## What is a fluid?

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

## What is applied fluid mechanics?

Applied fluid mechanics is a branch of science that covers principles and laws of fluid mechanics in both static and dynamic conditions. It also explains the various fluid applications over different systems like dams, canals, pipes, and many more.

### Laws governing fluid mechanics

Following are the laws governing fluid mechanics:

- Law of conservation of mass
- Law of conservation of energy
- Newton's second law of motion
- Principle of angular momentum
- Law of thermodynamics

### Need of fluid mechanics

Following are the needs of fluid mechanics:

- Study of weather forecasting.
- Design analysis of canals and dam system.
- Design analysis of turbo machines like fan, turbine, and others.
- Design analysis of piping and ducting systems.
- Design analysis of aerodynamic automobiles.

Fluid mechanics deals with the three aspects of the fluid namely, stationary or static fluid, kinematic fluid, and dynamic fluid.

### Static fluid mechanics

Fluid static is the branch of fluid mechanics in which stresses generated in a fluid system are determined at rest or in static conditions. The force exerted by the fluid on the system's surface with which it is in contact is called hydrostatic force.

The point of application of hydrostatic force on the surface is known as the center of pressure. The principle of hydrostatics is used to determine forces acting over the submerged objects.

### Fluid kinematics

Fluid kinematics is the branch of science that deals with the motion of fluids without referring to the forces causing its motion. Fluid kinematics describes the motion of fluid in a space-time relationship.

The two methods that describe the fluid motion are:

- Lagrangian method
- Eulerian method

#### Lagrangian method

In the Lagrangian method, any singular particle is selected whose motion is followed throughout the flow, and its various properties such as velocity, acceleration, and many more are described.

#### Eulerian method

In the Eulerian method, any point in the place occupied by the fluid is selected, and observations are done on their properties like density, velocity, pressure, and others.

#### Types of fluid flow

Following are the various types of fluid flow:

- Steady and unsteady flow
- Uniform and non-uniform flow
- One, two, and three-dimensional flow
- Rotational and irrotational flow
- Laminar and turbulent flow
- Compressible and incompressible flow

#### Types of flow pattern

Following are the various types of flow patterns:

- Streamlines and stream tubes
- Path lines
- Streak lines
- Time lines

### Fluid Dynamics

Fluid dynamics is the branch of fluid mechanics in which the study of fluid motion with the force-causing flow is done. Newton's second law of motion governs the dynamics of the fluid.

The various forces acting on the fluid mass is classified as:

- Body force
- Surface force
- Linear force

#### Body force

The body forces are proportional to the system's volume, so it is also called volume force. Weight, centrifugal force, and others are examples of body force.

#### Surface force

The surface forces are proportional to the surface area of the system. Pressure force, shear force, compressibility force, and others are examples of surface force.

#### Linear force

The linear force is proportional to the length of the system. Surface tension is an example of linear force.

## Important terms related to fluid mechanics

Following are the important terms related to fluid mechanics:

### Pressure

Pressure is the relation between the hydrostatic force and the system's area submerged in a fluid. The equation for the pressure is given as:

$\begin{array}{rcl}Pressure& =& \frac{Hydrostaticforce}{Surfacearea}\\ P& =& \frac{F}{A}\end{array}$

### Variation of pressure with depth

Fluid has a pressure that varies with depth. In static equilibrium, all the points have the same pressure at a particular depth. If it varies, the fluid would not be in equilibrium. The formula for the variation in pressure with depth is given as follows:

$P={P}_{0}+\rho gh$

The diagrammatical representation for variation of pressure with depth is shown as:

The pressure and pressure variation with depth is used to determine the pressure and force acting on the dams, canals, and many more. It also helps in the application of pipes and ducts used in dams to transfer water from one location to another.

### Pascal's law

Pascal's law states that a change in pressure at the surface in an incompressible fluid must be conveyed to every other point in the fluid in such a similar change. The equation for the change in pressure is given as:

$\u2206P=\rho g\left(\u2206h\right)$

The diagrammatical representation for Pascal's principle is shown below:

### Applications of Pascal's law

Following are the various applications of Pascal's law:

- The working principle of hydraulic lift, hydraulic jack, and hydraulic press is based on Pascal's law.
- Brakes used in automobiles.
- Also used in water towers, dams, and canals.

