## What is meant by fluid?

In general terms, anything that flows can be termed as a fluid. In other words, a fluid is any substance that cannot resist shear forces and deforms continuously under the application of external shear forces. Fluid materials differ completely from solid materials such as metals and alloys. For instance, if we consider two infinitesimally small cross-sectional areas of fluid materials and solid materials, and apply shear forces to these elements, both the elements will undergo deformation. Upon releasing the shear force, the element of the solid materials will regain its original orientation, but the element of the fluid materials will keep on deforming continuously under the action of the shear force.

A fluid material has two distinct properties:

- A fluid material has no particular geometric contour, it achieves the geometric shape of the container in which it is stored.
- The critical magnitude of shear force to cause deformation is very low. A small value of shear force is enough to initiate flow in fluid materials.

Fluid materials have no rigidity and they follow the continuum hypothesis. According to the continuum, the molecules of fluid materials are distributed evenly throughout the fluid domain without any voids. Hence, it allows during analysis to assume the fluid material to behave as continuous mass with evenly distributed molecules.

## Fluid kinematics and dynamics

Fluid kinematics is the study of fluids in motion. The forces that govern the motion are not taken into consideration. In this area, the geometry of the fluid particles associated with the fluid materials is considered. All the concepts of kinematics such as velocity, acceleration, and displacement, used in the analysis for solid bodies, are applied to the individual fluid particles or a combination of fluid particles of fluid materials for analysis.

Fluid dynamics is relatively concerned with the motion of the fluid while considering the effect of the forces on the bodies. A body moving inside a two-dimensional fluid flow field will experience two types of forces; namely, drag force and lift force. The drag force tends to retard the motion of the body, while the lift force provides an upward thrust to the body that makes the body experience lift.

## Fluid properties

There are some distinct properties that separate the fluid materials from the rest of the materials, some of the important fluids. They are outlined below:

**Density**: At the standard temperature and pressure (STP), density is the ratio between the mass of the fluid and its associated volume. Mathematically, $\rho =\frac{m}{v}$, where, $\rho $ denotes the density of the fluid, $m$ is the mass of the fluid, and $v$ is the volume of the fluid. The SI unit of density is $\frac{Kg}{{m}^{3}}$.**Viscosity**: Fluid flows in layers. Viscosity is the property of a fluid that resists the motion of one layer by another. The phenomenon of cohesion is due to the property of the viscosity of the fluid. The velocity variation of a viscous fluid is linear with the surface of contact of the medium where the fluid is flowing.-
**Specific volume**: The ratio of the volume of the fluid to the mass of the fluid gives the specific volume of the fluid material. Mathematically, $\vartheta =\frac{v}{m}$, where $v$ is the volume of the fluid, $m$ is the mass of the fluid, and $\vartheta $ signifies the specific volume of the fluid. The SI unit of specific volume is $\frac{{m}^{3}}{Kg}$.

## Newtonian and Non-Newtonian fluids

Newtonian fluids are those fluids that obey Newton's law of viscosity.

According to Newton's law of viscosity, the shear stress associated with a fluid element is proportional to the rate of shear strain. Mathematically,

$\tau \alpha \frac{dv}{dy}$. Here, the differential $\frac{dv}{dy}$, is known as the velocity gradient, or preferably the rate of shear strain.

Removing the proportionality sign; we get,

$\tau =\mu \frac{dv}{dy}$,

where $\mu $ is the coefficient of viscosity.

Non-Newtonian fluids, on the other hand, do not obey Newton's law of viscosity, they instead obey the power law, which is given by,

$\tau =A{\left(\frac{dv}{dy}\right)}^{n}+B$,

here, $A$ and $B$ are constants. $n$ is referred to as the power index.

Depending on the values of $A,B$, and $n$ different properties of fluids can be obtained.

## Fluid flow analysis

Fluids flow past objects and induce forces on them and change the inertia of the body. Also different parameters of the objects are influenced. Fluid mechanics provides numerous relations and principles that help in fluid-related problems. Relatively easy problems can be calculated with human efforts. However, when the problems shift toward complexity, human intervention becomes challenging and time-consuming. To ease such operations, applications of computers play a major role. The computers use fluid flow software to predict the fluid flow behavior and estimate unknown parameters. Such software is known as computational fluid dynamics (CFD) software. This software integrates the algorithms of the finite element method and provides a numerical solution to the given problem. The software aids in simulation and predicts the fluid flow and its associated changes in governing parameters. Simulation helps to determine the flaws in the design, and aids in diagnosis.

## Context and Applications

The topic is primarily taught in the third-year undergraduate courses of engineering and applied sciences. The topic is well found in subjects of fluid mechanics, fluid kinematics, and fluid dynamics. The subject is common for both mechanical engineering and civil engineering graduates.

- Bachelors of Technology in Mechanical Engineering
- Bachelors of Technology in Civil Engineering
- Masters of Technology in Civil Engineering
- Masters of Technology in Mechanical Engineering

## Practice Problems

1. Which of the following fundamental forces is encountered by a body under fluid flow?

- Drag force
- Shear force
- Axial force
- None of these

Correct option- a

Explanation: When a fluid flows past a solid body in a two-dimensional flow field, drag force and lift force are the two primary forces experienced by the body. The nature of the drag force is to retard the body's motion, while the lift force tends to lift the body against the gravitational force.

2. Which of the following force, a fluid element cannot resist?

- Lift force
- Drag force
- Shear force
- None of these

Correct option- c

Explanation: A fluid element cannot resist external shear forces and deforms continuously under the action of the shear forces. A fluid element unlike a solid element which provides resistance to deformations by inducing internal stresses, a fluid element cannot provide any resistance by inducing internal stresses, hence it keeps on flowing continuously till the external force is removed.

3. Which of the following is true for non-Newtonian fluids?

- Obeys Newton's law of viscosity
- Do not obey Newton's law of viscosity
- Obeys the power law
- Both b and c

Correct option- d

Explanation: Non-Newtonian fluids are those fluids that do not follow Newton's law of viscosity but obey the power law. For these fluids, the shear stress is not proportional to the rate of shear strain. The behavior of these fluids can be linear, parabolic, or cubic depending upon the magnitude of the power index.

4. Which of the following is the unit of density?

- $\frac{\mathrm{Kg}}{{m}^{3}}$
- $\frac{\mathrm{Kg}}{m}$
- $\frac{{m}^{3}}{\mathrm{kg}}$
- None of these

Correct option- a

Explanation: Density is the ratio between the mass and the volume of a fluid. The SI unit of density is given by $\frac{Kg}{{m}^{3}}$.

5. Which of the following is the unit of specific volume?

- $\frac{{m}^{2}}{\mathrm{Kg}}$
- $\frac{{m}^{3}}{\mathrm{Kg}}$
- $\frac{m}{\mathrm{Kg}}$
- $\frac{\mathrm{Kg}}{{m}^{3}}$

Correct option- b

Explanation: Specific volume is the ratio between the density of the substance and the density of the test fluid (water). Where, the density of the test fluid, i.e., water is generally considered to be 1000 $\frac{Kg}{{m}^{3}}$. The SI unit of specific volume is $\frac{{m}^{3}}{\mathrm{Kg}}$

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