# Fluid Mechanics

Fluid mechanics is the branch of science which deals with the behavior of fluids at rest and in motion. An understanding of behavior of fluids is important in process engineering for handling the problems on the flow of fluids through various process equipment's as well as to study other unit operations which include heat and mass transfer.

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Fluid mechanics is the branch of science which deals with the behavior of fluids at rest and in motion. An understanding of behavior of fluids is important in process engineering for handling the problems on the flow of fluids through various process equipments as well as to study other unit operations which include heat and mass transfer.

The weight age of this subject in GATE Chemical Engineering exam is about 7 to 9 marks. In this course, the areas of fluid mechanics which are important to unit operations are covered.

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Chapter 1

### Introduction & Fluid Properties

1.1 Introduction

1.1.1_States of Matter / Distinction between Solid & Fluid

1.1.2_Internal Forces

1.1.3_Concept of Continuum

1.2 FLUID PROPERTIES - I

1.2.1_Density at a point

1.2.2_Specific Weight & Specific Gravity

1.2.3_Bulk Modulus of Elasticity

1.2.4_Pressure

1.3 FLUID PROPERTIES - II

### 1.3.1_Absolute Viscosity & Kinematic Viscosity with their physical interpretation

1.4 FLUID PROPERTIES - III

1.4.1 to 1.4.6_Standard Problems

1.5 FLUID PROPERTIES - IV

1.5.1_Surface Tension

1.5.2_Phenomenon observed in nature due to surface tension

1.5.3_Standard Problems

1.6 GATE PROBLEMS

6 videos

1.1.1_States of Matter / Distinction between Solid & Fluid 1.1.2_Internal Forces 1.1.3_Concept of Continuum

1.2.1_Density at a point 1.2.2_Specific Weight & Specific Gravity 1.2.3_Bulk Modulus of Elasticity 1.2.4_Pressure

1.3.1_Absolute Viscosity & Kinematic Viscosity with their physical interpretation

1.5.1_Surface Tension 1.5.2_Phenomenon observed in nature due to Surface tension 1.5.3_Standard Problems

GATE Problems of Fluid Properties

Chapter 2

### Fluid Statics

2.1 FUNDAMENTAL EQUATION OF FLUID STATICS

2.1.1_Derivation of Fundamental Equation of Fluid Statics

2.1.2_Physics behind Fundamental Equation of Fluid Statics

2.1.3_Results from Fundamental Equation of Fluid Statics

2.2 PRESSURE & ITS MEASUREMENT

2.2.1_Scale of Pressure

2.2.2_Measurement of Atmospheric Pressure - Barometer

2.2.3_Measurement of System Pressure - Piezometer

2.2.4_U Tube Manometer - Positive Gauge Pressure

2.2.5_U Tube Manometer - Negative Gauge Pressure

2.3 SOME STANDARD PROBLEMS ON MANOMETERS

2.3.1_Multiple Fluid Manometers

2.3.2_Inverted Manometers

2.3.3_Inclined Manometers

2.3.4_ESE - 2008

2.3.5_Rotating Manometer

2.4 FORCES ON SUBMERGED BODIES - I

2.4.1_Forces on Plane Surfaces Immersed in Fluid at rest

2.4.2_Standard Problem

2.5 FORCES ON SUBMERGED BODIES - II

2.5.1_Forces on Curved Surfaces Immersed in Fluid at rest

2.5.2_Example Problem

2.5.3_Concept of Imaginary Surface

2.5.4 to 2.5.6_Standard Problems

2.6 BUOYANCY

2.6.1_Fundamentals of Buoyancy

2.6.2 to 2.6.8_Standard Problems

2.7 STABILITY OF UNCONSTRAINED BODIES IN FLUID

2.7.1_Introduction

2.7.2_Stability of Fully Submerged Bodies

2.7.3_Stability of Partially Submerged Bodies

2.7.4_Standard Problem

2.8 FLUID UNDER RIGID BODY MOTION / RELATIVE EQUILIBRIUM

2.8.1_An open tank containing a liquid that is subjected to a uniform acceleration in horizontal direction

2.8.2_Calculation of Maximum acceleration for no spill and calculation of spilled volume

2.8.3_Rotating open cylindrical tank

2.8.4_Calculation of maximum angular velocity for no spill and calculation of spilled volume

2.9 TO 2.13 GATE PROBLEMS

13 videos

2.1.1_Derivation of Fundamental Equation of Fluid Statics 2.1.2_Physics behind Fundamental Equation of Fluid Statics 2.1.3_Results from Fundamental Equation of Fluid Statics

