# Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Size: px
Start display at page:

Download "Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur"

Transcription

1 Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 07 Analysis of Force on the Bucket of Pelton Wheel and Power Generation Good afternoon, I welcome you to this session, where we will discuss today the analysis of force on the bucket of pelton wheel and the power generation. So, let us make a recapitulation of this pelton wheel, the first part of the pelton wheel, which we discussed in the last class. (Refer Slide Time: 00:38) That pelton wheel is an impulse hydraulic turbine, where a number of spoon shaped buckets are mounted on a wheel of disks, which rotates. The rotating shaft is mounted on the center of the disk, and a number of fixed nozzles, which converts the pressure of the liquid that is entrance to a high velocity jet. Directs the jet at the center of the bucket tangentially thism we recognized last time how that if we see this sectional plan wheel the spoon shape bucket is like this. There are here two halves two symmetric halves and the jet strikes the bucket tangentially that means, that direction of the incoming jet velocity is at tangent is in the direction of the tangent to a circle drawn through the centers of this bucket. This circle is known as the pitch circle.

2 And the water jet glides along the blade flows along the blade or bucket and then comes out. We also recognized that these fluid should come relative to the bucket in a direction exactly opposite to the incoming velocity to have a maximum change in the momentum by the fluid, so that a maximum force can be exerted on the bucket. But it is not done in practice, in practice a deflection of theta is equal to one sixty five degree; that means, the direction of the relative velocity of the jet with respect to the bucket is made. This is because that the fluid, otherwise will strike the back of the wing following the one. Now the vane is also moving with a velocity u. So, we also discussed that number of buckets are usually more than fifteen and number of fixed nozzles which are the stators at the fixed part of the machines varies from two to six. We have also recognized that there is a splitter read which divides the water into equal parts to this two halves of the bucket or vane or blade whatever you may say. Now we come to the force analysis, now for force analysis what we have to do, we have to make the velocity triangle; we will have to draw the velocity triangle diagram at the inlet and outlet. Let us do that now. (Refer Slide Time: 03:16) Now, let us draw the vane again in this fashion, this is the vane. Now this is the inlet velocity v 1, now this is the look here, this is the velocity u with, which it is moving. Now at the inlet here incoming water velocity and the bucket velocity is in the same line they are collinear. So, therefore, the inlet velocity diagram is like that if this is the v 1; that means, if this is v 1 - the inlet velocity of water. Let u is represented by this, this is u

3 same direction, all are in the same direction. So, therefore, this will be the relative velocity at the inlet of the flow. So, therefore, the velocity triangle or the vector is a line; that means, the vector diagram is simply a line, this is the v r one, simply a straight line because velocities are collinear the same direction. So, therefore, we can write the relative velocity v r 1 is equal to v 1 minus u. Here one thing you have to recognize that the tangential velocity of the bucket at inlet and outlet is same; that means, if you see this, the tangential velocity; this is the same plane, but the liquid enters and comes out. So, therefore, the radial location of the inlet and outlet from the axis of rotation remains the same. Now, if we draw the outlet velocity triangle, the outlet velocity triangle will look like that this is the v r 2 that is the relative velocity with respect to this and this is v 2. We can make this component. So here you see the outlet velocity triangle shows that the relative velocity of the fluid with respect to the bucket is such that it coincides with the angle at outlet of the bucket. This is for the smooth flow of the water to the bucket. You know that for smooth entry and smooth discharge of the water, the velocity of the fluid with relative to the water should glide along the velocity of the fluid, it relative to the bucket should glide along the bucket or vane. That means, the outlet the angle of the relative velocity, that is the relative velocity with respect to the bucket should make the same angle with that of the bucket, that means, this is nothing, but this angle we recognized as one sixty five degree it is made. This angle we call it as beta 2. So, therefore, beta two is usually 180 degree, 180 minus 165 that is 15 degree usually. It may be of differ in value; that means, the angle of blade at outlet is equal to the angle of the relative velocity at outlet. And inlet also the angle of blade, this is zero, so inlet velocity is having a zero angle with the tangential direction. That means, that both inlet and outlet the relative velocity should match the blade angle this I discussed earlier also. Now, we know the energy, we know that energy transferred per unit mass between the fluid and the rotor, if I write the energy giving by the fluid per unit mass to this bucket will be equal to v w 1 u 1 minus v w 2 u 2 from the general Euler s equation for fluid machines. Nomenclatures are we will explain that v w 1 is the tangential component of the inlet velocity. What is the value of v w 1 here, here v w 1 is equal to v 1, because v 1 itself in

