Fluid Mechanics 2021 Written by; Dasima Shahinan Zenty Razilanaty Jane Daniela
Authors DASIMA SHAHINAN ZENTY RAZILANATY JANE DANIELA POLITEKNIK KUCHING SARAWAK MINISTRY OF HIGHER EDUCATION KM22, JALAN MATANG, 93050 KUCHING, SARAWAK. Phone No. : (082) 845596/7/8 Fax No. : (082) 845023 E-mail : [email protected] Website : http://www.poliku.edu.my/ Copyright © 2021 Politeknik Kuching Sarawak e ISBN 978-967-2953-43-2 All rights reserved. No parts of this publication may be copied, stored in form or by any means, electronic, mechanical, photocopying and recording or otherwise or by any means for reproduced without the prior permission of Politeknik Kuching Sarawak. National Library of Malaysia Cataloguing-in-Publication Data Dasima Shahinan FLUID MECHANICS / DASIMA SHAHINAN, ZENTY RAZILANATY, JANE DANIELA. Mode of access: Internet eISBN 978-967-2953-43-2 1. Fluid mechanics. 2. Government publications--Malaysia. 3. Electronic books. BI. Title. 620.106 Published by: Politeknik Kuching Sarawak Ministry Of Higher Education
PREFACE 2
ABSTRACT Fluid Mechanics is one of the core disciplinary courses that must be taken by students studying mechanical engineering at the Malaysian polytechnic. This e-book is developed specifically for Malaysian Polytechnic students from Mechanical Engineering Department. Starting December 2014, the Department of Malaysian Polytechnic Education (Jabatan Pengajian Politeknik) has revised the syllabus for the Fluid Mechanics course which will be taught in semester two for a mechanical engineering student. The current code for the course is DJJ20073 which carry 3 credits for the whole semester. This e-book provides the fundamentals of fluid mechanics principles related to fluid properties and behaviour in static and dynamic situations. It also exposes the simple application in fluid mechanics. The objective of this e-book is to allow the student to read and study the note from their mobile phone. The application can be accessed easily from anywhere without any hassle from the printed notes. In addition, the application will motivate and attract students to be interested in studying this course. Keywords: fluid mechanics, physical properties, fluid, static, dynamic
C O N T E N T S Abstract Page 3 Chapter 1 •Introduction of Fluid Page 5 - 19 Chapter 2 •Physical Properties of Fluid Page 20 - 25 Chapter 3 •Fluid Statics Page 27 - 54 Chapter 4 •Fluid Dynamics Page 56 - 90 Chapter 5 •Energy Loss in Pipelines Page 92 - 102
CHAPTER ONE Introduction of Fluid Objectives: At the end of this chapter student will able to: 1. Explain fluid characteristics 2. Explain types of pressure 3. Explain the pressure in fluid 5
FLUID MECHANICS APPLICATION Oceanography Metrology Aeronautic Bio medic Turbulence 6
FLUID MECHANICS APPLICATION Water supply Acoustic 7
INTRODUCTION What is fluid mechanics? ❑ I t i s a b r a n c h o f a p p l i e d m e c h a n i c s c o n c e r n e d w i t h t h e s t a t i c s a n d d y n a m i c s o f f l u i d s . ❑ The analysis of the behavior of fluids is based on fundamental laws of mechanics which relate continuity of mass and energy with force and momentum also solid mechanics properties 8
INTRODUCTION What is fluid ? ❖ A substance which deforms continuously under the action of shearing forces, however small they may be ❖Liquid and gas are both fluids – lack of ability to resist deformation – flows under the action of the force ❖Its shape will change continuously as long as force is applied ❖If a fluid is at rest there are no shearing forces acting ❖All forces must be perpendicular to the planes which they acting 9
INTRODUCTION Shearing force, F, acting on a fluid element Characteristic of fluid ❑ Fluids can be defined as substances that have zero shear modulus or in simpler terms a fluid is a substance which cannot resist any shear force applied to it. ❑ not resisting deformation, or resisting it only lightly (viscosity) ❑ the ability to flow (also described as the ability to take on the shape of the container). 10
INTRODUCTION Liquid vs. Gas ➢ Although liquids and gasses behave in much the same way and share many similar characteristics, they also possess distinct characteristics of their own. ➢ Specifically a liquid is difficult to compress and often regarded as being incompressible. ➢ A gas is easily to compress and usually treated as such - it changes volume with pressure. ➢ A given mass of liquid occupies a given volume and will occupy the container it is in and form a free surface (if the container is of a larger volume). ➢ A gas has no fixed volume, it changes volume to expand to fill the containing vessel. It will completely fill the vessel so no free surface is formed 11
TYPES OF PRESSURE Definition pressure Atmospheric The pressure due to atmosphere a the surface of the earth depends upon the head of the air above the surface Gauge The pressure that measured with the help of pressure measuring instrument, in which the atmospheric pressure is taken as datum Absolute The pressure that is equals to the sum of the atmospheric and gauge pressure Vacuum In a perfect vacuum which is a completely empty space, the pressure is zero 12
FIND THE ANSWER & DISCUSS 13
