1 Theoretical Background of PELTON Turbine

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1 Theoretical Background of PELTON Turbine"

Transcription

1 c [m/s] linear velocity of water jet u [m/s) runner speed at PCD P jet [W] power in the jet de kin P T [W] power of turbine F [N] force F = dj Q [m 3 /s] discharge, volume flow ρ [kg/m 3 ] density of water (f(t)) θ angle of deflected jet r T [m] radius of turbine (PCD/) P el [W] power output of generator j [kg m/s] impulse, momentum ϕ nozzle conversion eff. of nozzle p [n/m ] pressure g [m/s ] gravitational constant a jet [m ] cross-section area of jet d nozzle [m] nozzle diameter ṁ = dm [kg/s] mass flow ρ Q ω [/s] πf = π RP M 60 p [N/m ] pressure Table : Glossary Useful Symbols Theoretical Background of PELTON Turbine. Physics of Water Turbines (Impulse Turbines).. Basic Assumptions The power output of an ideal turbine P T is derived from (a simplified) BERNOULLI s equation with the following assumptions: no friction no viscosity incompressible medium laminar flow steady flow The only parameters that have to be taken into account are the pressure and velocity differences at inlet and outlet of the turbine. ( p p P T = + c c ) dm ρ where p p ρ stands for the specific potential energy of the water flow, whereas denotes the specific kinetic energy. Thus the expression P T = c c ( c c ) dm describes the net power output of an ideal impulse turbine, where all potential energy is transformed into velocity (i.e. kinetic) energy. c i =linear flow velocity in [m/s]; p =pressure in [N/m ]; dm = ṁ: mass flow in [kg/s] impulse turbines are e.g. PELTON, TURGO & BANKI-OSSBERGER-MITCHELL crossflow turbines

2 Figure : Flow of Jet in Bucket (Vane) of PELTON turbine.. Impulse Turbine Impulse (i.e momentum) is defined as product of velocity and mass j = m v, thus being a quantity of motion. The pulse force is defined as the first derivative of the momentum: d(m v) = dj = F In a closed system the sum of all acting forces equals zero, thus the forces of deflection, acceleration (positive or negative) are in equilibrium with the pulse force(s). The runner of the turbine is driven by the negative acceleration of the periphal flow of the jet, with flow velocity c. The product of torque M T and the rotational speed of the turbine ω, which equals the power output P T, can be related to the flow rate Q = ρ dm and the periphal velocity u of the runner by means of: P T = M T ω = ρ Q (c c ) u with c and c the velocity components of the jet in the direction of u before and after touching the bucket. The efficiency of the turbine η is given by the ratio of the power output at the turbine shaft P T and the kinetic power P jet of the water jet. This leads to a general equation for the turbine efficiency: and then a variable k η = P T = ρ Q (c c ) u P jet ρ Q c k = u c is defined, which gives the ratio between the periphal velocity of the runner u and the linear velocity of the jet c (before hitting the runner). The optimal rotational speed ω opt can be calculated from the first derivative of the efficiency over k: and the solutions for the PELTON turbine are given below. dη dk = 0 (ω = ω opt)

3 Figure : PELTON turbine wheel plus nozzles 3

4 ..3 PELTON runner If the vane of a PELTON turbine does not move, the only effect is to reverse the jet s direction. Apart from some energy lost to friction (can be introduced by a bucket efficiency ϕ b ), the energy of the jet, and the magnitude of its velocity, stay the same as before. If the vane moves towards the jet, the water gains speed; if it pushes a vane moving away, it loses speed. In particular, if the water drives a vane moving at half its speed, then (neglecting friction) it loses all its velocity (and thus its kinetic energy) and just dribbles out of the moving vane. The velocity of the jet is reduced by the friction losses in the nozzles these losses are expressed by the friction loss coefficient ϕ n ( for polished surfaces and well designed nozzle shapes), giving the jet velocity c 0 as c 0 = ϕ n p g H = ϕ n ρ a function of head H or pressure p and it is generally assumed that c = c 0 the inlet velocity at the runner equals the jet velocity at the nozzle (see below how to determine the nozzle efficiency). It is possible to calculate the shaft power of the PELTON runner, assuming a deflection of the jet of θ = 65 (this axial component of the reflected jet is necessary to prevent the deflected water from hitting the following buckets). P T = M T ω = F u = ρ Q ( cosθ) (c u) u The efficiency of a PELTON turbine η is then calculated from the following equation η = P T = ρ Q ( cosθ) (c u) u P jet ρ Q c and this equation can be simplified by using the above given definition for k: η = ( cosθ) (c u) u c η = ( cosθ) ( k) k showing us, how the efficiency η depends on the ratio k = u/c 3. As pointed out above, with the first derivative set to zero, we obtain the value of k for maximum efficiency k(η max ) = 0.5 = u c i.e. for maximum efficiency the runner tip speed u should be equal half the jet velocity c 4. The maximum theoretical efficiency η max = ϕ n ( ϕ b cos β ) is in the range of 0.95 for optimal values of the nozzle efficiency ϕ n. Well designed PELTON reach an efficiency of 88-9% when they operate at 60-80% of full design flow.. Some Useful Relations for PELTON Turbines In the following some useful relations are listed. Some are needed to evaluate the experimental results. 3 Please see fig. 3 for a graph of this function 4 In real systems the optimal value for k is between 0.45 and