4 the tangential direction. And u 1 is equal to u 2, here what is the value of v w 2, v w 2 can be found out from that means, it is in the opposite direction to that of the v 1 or v w 1 and this is this much from the velocity triangle. So, with a negative sign, because the velocity is in the opposite direction to the incoming velocity, it can be written as v r 2 cos beta 2, this much cos of beta two minus u. So, u 1 is equal to u 2 is equal to u here. So, if I substitute these values of v w 1, v w 2 and u as the tangential velocity of the rotor that is u 1 u 2 then we get e by m is equal to Again V 1 can be written in terms on u as v r 1 plus u, because from the inlet velocity vector diagram, we see that V 1 is equal to v w 1 that that is equal to v r 1 plus u. So, therefore, we get v r 1 plus v r 2 cos of beta 2 into u, clear v r 1 plus v r 2 cos of beta 2 into u. (Refer Slide Time: 09:02) We can write it again that e by m per unit mass. Again I am writing v r 1 plus v r 2 cos of beta 2 into u, where v r 1 is the relative velocity of the fluid at inlet, which is simply the difference between the inlet velocity and the tangential velocity, because they are in the same line. V r 2 is the relative velocity of fluid at outlet, which we can find from the outlet velocity triangle, and beta two is the angle of the bucket at the outlet, and u is the tangential velocity of the bucket at its center, where the jet strikes. Now, you see that in the bucket, if you see this figure why the relative velocity at the inlet and outlet changes. Why the relative velocity at the outlet changes from that at the

5 inlet, why? You please recall our earlier discussion that the relative velocity at outlet will be differing from relative velocity of inlet for what reasons, what are the reasons for which the relative velocity of fluid at outlet will be different from that at the inlet. This is because of what? Here the fluid is throughout at atmospheric pressure, fluid is open jet. So, there is no question of change in pressure. So, pressure remains constant throughout the flow through the bucket. So, why the relative velocity will change, this is only because of friction, only because of friction. You consider the relative velocity in this way then as if the blade is fixed and fluid flows positive, that means, fluid flowing positive is fixed blade or a fixed surface, then why the velocity will change only because of friction. If the pressure remains constant, so that is only way that velocity can change is the friction. If the pressure remains constant that is an another important thing. So, therefore, v r two changes from that of v r 1, the value of v r 2 changes from that of v r one, because of friction, and the role of friction is to reduce the value of v r two from v r one. So, therefore, we can consider or we can write v r two in this fashion a some coefficient k times v r one where k is less than one this takes care of the friction; that means, v r two is reduced from v r one by a factor less than one. So, that we can express v r two in this fashion where k is the factor less than one and takes care of the friction in the bucket. So, therefore, we can write v r one into one plus k cos of beta two into u well and again I just substitute v r one as v one minus u from the inlet velocity triangle you can recall cos beta two into u. So, this is the energy per unit mass that is being transferred or given by the fluid to the bucket I think there is no difficulty its extremely simple. Now the total energy given per unit time that is the rate of energy, that is being transferred by the fluid to the rotor will be this multiplied by the mass flow rate. Because this is the energy given per unit mass if we multiply this if we multiply this with the mass flow rate of the fluid then you will get the rate of energy transferred by the fluid to the rotor. Now, what is the mass flow rate of the fluid it is density rho and the q is the volume flow rate. So, this is the mass into v one minus u into one plus k cos beta two into u. So, this is the expression for the rate of energy that is given by the fluid to the bucket now we define a efficiency eta known as bucket efficiency which is very important bucket