INTRODUCTION The topic to explore will be pressure and depth. If a fluid is within a container then the depth of an object placed in that fluid can be measured. The deeper the object is placed in the fluid, the more pressure it experiences. This is because of the weight of the fluid above it. The more dense the fluid above it, the more pressure is exerted on the object that is submerged, due to the weight of the fluid. 14
PRESSURE & DEPTH The formula that gives the pressure, p on an object submerged in a fluid is: Where, p gh • (rho) is the density of the fluid, • g is the acceleration of gravity • h is the height of the fluid above the object Ptotal = Patmosphere + Pfluid Ptotal = Patmosphere + ( ρgh ) 15
water PRESSURE & DEPTH The weight of liquid contained in the cylinder is ωhA where ; p hA A h = Specific weight of the liquid ( where is = 1000 kg/m3 x 9.81 m/s 2) h = Height of liquid in the cylinder A = Area of the cylinder base The pressure, at the bottom of the cylinder, will be due to the weight of the liquid contained in the cylinder. Let this pressure be p. Then, which can also be shown as , p gh 16
PRESSURE & DEPTH This equation shows that the intensity of pressure at any point, in a liquid, is proportional to its depth as measured from the surface (as is constant for the given liquid). It is thus obvious, that the pressure can be expressed in either one of the following two ways : a) As force per unit area ( N/m2) b) As height of equivalent liquid column p gh 17
EXAMPLE 1: A diver is working at a depth of 20 m below the surface of the sea. How much greater is the pressure intensity at this depth than at the surface? Take into consideration specific weight of water is 10000 N/m3 . 18
EXAMPLE 2: Find the height of a water column which is equivalent to the pressure of 2 N/m2 . ( Take into consideration specific weight of water, water = 1000 kg/m2 x 9.81 m/s 2 ) 19
T H E E N D O F C H A P T E R O N E
CHAPTER TWO Physical Properties of Fluid Objectives: At the end of this chapter student will able to: 1. Apply physical properties of fluid 21
The important properties that you must know PHYSICAL PROPERTIES OF FLUID The study of properties of fluids is basic for the understanding of flow or static condition of fluids. 1 2 3 4 5 6 Mass density, ρ is defined as the mass per unit volume. ( SI units, kg/m3 ) Specific gravity or relative density, s is the ratio of the weight of the substance to the weight of an equal volume of water at 4 ºC. Specific weight, is defined as the weight per unit volume. ( SI units, N/m3 ) Specific volume, v is defined as the reciprocal of mass density. It is used to mean volume per unit mass. (SI units, m3 /kg ). Compressibility define as change in volume due to change in pressure. Viscosity -A fluid at rest cannot resist shearing forces but once it is in motion, shearing forces are set up between layers of fluid moving at different velocities. The viscosity of the fluid determines the ability of the fluid in resisting these shearing stresses. 22 22
FORMULA mass,m volume,V weight,W volume,V Mass Density Specific gravity / Relative density Specific weight Specific volume s substance water volume,V mass,m 23
EXAMPLE What is the mass density, ρ of fluid (in kg/m3) if mass is 450 g and the volume is 9 cm3 What is the specific weight, kN/m3) if the weight of fluid is the volume is 500 cm2 . of fluid (in 10N and What is the specific gravity of fluid in Example above What is the specific volume, v of fluid in Example 1. 24
TUTORIAL Discuss in class Given specific weight of fluid is 6.54 kN/m3 and its mass is 8.3 kg, calculate the following: – volume of fluid – specific volume of fluid – density of fluid Given oil specific gravity is 0.89, find : – density of oil – specific weight of oil – specific volume of oil 25
T H E E N D O F C H A P T E R T W O
CHAPTER THREE Fluid Statics Objectives: At the end of this chapter student will able to: 1. Apply the concept of Pascal’s Law into the hydraulic jack 2. Apply concept of piezometer, barometer and manometer 3. Explain the concept of a bourdon gauge 4. Apply the concept of buoyancy 27
INTRODUCTION A fluid is a substance that flows easily. Gases and liquids are fluids, although sometimes the dividing line between liquids and solids is not always clear. Because of their ability to flow, fluids can exert buoyant forces, multiply forces in a hydraulic systems, allow aircraft to fly and ships to float. 28
PASCAL LAW Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container. 29
PASCAL LAW Pressure at any point is the same in all directions. This is known as Pascal Law and applies to fluids at rest 30
HYDRAULIC JACK Hydraulic system Hydraulic system uses an incompressible fluid, such as oil or water, to transmit forces from one location to another within the fluid. Most aircraft use hydraulics in the braking systems and landing gear. Pneumatic systems use compressible fluid, such as air, in their operation. Some aircraft utilize pneumatic systems for their brakes, landing gear and movement of flaps. 31