2.2.1_Scale of Pressure 2.2.2_Measurement of Atmospheric Pressure - Barometer 2.2.3_Measurement of System Pressure - Piezometer 2.2.4_U Tube Manometer - Positive Gauge Pressure 2.2.5_U Tube Manometer - Negative Gauge Pressure

2.3.1_Multiple Fluid Manometers 2.3.2_Inverted Manometers 2.3.3_Inclined Manometers 2.3.4_ESE - 2008 Problem 2.3.5_Rotating Manometer

2.4.1_Forces on Plane Surfaces Immersed in Fluid at rest 2.4.2_Standard Problem

2.5.1_Forces on Curved Surfaces Immersed in Fluid at rest 2.5.2_Example Problem 2.5.3_Concept of Imaginary Surface 2.5.4 to 2.5.6_Standard Problems

2.6.1_Fundamentals of Buoyancy 2.6.2 to 2.6.8_Standard Problems

2.7.1_Introduction 2.7.2_Stability of Fully Submerged Bodies 2.7.3_Stability of Partially Submerged Bodies 2.7.4_Standard Problem

2.8.1_An open tank containing a liquid that is subjected to a uniform acceleration in horizontal direction 2.8.2_Calculation of Maximum acceleration for no spill and calculation of spilled volume 2.8.3_Rotating open cylindrical tank 2.8.4_Calculation of maximum angular velocity for no spill and calculation of spilled volume

Chapter 3

### Fluid Kinematics

3.1 FUNDAMENTALS

3.1.1_Understanding Kinematics

3.1.2_Description of Fluid Flow_Lagrangian & Eulerian Approach

3.1.3_Variation of Flow Parameters with space and time_Stead v/s Unsteady Flows and Uniform v/s Non-uniform Flows

3.1.4_Flow visualization_Concept of Streamlines, Pathlines and Streaklines

3.2 FLUID TRANSLATION, ROTATION AND DEFORMATION - I

3.2.1_Acceleration of Fluid Particle in a Velocity Field

3.2.2_Linear Deformation of Fluid Element

3.3 FLUID TRANSLATION, ROTATION AND DEFORMATION - II

3.3.1_Angular deformation and concept of angular velocity

3.3.2_Vorticity

3.3.3_Concept of Rotational and Irrotational Flows

3.4 STREAM FUNCTION AND VELOCITY POTENTIAL

3.4.1_Stream function and its physical interpretation

3.4.2_Velocity potential and its physical interpretation

3.4.3_Relationship between Stream function and Velocity potential

3.4.4_Conditions for Ir-rotational Flows

3.5 SOME STANDARD PROBLEMS ON FLUID KINEMATICS

3.5.1 to 3.5.4_Standard Problems

3.6 to 3.8 GATE PROBLEMS

8 videos

3.1.1_Understanding Kinematics 3.1.2_Description of fluid flow_Lagrangian and Eulearian Approach 3.1.3_Variation of flow parameters with space and time_Steady v/s Unsteady Flows and Uniform v/s Non-uniform Flows 3.1.4_Flow Visualization_Concept of Streamlines, Pathlines and Streaklines

3.2.1_Acceleration of Fluid Particle in a Velocity Field 3.2.2_Linear Deformation of Fluid Element

3.3.1_ Angular Deformation and Concept of Angular Velocity 3.3.2_Vorticity 3.3.3_Concept of Rotational and Ir-rotational Flows

3.4.1_Stream Function and Its Physical Interpretation 3.4.2_Velocity Potential and Its Physical Interpretation 3.4.3_Relationship between Stream Function and Velocity Potential 3.4.4_Conditions for Ir-rotational Flows

Chapter 4

### Integral form of Conservation Equations

4.1 FUNDAMENTALS OF REYNOLDS TRANSPORT THEOREM

4.1.1_Need for Reynolds Transport Theorem (RTT)

4.1.2_Intensive and Extensive Properties

4.1.3_Understanding discharge and mass flow rate

4.2 APPLICATION OF RTT TO CONSERVATION OF MASS

4.2.1_Integral form of Continuity Equation

4.3 APPLICATION OF RTT TO CONSERVATION OF LINEARE MOMENTUM OR MOMENTUM THEOREM

4.3.1_The principle of conservation of linear momentum applied to a control volume

4.4 APPLICATION OF RTT TO CONSERVATION OF ANGULAR MOMENTUM

4.4.1_The principle of conservation of angular momentum applied to a control volume

4.4.2_Standard Problem (Lawn Sprinkler)