6 efficiency or sometimes we define it as wheel efficiency wheel efficiency because buckets are mounted on wheels wheel efficiency how is it defined. Now, the power that is being developed by the wheel due to the motion of the fluid is this much. So, this comes as the useful work or useful energy from the bucket cos beta two into u. What is the input to the bucket, what does bucket receive as the input energy you see here the bucket receives the input energy in the form of kinetic energy of the fluid; that means, it is the kinetic energy of the fluid total kinetic energy of the fluid; that means, mass times v one square by two. So, it is the rate at which the energy is received by the bucket at its inlet that is the rate of kinetic energy that is being received by the bucket at its inlet due to the incoming flow of water and the numerator is the power developed by the bucket per unit time. So, therefore, we get an expression from this about this eta rho q rho q cancels out. So, you can write one plus k cos beta two into you write in a fashion it is twice well. So, this will be well u square minus v one square. So, u by v one u by v one into one minus u by v one of course, a two will be there well. So, this is the expression for the bucket efficiency or wheel efficiency now wheel efficiency efficiency is the dimensionless parameter. So, it is expressed in terms of the dimensionless parameter. Now, what is that physical significance of this efficiency, physical significance of this efficiency is that how effectively the bucket can convert the incoming kinetic energy which is receives in the form of power developed. Now you can ask me sir why is the discrepancy is it due to friction, no, even if you make k is equal to one. You see this the value of eta is not always one; that means, it is not the friction it is not the friction, but it is it depends upon the deflection of the jet by the bucket. So, that the absolute kinetic energy at the outlet or the discharge should be minimum because the numerator is equal to the change in the kinetic energy of the jet; that means, some energy in the form of kinetic energy is always rejected at the discharge. So, how effectively it can utilize its kinetic energy in the form of work. So, that the discharged kinetic energy which is loss is which is a loss is minimum, so that is the physical concept of the efficiency. And it becomes a function, function of partition dimensionless parameter one is the k that is the friction with a scare of the friction

7 another is the bucket outlet angle and the ratio of u by v one; that means, the speed of the bucket and the speed of the incoming water jet or the inlet velocity of the water jet. Now, for a fixed bucket bucket with a fixed geometry k and beta two are fixed. So, therefore, the efficiency of the bucket is a function of the ratio u by v one which becomes a partition dimensionless parameters representing the operating conditions; that means, it is a function of u by v one (Refer Slide Time: 17:01) Now, if you plot these functions you will see you will get a curve like this. If you plot this function eta versus u by v one correct it is a parabola. You get an exactly the maximum efficiency is attained when this value is zero point five. And this become equal to zero, when u by v one is equal to one, it is very simple that if you make here sorry I can give a suffix or subscript w is value giving to denote that it is the efficiency of the wheel d eta w d u by v one. That means, if I differentiate this eta with respect to u by v one for a fixed blade fix geometry of the blade, we get that it is one minus two u by v one. I should not write that if I make this is equal to zero, it becomes one minus two u by v one is equal to zero, because the expression of this is not one minus two u by v one, it is multiplied by with a constant factor two into one plus k cos beta two if we make this is equal to zero. So, it is obvious that u by v one is equal to half and we can check the maximum condition analytically by checking that or noticing this fact that d u by that second

8 derivative is less than zero or simply by plotting the curve for the expression we will see this expression has a maximum. So, therefore, we see when u by v one reaches half the blade efficiency is maximum again when u by v one is equal to one blade efficiency is zero no power will be developed as you know that when the blade velocity is exactly equal to the incoming velocity of the water water cannot reach the blade. So, flow will be zero and more than that that blade will receive away from the jet before it strikes the blade. So, therefore, it again falls at one. So, this is the maximum value. Now, in actual cases we define a overall efficiency eta o which is equal to the power that is being delivered at the shaft divided by the input power input energy rather input energy to the wheel input energy to the turbine pelton turbine. Before coming to this, I like to tell you that the actual power developed by the wheel depends upon friction not only the fluid to blade friction. There are other frictions in the bearing in the mechanical system and the windage losses that is the friction with the air and the parts of the fluid machines and these losses also increase with the increase in speeds. So, therefore, it has been found practically that the maximum efficiency becomes lower than the theoretical efficiency calculated and it attains the maximum value always lower than that and also becomes zero. Even if the bucket velocity is less than v one and maximum is also attained at a value which is less than point five the value is point four six. So, this is the theoretical curve theoretical curve and this is the actual (( )); that means, in actual case considering the frictional losses we see that the maximum efficiency occurs at a value of u by v one that is the ratio of the bucket speed to the incoming water speed equal to point four six. Now, we come to the definition of eta o that is overall efficiency it is overall efficiency how you define now overall efficiency overall efficiency of a turbine as you know that is the p at shaft coupling; that means, this is the shaft power final power. So, this is less than this quantity; obviously, because this is the power developed by the rotor. So, this gets reduced by the mechanical losses that is losses in the mechanical system. So, that at finally, at the shafting the shaft coupling we get this power which is the numerator of the overall efficiency expression. Now, input energy to pelton turbine. Now you tell me which should what should be the input energy to a pelton turbine what should be the input energy. You see this figure,

