = 1/k**

In compressible fluids the velocity of sound is given by

c = (K/ρ)^{1/2}

C = velocity of sound in fluid, K = Bulk modulus,ρ=density

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