5 Figure 3: Theoretical PELTON Runner Turbine Efficiency vs. k Value Figure 4: PELTON Runner Relative Efficiency vs Rated Flow. 5

6 .. Pressure and Head Pressure and Head in a hydropower plant are related by or with p = H g ρ () H = p g ρ ρ HO 000 kg m 3 g = 9.8 m s p[ N m ] H[m] [N] = [ kg m s ].. Hydraulic Power We assume the absence of friction losses kinetic power of jet flow equals hydraulic power of the water flow and thus P jet = ṁc () = p V = p Q Q = V = ṁ ρ the power P H of the falling water can be expressed as P H = H g ṁ (3) P H = QρgH..3 How to calculate Turbine parameters The speed of the turbine runner at pitch circle diameter (PCD) is given by u = ω P CD/ with ω = π RP M/60 Whereas the the speed of the jet c has to be calculated by Q = V = c a jet a jet = π d jet 4 (4) c = Q a jet = 4 Q π d jet 6

7 Nozzle efficiency nozzle efficiency: If we divide the kinetic energy of the jet by the hydraulic energy from the pressure. we get an idea of the ϕ nozzle = ρqc pq = ρc p and c already known. 7

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference.

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference. FLUID MECHANICS TUTORIAL No.7 FLUID FORCES When you have completed this tutorial you should be able to Solve forces due to pressure difference. Solve problems due to momentum changes. Solve problems involving

More information

5.2 Rotational Kinematics, Moment of Inertia

5.2 Rotational Kinematics, Moment of Inertia 5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position

More information

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4 Theory of turbo machinery / Turbomaskinernas teori Chapter 4 Note direction of α 2 FIG. 4.1. Turbine stage velocity diagrams. Assumptions: Hub to tip ratio high (close to 1) Negligible radial velocities

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are:

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are: Problem 1. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields as shown in the figure. (b) Repeat part (a), assuming the moving particle is

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

Chapter 13, example problems: x (cm) 10.0

Chapter 13, example problems: x (cm) 10.0 Chapter 13, example problems: (13.04) Reading Fig. 13-30 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.

More information

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the

charge is detonated, causing the smaller glider with mass M, to move off to the right at 5 m/s. What is the This test covers momentum, impulse, conservation of momentum, elastic collisions, inelastic collisions, perfectly inelastic collisions, 2-D collisions, and center-of-mass, with some problems requiring

More information

du u U 0 U dy y b 0 b

du u U 0 U dy y b 0 b BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

More information

7. Kinetic Energy and Work

7. Kinetic Energy and Work Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic

More information

h b b h Q u da u 1 1 dy dz u 1 dy 1 dz u b h b h

h b b h Q u da u 1 1 dy dz u 1 dy 1 dz u b h b h P3.18 An incompressible fluid flows steadily through the rectangular duct in the figure. The exit velocity profile is given by u umax(1 y /b )(1 z /h ). (a) Does this profile satisfy the correct boundary

More information

ME19b. SOLUTIONS. Feb. 11, 2010. Due Feb. 18

ME19b. SOLUTIONS. Feb. 11, 2010. Due Feb. 18 ME19b. SOLTIONS. Feb. 11, 21. Due Feb. 18 PROBLEM B14 Consider the long thin racing boats used in competitive rowing events. Assume that the major component of resistance to motion is the skin friction

More information

Announcements. Dry Friction

Announcements. Dry Friction Announcements Dry Friction Today s Objectives Understand the characteristics of dry friction Draw a FBD including friction Solve problems involving friction Class Activities Applications Characteristics

