## Fluid Mechanics

Here we will learn –

**Branches of fluid****Approaches to studying fluid mechanics****Fluid Vs Solids upon sheering stress****The distinction between a solid and a liquid****The distinction between a gas and a liquid****Viscosity****Effects of Pressure and Temperature on Viscosity****Newton’s law of viscosity**

**1. Fluid Statics**– is the study of the mechanics of fluids at rest.

**2. Fluid Kinematics**– deals with velocities streamlines without considering forces or energy.

**3. Fluid Dynamics**– is considered with the relation between velocities accelerations and the forces, exerted by or upon fluid in motion.

**Approaches to studying fluid mechanics :**

**Analytical methods:**

**Computations :**

**Fluid Vs Solids upon sheering stress :**

*Liquid and gases are both regarded as liquids*

**.**

**Fluid**

**The distinction between a solid and a liquid**

**The distinction between a gas and a liquid : **

**Fluid as a continuum : **

**Viscosity :**

**Effects of Pressure and Temperature on Viscosity :**

Viscosity will change with pressure but under normal condition, this change is negligible in gases but viscosity increases with pressure in the liquid. A different scenario is seen for temperature as the temperature increases, the viscosity of all liquids decrease, while all viscosity of gages increases. This is because the force of cohesion, which diminishes with temperature, predominates with liquids, while with gases the predominating factor is the interchange of the molecules between the layers of different velocities. Thus a rapidly moving molecule shifting into a slower moving layer tends to speed up the latter and a slow-moving molecule entering a faster moving layer tends to slow down faster-moving layer. This Molecular interchange set up a shear or produce a friction force between adjacent layers. Increased molecular activity and higher temperature cause the viscosity of gages to increase with temperature.

## Newton’s law of Viscosity:

Newton’s law of viscosity states that “Shear stress acting on a flowing fluid is directly proportional to velocity gradient.”

Let us consider, a number of fluid layers, between two parallel plates, separated by a distance y, the lower surface is assumed to be stationary, while the upper one is moved paralleled is it, with a viscosity u, by the applied force F.

Fluid layers between two plates |

Taking two layers under consideration, Layer 2 and layer 3 separated by distance. The velocity of the adjacent layers is u and u+du respectively. For: deformation dθ due to force F the exact distance traveled by layer 3 is estimated to du × dt.

Now, tan dθ = duXdt/dy

⇒ dθ = duXdt/dy [as, dθ is very small]

⇒ dθ/dt = du/dy

That is the rate of deformation is equal to velocity gradient.

Hence, shear stress,

τ∝ dθ/dt ∝ du/dy ………(1)

Shear stress is proportional to the rate of deformation as well as velocity gradient.

From 1,

τ = μ du/dy ………(2) [μ= viscosity]

This is the mathematical explanation Of Newton’s law of viscosity.

**Classification of Fluid**

Depending on compressibility fluids are two types:

**1. Incomprehensible fluid:** Fluid those can not be compressed upon pressure, that is density remain constant. There is no such thing in reality. This term is applied where the change in density with pressure is so small to be negligible. This happens usually with the liquids.

**2. Compressible fluid:** Density changes here upon pressure. Usually, gages are terms as a compressible fluid.

Depending on Viscosity fluids can be divided into three types:

**Newtonian fluid: **Fluids which follow Newton’s law of viscosity that is viscosity which does not change with the rate of deformation or shear stress teems as a Newtonian fluid.

Eg: water, oil.

**Non-Newtonian fluid: **Fluid which doesn’t follow Newton’s law of viscosity that is viscosity changes with the rate of deformation or shear stress.

Eg: suspension, Ketchup.

**Ideal Fluid: **Fluid which has zero viscosity is termed as Ideal fluid.

Eg: No fluid is an ideal fluid.