HYDRAULIC JACK A principle of Hydraulic Jack ❑ Hydraulic jack is used to lift a heavy load with the help of a light force. ❑ A force F is applied to the small cylinder and forces oil/water out into large cylinder, thus the piston raise the load W. ❑ The force acting on area, A1, produced pressure P1 which transmitted equally in all direction through the liquid. ❑ If the two pistons are at the same level, the pressure, P2 acting on the large piston must equal P1. 32
EXAMPLE 1: A force, P of 500 N is applied to the smaller cylinder of a hydraulic jack. The area, a of a small piston is 20 cm2 while the area, A of a larger piston is 200 cm2 . What mass can be lifted on the larger piston? Solution: (Try first and discuss your answer in class) 33
TUTORIAL A force, P of 650 N is applied to the smaller cylinder of an hydraulic jack. The area, a of a small piston is 15 cm2 and the area A of a larger piston is 150 cm2 . What load, W can be lifted on the larger piston if : (a) the pistons are at the same level ? (b) the large piston is 0.65 m below the smaller piston ? (c) the small piston is 0.40 m below the larger piston ? Consider the mass density ρ of the liquid in the jack is 10 3 kg/m3 34
BUOYANCY Principle of Archimedes Upthrust on body = weight of fluid displaced by the body Archimedes Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object. 35
BUOYANCY The upthrust will act through the centre of gravity of the displaced fluid, which is called the centre of buoyancy. The positions of G1 and G2 are not necessarily on the same vertical line, and the centre of buoyancy of the whole body is, therefore, not bound to pass through the centroid of the whole body. 36
EXAMPLE 1: A rectangular pontoon has a width B of 6 m, a length l of 12 m, and a draught D of 1.5 m in fresh water (density 1000 kg/m3). Calculate : a) the weight of the pontoon b)its draught in sea water (density 1025 kg/m3) c) the load (in kiloNewtons) that can be supported by the pontoon in fresh water if the maximum draught permissible is 2 m. * Discuss your solution in the class 37
PRESSURE MEASUREMENT Barometer Bourdon Gauge Piezometer Manometer 38
PRESSURE MEASUREMENT 1. Piezometer A Piezometer is used for measuring pressure inside a vessel or pipe in which liquid is there. A tube may be attached to the walls of the container (or pipe) in which the liquid resides so that liquid can rise in the tube. By determining the height to which liquid rises and using the relation p1 = ρgh, gauge pressure of the liquid can be determined. It is important that the opening of the device is to be tangential to any fluid motion, otherwise an erroneous reading will result. 39
PRESSURE MEASUREMENT 2. Barometer A Barometer is a device used for measuring atmospheric pressure. A simple Barometer consists of a tube of more than 30 inch (760 mm) long inserted into an open container of mercury with a closed and evacuated end at the top and open tube end at the bottom and with mercury extending from the container up into the tube. Strictly, the space above the liquid cannot be a true vacuum. It contains mercury vapour at its saturated vapour pressure, but this is extremely small at room temperatures (e.g. 0.173 Pa at 20 oC). The atmospheric pressure is calculated from the relation patm = ρgh where ρ is the density of fluid in the barometer. There are two types of Barometer; Mercury Barometer and Aneroid Barometer. 40
PRESSURE MEASUREMENT 2. Barometer Example: What is the atmospheric pressure in N/m2 if the level of mercury in a Barometer tube is 760 mm above the level of the mercury in the reservoir? Given the specific gravity of mercury is 13.6 and specific weight of water is * Discuss your solution in the class 41
PRESSURE MEASUREMENT 3. Bourdon Gauge The mechanism: • The pressure sensing element is a tube of oval cross-section bent to a circular shape. • One end of the tube is fixed to the gauge case and is connected to the fluid whose pressure is to be measured. • The other end is closed and is free to move as it is connected via mechanical linkage and gear sector to a pointer. • As measured fluid pressure increases above the surroundings, the tube cross-section tends to become circular and causes the tube to deflect at the second end. • This motion is transmitted via linkage to the pointer, which would directly indicate on the calibrated scale or dial on the gauge pressure. 42
PRESSURE MEASUREMENT 4. Manometer Simple U tube Differential U tube Inverted U tube 43
PRESSURE MEASUREMENT 4.1 Manometer – Simple U tube 44
PRESSURE MEASUREMENT 4.1 Manometer – Simple U tube 45
PRESSURE MEASUREMENT 4.1 Manometer – Simple U tube 46
PRESSURE MEASUREMENT 4.1 Manometer – Simple U tube Example 1: A U-tube manometer similar to that shown in Figure 3.6 is used to measure the gauge pressure of water (mass density ρ = 1000 kg /m3). If the density of mercury is 13.6 × 10 3 kg /m3 , what will be the gauge pressure at A if h1 = 0.45 m and D is 0.7 m above BC. 47
PRESURE MEASUREMENT 4.1 Manometer – Simple U tube Example 2: A U-tube manometer similar to that shown in below is used to measure the gauge pressure of a fluid P of density ρ = 1000 kg/m3 . If the density of the liquid Q is 13.6 × 10 3 kg/m3 , what will be the gauge pressure at A if h1 = 0.15 m and h2 = 0.25 m above BC. Take into consideration patm = 101.3 kN/m2 . 48
PRESURE MEASUREMENT 4.2 Manometer – Differential U tube Pressure at C = Pressure at D 49