10 (Refer Slide Time: 24:53) So, eta o will be the power total power at the shaft coupling and the input energy; that means, the rho q g into h minus h f where h f is the friction loss in the pipeline leading from the reservoir to the nozzle inlet; that means, the inlet to the fluid machines. Now, nozzle is a part of the fluid machine, which converts the energy into kinetic energy. So, therefore, if I want to find out the kinetic energy at the inlet to the bucket at the inlet to the bucket if I want to find out the if I have to find out the kinetic energy at inlet to the bucket. Then this kinetic energy can be found out by application of the Bernoulli's equation between the nozzle inlet and outlet. That means, if I apply the Bernoulli's equation between the nozzle inlet and outlet simply per unit mass the total energy here or per unit weight total head here is h minus h f and that becomes is equal to v square by two g. If I write the Bernoulli's equation for an implicit fluid this total head is the head above the atmospheric pressure. So, therefore, here the pressure is zero and we take the datum as the to the central line of the buckets; that means, the plane at where the jet is striking the buckets. So, therefore, it is very simple that v two becomes equal to two g; that means, the net energy at the inlet is exploited fully in terms of the velocity, but it is multiplied with a term known as coefficient of velocity which is same as that term k. We discussed regarding the flow through flow of the liquid through the bucket which took care of the friction between the liquid and the bucket surface. Here also c v takes

11 care of the friction in the nozzle, which reduces the velocity from that of two g h minus h f which has been deduced by considering the fluid to be inviscid, and by the application of Bernoulli's equation. So, therefore, you will have to know very carefully that v one is c v two g h minus h f. So, therefore, v one square by two is equal to c v into c v square rather into g into h minus h f. So, you see there is the relationship between the kinetic energy at the inlet to the bucket and the energy at the entrance to the nozzle. So, this is they are not equal because of this c v quantity c v square because of the friction. So, these are the stages. So, initially, we get the energy at the entrance to the nozzle or entrance to the machine in the form of h minus h f for unit weight. This is being converted to kinetic energy v one square by two; that means, kinetic energy per unit weight; that means, kinetic head or the dynamic head through the expansion of the flow or the to the flow of the liquid through the nozzle. And we get this head which is less than the head at the entrance by the factor c v square which takes care of the friction in the nozzle. And the shaft power is the power which is developed at the shaft coupling. So, you see this is the power that is developed by the fluid to the rotor the rotor extract this power because of the deflection of the fluid flow through it and this power is getting reduced to p because of mechanical friction. So, these are the stages how the energy is transferred from the inlet to the fluid machines inlet to the pelton wheel down to the shaft coupling final power. So, I think today I will finish here stop here. So, next class I will discuss the specific speed. Thank you.

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Specific Speed, Governing and Limitation

### Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 09 Introduction to Reaction Type of Hydraulic

### Introduction to Fluid Machines and Compressible Flow Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No. # 24 Axial Flow Compressor Part I Good morning

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 1 Introduction to Fluid Machines Well, good

### (Refer Slide Time: 0:45)

(Refer Slide Time: 0:45) Fluid Machines. Professor Sankar Kumar Som. Department Of Mechanical Engineering. Indian Institute Of Technology Kharagpur. Lecture-3. Impulse and Reaction Machines: Introductory

### Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Centrifugal Compressor Part I Good morning

### (Refer Slide Time: 4:41)

Fluid Machines. Professor Sankar Kumar Som. Department Of Mechanical Engineering. Indian Institute Of Technology Kharagpur. Lecture-30. Basic Principle and Energy Transfer in Centrifugal Compressor Part

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 15 Conservation Equations in Fluid Flow Part III Good afternoon. I welcome you all

### Basic Thermodynamics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Basic Thermodynamics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture 12 Second Law and Available Energy III Good morning. I welcome you to this session.

