## Fluid mechanics - Density, Specific Gravity, Viscosity, Vapour pressure etc

### Blog Contents -

- Fluid mechanics [Fluid properties]
- Classification of fluids
- Density of fluid.
- Weight density
- Specific volume
- Specific Gravity of fluid.
- Viscosity of fluid.
- Vapour pressure of fluid.

### Interview Questions from this blog

- What is definition of fluid?
- Classifications of fluid
- What are Newtonian fluids and Non Newtonian fluids?
- Why density is depend on Temperature & Pressure?
- What is classification of Non Newtonian fluid?
- What is relation between mass density & mass density?
- What is relation between Vapour Pressure & Temperature?
- How vapour change with molecular forces?

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### Fluid definitions

Fluid is a substance which under goes continuous deformation (flows) when subjected to external force or gravity.

Other definitions

- Fluid is a substance which one’s particles easily move and change their respective position with other particles when substance is free or under pressure or under gravity
- Fluid is capable to flow when allowed to flow freely. or Fluid is a substance tends to conform to the containers outline or free to flow
- Fluid has no definite shape but when it fill in any Container it follow container's shape called Fluid

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### Classification of fluid

Fluid classification is as per below

Classification of fluid |

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#### Definitions of Fluids of each type:

Ideal Fluid -- Ideal fluid is a fluid which does not offer any resistance in flow / deformation / shape change.
- Fluid doesn't has viscosity
- It is friction-less & In compressible.
- Ideal fluid is not exists It is imaginary fluid.

Real Fluid

- Fluid found in nature and reality called real fluid.
- Real fluid offers resistance when it is in motion.

- Fluids which's density depends on Temperature & Pressure called Compressible fluid.
- Fluid of which the density is sensible to change in temperature or pressure called Compressible fluid
- Generally gases are compressible fluids.

- If density of fluid is not affected by change in temperature or pressure applied in temperature that fluid is called Incompressible fluid.
- Generally liquids are incompressible

- Fluids which follows Newton's law of viscosity are called Newtonian fluids.
- Newton's law of viscosity : The fluids for which the ratio of the shear stress to the rate of shear is constant

- Fluids which are not following newton's law of viscosity calling Non Newtonian fluid

### Density of fluid [Mass density]

- Density ⍴ or mass density of fluid is ratio of Mass of fluid m per unit Volume V
- SI unit of Density is Kg/m3
- Density of water at 4℃ [277K] is 1000 kg/m3

Density ⍴ = Mass (m) / Unit Volume (V)

- Density is dependent on Temperature and Pressure.

- As per Ideal Gas Law

PV = nRT

- When Temperature is increases Volume of fluids increases.
- When Pressure is Increases Volume of fluid decreases.
- Generally Density of fluid is not much change in slight change in Temperature.
- Gas density is change higher than liquid in raise temperature.

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Example of Density -

Copper cube sink in water, but in mercury it float.

#### Case 1 : Copper Cube in Mercury

**Why? -**

Density of Mercury : 13600 kg/m3

Density of Copper : 9000 kg/m3

Copper is light in comparison.

This is the reason Copper cube if floating

#### Case 1 : Copper Cube in Water

**Why? -**

Density of Water : 999 kg/m3

Density of Copper : 9000 kg/m3

Water is light in comparison.

This is the reason Copper cube if floating

Density Chart - Download now

### Weight density

- Weight of fluid per unit volume.
- Weight density of Water at 4°C : 9810 N/m3
- Relation between Mass density & Weight density

w = ⍴ g

- g = gravitational force 9.81 m/s2

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### Specific Volume

- It is volume in unit mass
- unit : m3/kg

### Specific Gravity [ Sp.Gr., Relative Density]

Its ratio of**Density of fluid**to

**Density of standard fluid.**

**Standard fluids**

Liquid - Water at 4℃, 1 Atmospheric pressure.

Air - Air at 20℃, 1 Atmospheric

Unit : Unit less [You can consider kg/m3]

Unit Calculation -

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### Viscosity

Fluid is a substance able to flow but there is resistance in flow is called Viscosity- Honey has more viscosity so it is not flow freely.
- Water has less viscosity so it flows more freely.
- It is not depend on Pressure.
- Viscosity decrease when temperature increase. [ When temperature rises molecular vibration also increases which makes fluid free and reduce it's viscosity].
- Viscosity governed by Cohesive forces[Attractive forces].

#### Viscosity calculation

Force is proportional to velocity and area and inversely proportional to DistanceF = Force required to move fluid from two parallel layers 1 & 2.F ∝ u A / Y

F = μ u A / Y

μ = Viscosity of fluid

Coefficient of Viscosity, Dynamic Viscosity

F / A = μ u / Y

𝛕 = μ * u / Y𝛕 = F / A

We need velocity gradient to measure viscosity.μ = 𝛕 / (du/dY)

Velocity gradient is velocity of fluid with respect to distance traveled.

This is Newton's law of viscosity

- Viscosity μ is Shear stress required to produce unit flow [Shear deformation].
- Unit : N.s/m^2 [SI Unit]
- Kinetic Viscosity of fluid is ration of viscosity of fluid to density. 𝝂 = μ/⍴

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### Newtonian & Non Newtonian fluid

#### Newtonian fluid definitions

- Shear stress to Rate of shear Ratio of is constant
- Fluids which has velocity gradient equal to Shear stress applied.
- Fluid which has 45° angle graph in Shear stress vs Velocity gradient du/dy
- Examples - All gases, Air; Liquids - Kerosene, alcohol, glycerin.

#### Non Newtonian fluid definitions

- Fluid for which Share stress vs Velocity gradient is not constant
- Fluids not follow Newton's law of Viscosity.

Examples - There are three types of Newtonian fluids

- Bingham fluids
- Pseudo plastic
- Dilatent fluid

1. Bingham fluids

- When Shear stress is small it resist to flow.
- When Shell stress is larger it follow linear shear stress vs flow called Bingham fluids of Plastics.
- Examples - Toothpaste, Jellies, Paints, Slurries.
- 𝜏 = 𝜏0; du/dy=0; 𝜏>𝜏0 𝜏=𝜏0 + η du/dy. 𝜏0 = yield stress, η = rigidity coefficient

2. Pseudo plastic or fluids [shear rate thinning fluid]

- Viscosity decrease with increase in velocity.
- Examples - Blood, High molecular weight solution, paper pulp, rubber latex.

3. Dilatent fluids [shear rate ticking fluid]

- Viscosity increases when velocity increases.
- Examples - Suspensions of starch, pulp in water, emulsions.

Experimental curve of Shear stress vs Velocity given by Ostwald-de-waele equation

𝜏 = k (du/dy)

^{n}Where k & n are arbitrary

n = 1 k = μ : Newtonian fluid

n < 1 : Pseudo plastic

n > 1 : Dilatant fluids

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### Vapour Pressure

Pressure formed by vapour of liquid over the surface of liquid in closed container which is in thermodynamic equilibrium state at a given temperature.- Pure water's Vapour pressure is 1 atmosphere at 100℃
- All liquids have tendency to vaporize.
- Molecules of liquid escaping through free surface of liquid to space.
- Vapour accumulation develop pressure on liquid surface and towards container vessel.

PM_{avg}= ρRT

#### Vapour pressure vs Temperature

- Vapour pressure increase with increase in temperature
- Water Vapour pressure Vs Temperature Graph

- Vapour pressure is not affected by surface area.
- Water vapour pressure is same on small container & large vessels.
- Vapour pressure is depends on dipole-dipole forces & London dispersion forces.

#### Watch video in Hindi -

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