# Fluid Flow

## What is Fluid Flow?

Fluid Flow is a part of fluid mechanics and deals with fluid dynamics. It involves the motion of a fluid subjected to unbalanced forces. This motion continues as long as unbalanced forces are applied.

For example, if you are pouring water from a mug, the velocity of water is very high over the lip, moderately high approaching the lip, and very low at the bottom of the mug. The unbalanced force is gravity, and the flow continues as long as the water is available and the mug is tilted.

## Types of Fluids

### Ideal fluid

A fluid is said to be ideal when it cannot be compressed and the viscosity doesn’t fall in the category of an ideal fluid. It is an imaginary fluid which doesn’t exist in reality.

### Real fluid

All the fluids are real as all the fluid possess viscosity.

### Newtonian fluid

When the fluid obeys Newton’s law of viscosity, it is known as a Newtonian fluid.

### Non-Newtonian fluid

When the fluid doesn’t obey Newton’s law of viscosity, it is known as Non-Newtonian fluid.

### Ideal plastic fluid

When the shear stress is proportional to the velocity gradient and shear stress is more than the yield value, it is known as ideal plastic fluid.

### Incompressible fluid

When the density of the fluid doesn’t change with the application of external force, it is known as an incompressible fluid.

### Compressible fluid

When the density of the fluid changes with the application of external force, it is known as compressible fluid.

The table below represents the density and viscosity of different types of fluids

 Types of fluid Density Viscosity Ideal fluid Constant Zero Real fluid Variable Non-zero Newtonian fluid Constant/ Variable $T=u(\frac{\mathrm{d} u}{\mathrm{d} y})$ Non-Newtonian fluid Constant/ Variable $T\neq u(\frac{\mathrm{d} u}{\mathrm{d} y})$ Incompressible fluid Constant Non-zero/ zero Compressible fluid Variable Non-zero/ zero

## Classification of flows on the basis of Mach number

• Incompressible flow has M<0.3.
• Compressible subsonic flow has M between 0.3 to 1.

The different types of fluid flow are represented in the graph below:

## Types of Fluid Flow

Fluid flow has all kinds of aspects — steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational, to name a few. Some of these characteristics reflect the properties of the liquid itself, and others focus on how the fluid is moving.

Fluid flow can be steady or unsteady, depending on the fluid’s velocity:

• Steady: In steady fluid flow, the velocity of the fluid is constant at any point.
• Unsteady: When the flow is unsteady, the fluid’s velocity can differ between any two points.

### Viscous or Non-viscous Flow

Liquid flow can be viscous or non-viscous.

Viscosity is a measure of the thickness of a fluid, and very gloppy fluids such as motor oil or shampoo are called viscous fluids.

## Fluid Flow Equation

Mass flow rate is the rate of movement of a massive fluid through a unit area. In simple words it is the movement of mass per unit time. The formula for mass flow rate is given as follows:

$Mass\;flow\;rate = \rho \: A\; V$

From the equation, we can see that mass flow rate depends on the density, velocity and the area of cross-section of the fluid.

### Solved Example

A fluid moves through a tube of 15 m/s, the tube has a transverse area of 0.4 m2. If the density of the fluid is ρ = 1.5 grams/m3, what is the amount of mass flowing through the tube?
To calculate the total mass of fluid flowing through the tube, we use

$Mass\,flow\,rate = \rho \, A\, V$

Substituting the values in the above equation, we get

$Mass\,flow\,rate = 1.5 × 15 × 0.4 = 9\,g/s$

### Fluid Flow Through a Pipe

The general capacity of the pipes varies on its size. The table given below shows the capacity of the flow of fluid based on its size.

 Pipe size (in inch) Maximum Flow (in gal/min) Velocity (in ft/s) Head Loss in (ft / 100 ft) 2 45 4.3 3.9 2.5 75 5.0 4.1 3 130 5.6 3.9 4 260 6.6 4.0 6 800 8.9 4.0 8 1600 10.3 3.8 10 3000 12.2 4.0 12 4700 13.4 4.0 14 6000 14.2 4.0 16 8000 14.5 3.5 18 10000 14.3 3.0 20 12000 13.8 2.4 24 18000 14.4 2.1