### Steam and Gas Power Systems Prof. Ravi Kumar Department of Mechanical industrial engineering Indian Institute of Technology Roorkee

Steam and Gas Power Systems Prof. Ravi Kumar Department of Mechanical industrial engineering Indian Institute of Technology Roorkee Module No # 06 Lecture No # 26 Impulse Reaction Steam Turbines Hello

### nozzle which is fitted to a pipe through which the liquid is flowing under pressure.

Impact of Jets 1. The liquid comes out in the form of a jet from the outlet of a nozzle which is fitted to a pipe through which the liquid is flowing under pressure. The following cases of the impact of

### Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 42 Flows with a Free Surface Part II Good morning. I welcome you to this session

### HYDRAULIC TURBINES. Hydraulics and Hydraulic Machines

HYDRAULIC TURBINES Introduction: The device which converts h ydraulic energy into mechanical energy or vice versa is known as Hydraulic Machines. The h ydraulic machines which convert h ydraulic energy

### Steam and Gas Power Systems Prof. Ravi Kumar Department Of Mechanical and Industrial Engineering Indian Institute of Technology - Roorkee

Steam and Gas Power Systems Prof. Ravi Kumar Department Of Mechanical and Industrial Engineering Indian Institute of Technology - Roorkee Module No # 05 Lecture No # 23 Impulse Steam Turbine Hello I welcome

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur. Lecture - 9 Fluid Statics Part VI

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 9 Fluid Statics Part VI Good morning, I welcome you all to this session of Fluid

### ME 316: Thermofluids Laboratory

ME 316 Thermofluid Laboratory 6.1 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS ME 316: Thermofluids Laboratory PELTON IMPULSE TURBINE 1) OBJECTIVES a) To introduce the operational principle of an impulse

### Hydraulic Turbines. Table 6.1 Parameters of hydraulic turbines. Power P (kw) Speed N (rpm)

6 Hydraulic Turbines Problem 1 There are 10 solved examples and 7 exercise problems (exclude Problems 1, 2, and 10) in this chapter. Prepare a table to mention the values of all the parameters, such as

### Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No - 03 First Law of Thermodynamics (Open System) Good afternoon,

### Basic Thermodynamics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Basic Thermodynamics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 09 Second Law and its Corollaries-IV Good afternoon to all of you to this session

### Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture 2 First Law of Thermodynamics (Closed System) In the last

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur. Lecture - 8 Fluid Statics Part V

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Fluid Statics Part V Good morning, I welcome you all to the session of fluid mechanics.

### (Refer Slide Time: 0:55)

Fluid Dynamics And Turbo Machines. Professor Dr Dhiman Chatterjee. Department Of Mechanical Engineering. Indian Institute Of Technology Madras. Part C. Module-2. Lecture-8. Hydraulic Turbines: Pelton Turbine.

### mywbut.com Hydraulic Turbines

Hydraulic Turbines Hydro-electric power accounts for up to 0% of the world s electrical generation. Hydraulic turbines come in a variety of shapes determined by the available head and a number of sizes

### Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 5 Channel Transitions Lecture - 1 Channel Transitions Part 1 Welcome back

### Advanced Hydrology Prof. Dr. Ashu Jain Department of Civil Engineering Indian Institute of Technology, Kanpur. Lecture 6

Advanced Hydrology Prof. Dr. Ashu Jain Department of Civil Engineering Indian Institute of Technology, Kanpur Lecture 6 Good morning and welcome to the next lecture of this video course on Advanced Hydrology.

### Introduction to Fluid Machines (Lectures 49 to 53)

Introduction to Fluid Machines (Lectures 49 to 5) Q. Choose the crect answer (i) (ii) (iii) (iv) A hydraulic turbine rotates at N rpm operating under a net head H and having a discharge Q while developing

### Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Indian Institute of Technology, IIT Bombay Module No. # 01 Lecture No. # 08 Cycle Components and Component

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 11 Kinematics of Fluid Part - II Good afternoon, I welcome you all to this session

### (Refer Slide Time: 0:57)

Fluid Dynamics And Turbo Machines. Professor Dr Dhiman Chatterjee. Department Of Mechanical Engineering. Indian Institute Of Technology Madras. Part B. Module-2. Lecture-4. Representation of Turbo Machines

### COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics

COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid

### Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 7 Instability in Rotor Systems Lecture - 2 Fluid-Film Bearings

### Basic Thermodynamics. Prof. S. K. Som. Department of Mechanical Engineering. Indian Institute of Technology, Kharagpur.