4 videos

4.1.1_Need for Reynolds Transport Theorem 4.1.2_Intensive & Extensive Properties 4.1.3_Understanding Discharge and Mass Flow Rate

4.3.1_The principle of conservation of linear momentum applied to a control volume

4.4.1_The principle of conservation of angular momentum applied to a control volume 4.4.2_Standard Problem of Lawn Sprinkler

Chapter 5

### Dynamics of Inviscid Flows - Fundamentals & Applications

5.1 PHYSICS OF EULER'S EQUATION - I

5.1.1_Fundamental Equation of Motion for In-viscid Flow in Cartesian Coordinates

5.2 PHYSICS OF EULER'S EQUATION - II

5.2.1_Pressure Differential between two pointsin an Inviscid Flow Field

5.2.2_Derivation of Bernoulli's Equation and Its Assumption

5.2.3_Physics behind Bernoulli's Equation

5.3 APPLICATION OF BERNOULLI'S EQUATION - I

5.3.1_Hydraulic Siphon

5.3.2_Flow Measurement - Venturimeter

5.4 APPLICATION OF BERNOULLI'S EQUATION - II

5.4.1_Orifice meter

5.4.2_Concept of Static, Stagnation and Dynamic Pressure

5.4.3_Pitots tube

5.5 VORTEX FLOWS

5.6 GATE PROBLEMS - I

5.7 GATE PROBLEMS - II

5.8 GATE PROBLEMS - III

8 videos

5.1.1_Fundamental Equation of Motion for Inviscid Flow in Cartesian Coordinates

5.2.1_Pressure Differential between two points in an Inviscid Flow Field 5.2.2_Derivation of Bernoulli's Equation and Its Assumption 5.2.3_Physics behind Bernoulli's Equation

5.3.1_Hydraulic Siphon 5.3.2_Flow Measurement, Venturimeter

5.4.1_Orifice Meter 5.4.2_Concept of Static, Stagnation and Dynamic Pressure 5.4.3_Pitot Tube

Chapter 6

### Dynamics of Viscous Incompressible Flow

6.1 SOME EXACT SOLUTION OF NAVIER STOKES EQUATION - I

6.1.1_Introduction to Navier Stokes Equation

6.1.2_Plane Poiseullie flow

6.2 SOME EXACT SOLUTION OF NAVIER STOKES EQUATION - II

6.2.1_Couette Flow

6.3 SOME EXACT SOLUTION OF NAVIER STOKES EQUATION - III

6.3.1_Hagen Poiseullie Flow

6.4 VISCOUS FLOW THROUGH PIPES

6.4.1_Minor Losses

6.4.2_Losses due to sudden expansion

6.4.3_Exit Loss

6.4.4_Losses due to sudden contraction

6.4.5_Entry Loss

6.4.6_Losses in pipe bends

6.4.7_Flow through branched pipes

﻿6.5 GATE PROBLEMS

5 videos

6.1.1_Introduction to Navier Stokes Equation 6.1.2_Plane Poiseullie Flow or fully developed flow between two parallel plates

6.4.1_Minor loses 6.4.2_Losses due to sudden contraction 6.4.3_Exit Loss 6.4.4_Losses due to sudden contraction 6.4.5_Entry loss 6.4.6_Losses in pipe bends 6.4.7_Flow through branched pipes

Chapter 7

### Boundary Layer Theory

7.1 BOUNDARY LAYER THEORY - I

7.1.1_Introductory Concepts

7.1.2_Boundary Layer Equations

7.1.3_Blausius Exact Solutions

7.2 BOUNDARY LAYER THEORY - II

7.2.1_Displacement Thickness

7.2.2_Momentum Thickness

7.2.3_Von Karman Momentum Integral Equation

7.2.4_Derivation of profile based results

7.2.5_Overall drag coefficient

7.3 BOUNDARY LAYER THEORY - III

7.3.1_Boundary Layer Theory for Turbulent Flows

7.3.2_Results - Summary

7.3.3_Standard Problems

7.3.4_Boundary Layer Separation

7.3.5_Forces on body immersed in fluid under motion

7.3.6_Cricket ball dynamics

7.4 GATE PROBLEMS OF BOUNDARY LAYER THEORY

4 videos

7.1.1_Introductory concepts 7.1.2_Boundary layer equations 7.1.3_Blausius Exact Solutions

7.2.1_Displacement Thickness 7.2.2_Momentum Thickness 7.2.3_Von Karman momentum integral equation 7.2.4_Derivation of profile based results 7.2.5_Overall Drag Coefficient