### Viscosity

Viscosity is described as an essential property of the fluid that provides resistance to fluid deformation by shear stress. Following are the various types of viscosity:

- Dynamic viscosity
- Kinematic viscosity

### Applications of viscosity

Following are the various practical applications of viscosity:

- Designing of the sewer or water line based on their viscosity and flow behavior.
- Drilling for oil and gas based on their viscosity.
- Maintain performance of machines like engine, brake, and others.

### Archimedes principle

The Archimedes principle says that a body is either partially or completely submerged in a fluid; a buoyant force from the fluid acts on the body.

The direction of the buoyant force is opposite to gravitational force and has a magnitude equal to the weight of the fluid displaced by the body.

The diagrammatical representation of Archimedes principle is shown below:

### Applications of Archimedes' principle:

Following are the various applications of Archimedes principle:

- Hydrometer used for density measurement works on this principle.
- Lactometers used for milk's purity are also based on the Archimedes principle.
- Designing of ships, boats, and submarines.

### Bernoulli's principle

Bernoulli's principle states that if the speed of a fluid element increases as the element travels along a smooth horizontal surface, the pressure of the fluid decreases linearly.

The diagrammatical representation of Bernoulli's principle is shown below:

Bernoulli's equation for the incompressible fluid flow is given as,

$\frac{{v}^{2}}{2}+gz+\frac{P}{\rho}=constant$

### Application of Bernoulli's principle:

Following are the various common practical devices that work on Bernoulli's principle:

- Pitot tube
- Pumps
- Turbine
- Carburetors
- Fluid Ejectors
- Stagnation tube
- Free jet
- Syringe

## Common Mistakes

Following are the common mistakes performed by students:

- Sometimes, students get confused between fluid kinematics and fluid dynamics.
- Sometimes, students forget the governing laws and the need of fluid mechanics.
- Sometimes, students get confused between the Lagrangian and Eulerian methods.
- Sometimes, students get confused that doctor's syringe is based on Archimedes' or Bernoulli's principle.

## Context and Application

The topic of applied fluid mechanics is significant in various courses and professional exams of undergraduate, graduate, postgraduate, doctorate levels. For example:

- Diploma in Mechanical Engineering
- Diploma in Civil Engineering
- Bachelor of Technology in Mechanical Engineering
- Bachelor of Technology in Civil engineering
- Bachelor of Technology in Chemical Engineering
- Master of Technology in Fluid Mechanics
- Doctor of Philosophy in Fluid Machines

## Related Concept

- Fluid Behavior
- Hydraulic machines
- Pneumatic machines
- Turbo machinery

## Practice Problems

**Q1.** Which of the following is not a type of fluid flow?

- Non-uniform
- Path line
- Turbulent
- Compressible

Correct option: **(b)**

**Q2.** _____is the branch of fluid mechanics in which the study of fluid motion with the force-causing flow is done.

- Fluid statics
- Fluid kinematics
- Fluid dynamics
- None of these

Correct option: **(c)**

**Q3**. A vessel of height h is filled with water and it is assumed that the pressure at the top surface of the water in a vessel is zero. What is the pressure at the bottom of the vessel? Take density of water is

$1000\mathrm{kg}/{\mathrm{m}}^{3}$

- 1000gh
- 100gh
- 10gh
- None of these

Correct option: **(a)**

**Q4**. Lactometer works on which principle?

- Bernoulli's principle
- Principle of angular momentum
- Archimedes principle
- Pascal's law

Correct option: **(c)**

**Q5**. Which of the following is correct Bernoulli's equation for the incompressible fluid flow?

- $\frac{{v}^{2}}{2}+g{z}^{2}+\frac{P}{\rho}=constant$
- $\frac{v}{2}+gz+\frac{P}{\rho}=constant$
- $\frac{v}{2}+2gz+\frac{P}{\rho}=constant$
- $\frac{{v}^{2}}{2}+gz+\frac{P}{\rho}=constant$

Correct option: **(d)**

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