Basic Thermodynamics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 06 Second Law and its Corollaries I Good afternoon, I welcome you all to this

### Lecture D Steady State Heat Conduction in Cylindrical Geometry

Conduction and Convection Heat Transfer Prof. S.K. Som Prof. Suman Chakraborty Department of Mechanical Engineering Indian Institute of Technology Kharagpur Lecture - 08 1D Steady State Heat Conduction

### Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati

Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 2 Uniform Flow Lecture - 1 Introduction to Uniform Flow Good morning everyone,

### Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

### Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 7 Instability in rotor systems Lecture - 4 Steam Whirl and

### Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S.K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 49 Introduction to Turbulent Flow part -II Good morning I welcome you all to this

### Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi

Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Lecture No. # 09 Electromagnetic Wave Propagation Inhomogeneous Plasma (Refer Slide Time: 00:33) Today, I

### Chapter Four fluid flow mass, energy, Bernoulli and momentum

4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering

### Introduction to Turbomachinery

1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial

### MOMENTUM PRINCIPLE. Review: Last time, we derived the Reynolds Transport Theorem: Chapter 6. where B is any extensive property (proportional to mass),

Chapter 6 MOMENTUM PRINCIPLE Review: Last time, we derived the Reynolds Transport Theorem: where B is any extensive property (proportional to mass), and b is the corresponding intensive property (B / m

### Conservation of Momentum using Control Volumes

Conservation of Momentum using Control Volumes Conservation of Linear Momentum Recall the conservation of linear momentum law for a system: In order to convert this for use in a control volume, use RTT

### Engineering Mechanics Prof. Siva Kumar Department of Civil Engineering Indian Institute of Technology, Madras Statics - 5.2

Engineering Mechanics Prof. Siva Kumar Department of Civil Engineering Indian Institute of Technology, Madras Statics - 5.2 Now what we want to do is given a surface which is let s assume the surface is

### Hydraulics Prof. Dr. Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati

Hydraulics Prof. Dr. Arup Kumar Sarma Department of Civil Engineering Indian Institute of Technology, Guwahati Module No. # 08 Pipe Flow Lecture No. # 05 Water Hammer and Surge Tank Energy cannot be consumed

### Basic Thermodynamics Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Basic Thermodynamics Prof. S.K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 17 Properties of Pure Substances-I Good morning to all of you. We were discussing

### Basic Fluid Mechanics

Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle

### To investigate the performance of the Pelton Wheel turbine with different range of flow rates and rotational speeds.

Experiment No. 1 PELTON WHEEL TURBINE Objective To investigate the performance of the Pelton Wheel turbine with different range of flow rates and rotational speeds. Summary of theory Pelton Wheel turbine

### Basic Thermodynamics Prof. S K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur. Lecture - 21 Vapors Power Cycle-II

Basic Thermodynamics Prof. S K Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Vapors Power Cycle-II Good morning to all of you. Today, we will be continuing

### Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics

Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics Module 10 - Lecture 24 Kinematics of a particle moving on a curve Today,

### Consider a control volume in the form of a straight section of a streamtube ABCD.

6 MOMENTUM EQUATION 6.1 Momentum and Fluid Flow In mechanics, the momentum of a particle or object is defined as the product of its mass m and its velocity v: Momentum = mv The particles of a fluid stream

### Specific Static rotor work ( P P )

The specific Static Rotor ork p 1 ρ Specific Static rotor work ( P P ) here P, P static pressures at points, (P P ) static pressure difference of the rotor ρ density, in case of a compressible medium average

### Basic Thermodynamics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Basic Thermodynamics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 15 Joule-Kelvin Expansion; Properties of Pure Substances Good morning. Last

### (Refer Slide Time: 2:43-03:02)

Strength of Materials Prof. S. K. Bhattacharyya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture - 34 Combined Stresses I Welcome to the first lesson of the eighth module

### (Refer Slide Time: 2:14)

Fluid Dynamics And Turbo Machines. Professor Dr Shamit Bakshi. Department Of Mechanical Engineering. Indian Institute Of Technology Madras. Part A. Module-1. Lecture-3. Introduction To Fluid Flow. (Refer

### Semiconductor Optoelectronics Prof. M. R. Shenoy Department of physics Indian Institute of Technology, Delhi

Semiconductor Optoelectronics Prof. M. R. Shenoy Department of physics Indian Institute of Technology, Delhi Lecture - 18 Optical Joint Density of States So, today we will discuss the concept of optical

### Process Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur

Process Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur Lecture - 10 Dynamic Behavior of Chemical Processes (Contd.) (Refer Slide

### Marine Hydrodynamics Prof.TrilochanSahoo Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Marine Hydrodynamics Prof.TrilochanSahoo Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Lecture - 10 Source, Sink and Doublet Today is the tenth lecture

### EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER

EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the co-efficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1

### In this lecture... Radial flow turbines Types of radial flow turbines Thermodynamics and aerodynamics Losses in radial flow turbines