More information

CH-205: Fluid Dynamics

CH-205: Fluid Dynamics CH-05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, ρ = 1000 kg/m 3, gravitational acceleration, g

More information

Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling. Process Dynamics and Control Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

More information

Open channel flow Basic principle

Open channel flow Basic principle Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure

More information

TURBINE SELECTION RANGE

TURBINE SELECTION RANGE GILKES GILKESTURGO TURGOIMPULSE IMPULSEHYDRO HYDROTURBINE TURBINE TURBINE SELECTION On 17th August 1856 we received our first order for a water turbine. It produced mechanical power to drive agricultural

More information

Homework 4. problems: 5.61, 5.67, 6.63, 13.21

Homework 4. problems: 5.61, 5.67, 6.63, 13.21 Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find

More information

Chapter 24 Physical Pendulum

Chapter 24 Physical Pendulum Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...

More information

Chapter 8 Fluid Flow

Chapter 8 Fluid Flow Chapter 8 Fluid Flow GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and use it in an operational

More information

No Brain Too Small PHYSICS. 2 kg

No Brain Too Small PHYSICS. 2 kg MECHANICS: ANGULAR MECHANICS QUESTIONS ROTATIONAL MOTION (2014;1) Universal gravitational constant = 6.67 10 11 N m 2 kg 2 (a) The radius of the Sun is 6.96 10 8 m. The equator of the Sun rotates at a

More information

Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79

Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life? - car brakes - driving around a turn - walking - rubbing your hands together

More information

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies

CHAPTER 11. The total energy of the body in its orbit is a constant and is given by the sum of the kinetic and potential energies CHAPTER 11 SATELLITE ORBITS 11.1 Orbital Mechanics Newton's laws of motion provide the basis for the orbital mechanics. Newton's three laws are briefly (a) the law of inertia which states that a body at

More information

1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ") # x (t) = A! n. t + ") # v(0) = A!

1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ) # x (t) = A! n. t + ) # v(0) = A! 1.1 Using Figure 1.6, verify that equation (1.1) satisfies the initial velocity condition. Solution: Following the lead given in Example 1.1., write down the general expression of the velocity by differentiating

More information

Tennessee State University

Tennessee State University Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an F-grade. Other instructions will be given in the Hall. MULTIPLE CHOICE.

More information

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass

More information

Problem Set V Solutions

Problem Set V Solutions Problem Set V Solutions. Consider masses m, m 2, m 3 at x, x 2, x 3. Find X, the C coordinate by finding X 2, the C of mass of and 2, and combining it with m 3. Show this is gives the same result as 3

More information

Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

More information

University Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples

University Physics 226N/231N Old Dominion University. Newton s Laws and Forces Examples University Physics 226N/231N Old Dominion University Newton s Laws and Forces Examples Dr. Todd Satogata (ODU/Jefferson Lab) satogata@jlab.org http://www.toddsatogata.net/2012-odu Wednesday, September

More information

* Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.

* Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No. * Biot Savart s Law- Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying

More information

Unit 4 Practice Test: Rotational Motion

Unit 4 Practice Test: Rotational Motion Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle

More information

Physics 1A Lecture 10C

Physics 1A Lecture 10C Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium

More information

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids

Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness

More information

Physics in the Laundromat

Physics in the Laundromat Physics in the Laundromat Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (Aug. 5, 1997) Abstract The spin cycle of a washing machine involves motion that is stabilized

More information

B) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B

B) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time

More information

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

More information

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces. Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a

More information

RECYCLED MICRO HYDROPOWER GENERATION USING HYDRAULIC RAM PUMP (HYDRAM)

RECYCLED MICRO HYDROPOWER GENERATION USING HYDRAULIC RAM PUMP (HYDRAM) IMPACT: International Journal of Research in Engineering & Technology (IMPACT: IJRET) Vol., Issue 3, Aug 23, - Impact Journals RECYCLED MICRO HYDROPOWER GENERATION USING HYDRAULIC RAM PUMP (HYDRAM) C.

More information

FLUID MECHANICS. TUTORIAL No.8A WATER TURBINES. When you have completed this tutorial you should be able to

FLUID MECHANICS. TUTORIAL No.8A WATER TURBINES. When you have completed this tutorial you should be able to FLUID MECHAICS TUTORIAL o.8a WATER TURBIES When you have completed this tutorial you should be able to Explain the significance of specific speed to turbine selection. Explain the general principles of

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS TUTORIAL 1 - ANGULAR MOTION CONTENT Be able to determine the characteristics

More information

Name: Partners: Period: Coaster Option: 1. In the space below, make a sketch of your roller coaster.