7.3.1_Boundary layer theory for turbulent flows 7.3.2_Results-Summary 7.3.3_Standard Problems 7.3.4_Boundary layer separation 7.3.5_Forces on body immersed in fluid under motion 7.3.6_Cricket Ball Dynamics

Chapter 8

### Principle of Similarity and Dimensional Analysis

8.1 DIMENSIONAL ANALYSIS & PRINCIPLE OF SIMILARITIES - I

8.1.1_Dimension Analysis-Importance of dimension analysis

8.1.2_Buckingham π theorem

8.1.3_Interpretation of results

8.2 PRINCIPLE OF SIMILARITIES

8.2.1_Principle of similarities: Concept and size of similarities

8.2.2_Different forces acting on fluid

8.2.3_Dimensionless Numbers

8.2.4_Applications in different cases

8.2.5_Standard problem

2 videos

8.1.1_Dimension Analysis-Importance of dimension analysis 8.1.2_Buckingham π theorem 8.1.3_Interpretation of results

Chapter 9

### Turbulent Flow

9.1_Introduction

9.2_Reynold's Experiment

9.3_Physics of Reynold's number

9.4_Statistical Description of turbulent flows

### Full video will be available from : 31st May 2019

1 videos

9.1_Introduction 9.2_Reynold's Experiment 9.3_Physics of Reynold's number 9.4_Statistical Description of turbulent flows

Chapter 10

### Fluid Machines

10.1 FLUID MACHINES - I

10.1.1_Reynolds Transport Theorem Applied to Law of Conservation of Angular Momentum

10.1.2_Lawn Sprinkler

10.1.3_Introduction and Classification of Fluid Machines

10.1.4_Different Components of Velocity

10.2 FLUID MACHINES - II

10.2.1_Fundamental Equation of Energy Transfer in Rotodynamic Machines

10.2.2_Velocity Diagrams

10.2.3_Different Components of Energy Transfer

10.2.4_Physical Interpretation of Different Components of Energy Transfer

10.2.5_Degree of Reaction

10.3 FLUID MACHINES - III

10.3.1_Impulse hydraulic turbine: The Pelton Wheel/Pelton Turbine

10.3.2_Analysis of Pelton Bucket

Standard Problems

10.4 FLUID MACHINES - IV

10.4.1_Reaction Hydraulic Turbine: Francis Turbine

10.4.2_Analysis of Francis Runner

10.4.3_Standard Problem on Francis Turbine

10.4.4_Reaction hydraulic turbine: Kaplan turbine

10.4.5_Standard Problem on Kaplan Turbine

10.5 FLUID MACHINES - V

10.5.1_Laws of similarities

10.5.2_Concept of specific speed

10.5.3_Comparison of turbines

10.6 FLUID MACHINES - VI

10.6.1_Centrifugal Pump - Introduction

10.6.2_Velocity Diagram for Centrifugal Pump Impeller

10.6.3_General Pumping System

10.6.4_Thomas Cavitation Parameter

10.6.5_Manometric Efficiency

10.7 GATE PROBLEMS

7 videos

10.1.1_Reynolds Transport Theorem Applied to Law of Conservation of Angular Momentum 10.1.2_Lawn Sprinkler 10.1.3_Introduction and Classification of Fluid Machines 10.1.4_Different Components of Velocity

10.2.1_Fundamental Equation of Energy Transfer in Rotodynamic Machines 10.2.2_Velocity Diagrams 10.2.3_Different Components of Energy Transfer 10.2.4_Physical Interpretation of Different Components of Energy Transfer 10.2.5_Degree of Reaction

10.3.1_Impulse hydraulic turbine: The Pelton Wheel/Pelton Turbine 10.3.2_Analysis of Pelton Bucket Standard Problems

10.4.1_Reaction Hydraulic Turbine: Francis Turbine 10.4.2_Analysis of Francis Runner 10.4.3_Standard Problem on Francis Turbine 10.4.4_Reaction hydraulic turbine: Kaplan turbine 10.4.5_Standard Problem on Kaplan Turbine

10.5.1_Laws of similarities 10.5.2_Concept of specific speed 10.5.3_Comparison of turbines

10.6.1_Centrifugal Pump - Introduction 10.6.2_Velocity Diagram for Centrifugal Pump Impeller 10.6.3_General Pumping System 10.6.4_Thomas Cavitation Parameter 10.6.5_Manometric Efficiency

Chapter 11

### Flow past immersed bodies

Flow past immersed bodies

Chapter 12

Fluidization

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