Lect- 35 1 In this lecture... Radial flow turbines Types of radial flow turbines Thermodynamics and aerodynamics Losses in radial flow turbines Radial turbines Lect-35 Development of radial flow turbines

### Theory of turbo machine Effect of Blade Configuration on Characteristics of Centrifugal machines. Unit 2 (Potters & Wiggert Sec

Theory of turbo machine Effect of Blade Configuration on Characteristics of Centrifugal machines Unit (Potters & Wiggert Sec. 1..1, &-607) Expression relating Q, H, P developed by Rotary machines Rotary

### Turbomachinery Aerodynamics Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay

Turbomachinery Aerodynamics Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Lecture No. # 26 Tutorial 4: 3D Flows in Axial Flow Turbines We

### Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory and Practice of Rotor Dynamics Prof. Dr. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 2 Simpul Rotors Lecture - 2 Jeffcott Rotor Model In the

### Dynamics of Machines Prof. Amitabha Ghosh Department of Mechanical Engineering Indian Institute of Technology, Kanpur

Dynamics of Machines Prof. Amitabha Ghosh Department of Mechanical Engineering Indian Institute of Technology, Kanpur Module - 3 Lecture - 3 Balancing Machines and Field Balancing of Rotating Discs We

### Process Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur

Process Control and Instrumentation Prof. A. K. Jana Department of Chemical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Dynamic Behavior of Chemical Processes (Contd.) (Refer Slide

### Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 21 Psychometric Processes Good afternoon, yesterday we

### MASS, MOMENTUM, AND ENERGY EQUATIONS

MASS, MOMENTUM, AND ENERGY EQUATIONS This chapter deals with four equations commonly used in fluid mechanics: the mass, Bernoulli, Momentum and energy equations. The mass equation is an expression of the

### ENERGY TRANSFER BETWEEN FLUID AND ROTOR. Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia

ENERGY TRANSFER BETWEEN FLUID AND ROTOR Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia Basic Laws and Equations Continuity Equation m m ρ mass

### Chapter Four Hydraulic Machines

Contents 1- Introduction. - Pumps. Chapter Four Hydraulic Machines (لفرع الميكانيك العام فقط ( Turbines. -3 4- Cavitation in hydraulic machines. 5- Examples. 6- Problems; sheet No. 4 (Pumps) 7- Problems;

### Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 09 Free Surface Effect In the

### Theory & Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati

Theory & Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 8 Balancing Lecture - 1 Introduce To Rigid Rotor Balancing Till

### Industrial Instrumentation Prof. A. Barua Department of Electrical Engineering Indian Institute of Technology Kharagpur. Lecture - 14 Flowmeter ΙΙΙ

Industrial Instrumentation Prof. A. Barua Department of Electrical Engineering Indian Institute of Technology Kharagpur Lecture - 14 Flowmeter ΙΙΙ Welcome to lesson 14 of Industrial Instrumentation. In

### Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay

Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection

### Chapter Four Hydraulic Machines

Contents 1- Introduction. 2- Pumps. Chapter Four Hydraulic Machines (لفرع الميكانيك العام فقط ( Turbines. -3 4- Cavitation in hydraulic machines. 5- Examples. 6- Problems; sheet No. 4 (Pumps) 7- Problems;

### Fluid Mechanics Indian Institute of Technology, Kanpur Prof. Viswanathan Shankar Department of chemical Engineering. Lecture No.

Fluid Mechanics Indian Institute of Technology, Kanpur Prof. Viswanathan Shankar Department of chemical Engineering. Lecture No. # 05 Welcome to this fifth lecture on this nptel course on fluid mechanics

### Mechanics, Heat, Oscillations and Waves Prof. V. Balakrishnan Department of Physics Indian Institute of Technology, Madras

Mechanics, Heat, Oscillations and Waves Prof. V. Balakrishnan Department of Physics Indian Institute of Technology, Madras Lecture 08 Vectors in a Plane, Scalars & Pseudoscalers Let us continue today with

### INSTITUTE OF AERONAUTICAL ENGINEERING

LECTURE NOTES ON Hydraulics and Hydraulic Machines Department of Civil Engineering INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal 500 043, Hyderabad mechanis m COURTESY IARE Governors for Turbines Pendulum

### Advanced Chemical Reaction Engineering Prof. H. S. Shankar Department of Chemical Engineering IIT Bombay. Lecture - 03 Design Equations-1