Name: Partners: Period: Coaster Option: 1. In the space below, make a sketch of your roller coaster. 1. In the space below, make a sketch of your roller coaster. 2. On your sketch, label different areas of acceleration. Put a next to an area of negative acceleration, a + next to an area of positive acceleration,

More information

Experiment 3 Pipe Friction

Experiment 3 Pipe Friction EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional

More information

Rotational inertia (moment of inertia)

Rotational inertia (moment of inertia) Rotational inertia (moment of inertia) Define rotational inertia (moment of inertia) to be I = Σ m i r i 2 or r i : the perpendicular distance between m i and the given rotation axis m 1 m 2 x 1 x 2 Moment

More information

Manufacturing Equipment Modeling

Manufacturing Equipment Modeling QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,

More information

Chapter 3 Process Variables. Mass and Volume

Chapter 3 Process Variables. Mass and Volume Chapter 3 Process Variables Process: to a chemical engineer, the set of tasks or operations that accomplish a chemical or material transformation to produce a product Feed or inputs: raw materials and

More information

2. Parallel pump system Q(pump) = 300 gpm, h p = 270 ft for each of the two pumps

2. Parallel pump system Q(pump) = 300 gpm, h p = 270 ft for each of the two pumps Pumping Systems: Parallel and Series Configurations For some piping system designs, it may be desirable to consider a multiple pump system to meet the design requirements. Two typical options include parallel

More information

Chapter 28 Fluid Dynamics

Chapter 28 Fluid Dynamics Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example

More information

If you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ

If you put the same book on a tilted surface the normal force will be less. The magnitude of the normal force will equal: N = W cos θ Experiment 4 ormal and Frictional Forces Preparation Prepare for this week's quiz by reviewing last week's experiment Read this week's experiment and the section in your textbook dealing with normal forces

More information

Chapter 13. Gravitation

Chapter 13. Gravitation Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67

More information

Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4. Forces and Newton s Laws of Motion. continued Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

More information

Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43

Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state

More information

Chapter 7 Energy and Energy Balances

Chapter 7 Energy and Energy Balances CBE14, Levicky Chapter 7 Energy and Energy Balances The concept of energy conservation as expressed by an energy balance equation is central to chemical engineering calculations. Similar to mass balances

More information

Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Static s Kinematics Dynamics Fluid Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

More information

Center of Gravity. We touched on this briefly in chapter 7! x 2

Center of Gravity. We touched on this briefly in chapter 7! x 2 Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.

More information

Physics of the tractor pull. How to use the tractor pull as a context rich setting to cover Minnesota Physical Science Standards.

Physics of the tractor pull. How to use the tractor pull as a context rich setting to cover Minnesota Physical Science Standards. Physics of the tractor pull. How to use the tractor pull as a context rich setting to cover Minnesota Physical Science Standards. Richard Lahti, Assistant Professor of Chemistry and Physics at Minnesota

More information

Energy transformations

Energy transformations Energy transformations Objectives Describe examples of energy transformations. Demonstrate and apply the law of conservation of energy to a system involving a vertical spring and mass. Design and implement

More information

Experiment P-6 Friction Force

Experiment P-6 Friction Force 1 Experiment P-6 Friction Force Objectives To learn about the relationship between force, normal force and coefficient. To observe changes in the force within different surfaces and different masses. To

More information

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

More information

Proof of the conservation of momentum and kinetic energy

Proof of the conservation of momentum and kinetic energy Experiment 04 Proof of the conservation of momentum and kinetic energy By Christian Redeker 27.10.2007 Contents 1.) Hypothesis...3 2.) Diagram...7 3.) Method...7 3.1) Apparatus...7 3.2) Procedure...7 4.)

More information

GRADE 11 EXEMPLAR PAPERS PHYSICAL SCIENCE: PAPER I

GRADE 11 EXEMPLAR PAPERS PHYSICAL SCIENCE: PAPER I GRADE 11 EXEMPLAR PAPERS PHYSICAL SCIENCE: PAPER I Time: 3 hours 150 marks PLEASE TURN OVER GRADE 11: PHYSICAL SCIENCE EXEMPLAR: PAPER I Page 2 of 13 QUESTION 1 1.1 Give one word/term for the following

More information

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 2 BELT DRIVES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 2 BELT DRIVES MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL BELT DRIVES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential pulley

More information

Chapter 6 Work and Energy

Chapter 6 Work and Energy Chapter 6 WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system

More information

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1 Answer, Key Homework 2 David McIntyre 1 This print-out should have 14 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

Compressor and turbines

Compressor and turbines Compressor and turbines In this chapter, we will look at the compressor and the turbine. They are both turbomachinery: machines that transfer energy from a rotor to a fluid, or the other way around. The

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

More information

EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP

EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP EXPERIMENT NUMBER 7 PERFORMANCE TEST OF A CENTRIFUGAL PUMP OBJECTIVE The primary objectives of this experiment is to measure the performance of a centrifugal pump and compare the results to the manufacturers

More information

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

PHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in

More information

Viscous flow in pipe

Viscous flow in pipe Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................