(Refer Slide Time: 00:19) Advanced Chemical Reaction Engineering Prof. H. S. Shankar Department of Chemical Engineering IIT Bombay Lecture - 03 Design Equations-1 We are looking at advanced reaction engineering;

### Page 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)

Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani

### Contents. 2 Basic Components Aerofoils Force Generation Performance Parameters xvii

Contents 1 Working Principles... 1 1.1 Definition of a Turbomachine... 1 1.2 Examples of Axial Turbomachines... 2 1.2.1 Axial Hydraulic Turbine... 2 1.2.2 Axial Pump... 4 1.3 Mean Line Analysis... 5 1.4

### Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A M Pradeep Department of Aerospace Engineering Indian Institute of Technology, Bombay Lecture No. #03 Jet Engine Basic Performance Parameters We are talking

### Fluid Mechanics II. Newton s second law applied to a control volume

Fluid Mechanics II Stead flow momentum equation Newton s second law applied to a control volume Fluids, either in a static or dnamic motion state, impose forces on immersed bodies and confining boundaries.

### Advanced Hydrology Prof. Dr. Ashu Jain Department of Civil Engineering Indian Institute of Technology, Kanpur. Lecture - 13

Advanced Hydrology Prof. Dr. Ashu Jain Department of Civil Engineering Indian Institute of Technology, Kanpur Lecture - 13 Good morning friends and welcome to the video course on Advanced Hydrology. In

### Mechanical Vibrations Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology, Guwahati

Mechanical Vibrations Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology, Guwahati Module - 12 Signature analysis and preventive maintenance Lecture - 3 Field balancing

### Constrained and Unconstrained Optimization Prof. Adrijit Goswami Department of Mathematics Indian Institute of Technology, Kharagpur

Constrained and Unconstrained Optimization Prof. Adrijit Goswami Department of Mathematics Indian Institute of Technology, Kharagpur Lecture - 01 Introduction to Optimization Today, we will start the constrained

### MECA-H-402: Turbomachinery course Axial compressors

MECA-H-40: Turbomachinery course Axial compressors Pr. Patrick Hendrick Aero-Thermo-Mecanics Year 013-014 Contents List of figures iii 1 Axial compressors 1 1.1 Introduction...............................

### Chapter 7 The Energy Equation

Chapter 7 The Energy Equation 7.1 Energy, Work, and Power When matter has energy, the matter can be used to do work. A fluid can have several forms of energy. For example a fluid jet has kinetic energy,

### Design and Analysis of Experiments Prof. Jhareswar Maiti Department of Industrial and Systems Engineering Indian Institute of Technology, Kharagpur

Design and Analysis of Experiments Prof. Jhareswar Maiti Department of Industrial and Systems Engineering Indian Institute of Technology, Kharagpur Lecture - 27 Randomized Complete Block Design (RCBD):

### Experiment (3): Impact of jet

Experiment (3): Impact of jet Introduction: Impact of jets apparatus enables experiments to be carried out on the reaction force produced on vanes when a jet of water impacts on to the vane. The study

### M E 320 Professor John M. Cimbala Lecture 23

M E 320 Professor John M. Cimbala Lecture 23 Today, we will: Discuss diffusers and do an example problem Begin discussing pumps, and how they are analyzed in pipe flow systems D. Diffusers 1. Introduction.

### Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi

Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Module No. # 01 Lecture No. # 22 Adiabatic Invariance of Magnetic Moment and Mirror Confinement Today, we

### equation 4.1 INTRODUCTION

4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a

### Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay

Special Theory Of Relativity Prof. Shiva Prasad Department of Physics Indian Institute of Technology, Bombay Lecture - 6 Length Contraction and Time Dilation (Refer Slide Time: 00:29) In our last lecture,

### SUMMER 14 EXAMINATION

Important Instructions to examiners: 1) The answers should be examined by key words and not as word-to-word as given in the model answer scheme. 2) The model answer and the answer written by candidate

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 8 Introduction to Vapour Power Cycle Today, we will continue

### CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

### CHAPTER TWO CENTRIFUGAL PUMPS 2.1 Energy Transfer In Turbo Machines

7 CHAPTER TWO CENTRIFUGAL PUMPS 21 Energy Transfer In Turbo Machines Fig21 Now consider a turbomachine (pump or turbine) the total head (H) supplied by it is The power delivered to/by the fluid simply

### Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati

Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Module No. - 01 Basics of Statics Lecture No. - 01 Fundamental of Engineering Mechanics