More information

Laboratory Experience with a Model Jet Turbine

Laboratory Experience with a Model Jet Turbine Session 2166 Laboratory Experience with a Model Jet Turbine John E. Matsson Oral Roberts University Abstract This paper describes the experience gained from the operation of a JetCat model turbojet engine

More information

Physics 11 Assignment KEY Dynamics Chapters 4 & 5

Physics 11 Assignment KEY Dynamics Chapters 4 & 5 Physics Assignment KEY Dynamics Chapters 4 & 5 ote: for all dynamics problem-solving questions, draw appropriate free body diagrams and use the aforementioned problem-solving method.. Define the following

More information

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc.

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. 1 Centrifugal Pump- Definition Centrifugal Pump can be defined as a mechanical device used to transfer liquid of various types. As

More information

Response to Harmonic Excitation Part 2: Damped Systems

Response to Harmonic Excitation Part 2: Damped Systems Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost

More information

CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT

CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT Rev 8/15 AW/GW CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT The objective of this experiment is to familiarize the student with several types of flow-measuring devices commonly used in the laboratory

More information

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

Wind Turbine Power Calculations

Wind Turbine Power Calculations Wind Turbine Power Calculations RWE npower renewables Mechanical and Electrical Engineering Power Industry INTRODUCTION RWE npower is a leading integrated UK energy company and is part of the RWE Group,

More information

OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS

OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid

More information

Transport resistance versus lever arm of rolling friction

Transport resistance versus lever arm of rolling friction Transport resistance versus lever arm of rolling friction 1) Introduction The stationary torque requirement of a roller application (roller conveyor; travelling drive) can be determined in different ways.

More information

Mass and Energy Analysis of Control Volumes

Mass and Energy Analysis of Control Volumes MAE 320-Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady- and unsteady-flow

More information

Mechanics 1: Conservation of Energy and Momentum

Mechanics 1: Conservation of Energy and Momentum Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation

More information

Exemplar Problems Physics

Exemplar Problems Physics Chapter Eight GRAVITATION MCQ I 8.1 The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration

More information

Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.

Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena. Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems

More information

Solution Derivations for Capa #11

Solution Derivations for Capa #11 Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform

More information

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

More information

This chapter deals with three equations commonly used in fluid mechanics:

This chapter deals with three equations commonly used in fluid mechanics: MASS, BERNOULLI, AND ENERGY EQUATIONS CHAPTER 5 This chapter deals with three equations commonly used in fluid mechanics: the mass, Bernoulli, and energy equations. The mass equation is an expression of

More information

Performance. 15. Takeoff and Landing

Performance. 15. Takeoff and Landing Performance 15. Takeoff and Landing The takeoff distance consists of two parts, the ground run, and the distance from where the vehicle leaves the ground to until it reaches 50 ft (or 15 m). The sum of

More information

Chapter 8: Flow in Pipes

Chapter 8: Flow in Pipes Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks

More information

Conceptual Questions: Forces and Newton s Laws

Conceptual Questions: Forces and Newton s Laws Conceptual Questions: Forces and Newton s Laws 1. An object can have motion only if a net force acts on it. his statement is a. true b. false 2. And the reason for this (refer to previous question) is

More information

Lab 7: Rotational Motion

Lab 7: Rotational Motion Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125

More information

THERMAL POWER PLANTS Vol. III - Steam Turbine Impulse and Reaction Blading - R.A. Chaplin STEAM TURBINE IMPULSE AND REACTION BLADING

THERMAL POWER PLANTS Vol. III - Steam Turbine Impulse and Reaction Blading - R.A. Chaplin STEAM TURBINE IMPULSE AND REACTION BLADING STEAM TURBINE IMPULSE AND REACTION BLADING R.A. Chaplin Department of Chemical Engineering, University of New Brunswick, Canada Keywords: Steam Turbines, Turbine Blades, Velocity Diagrams, Impulse, Reaction,

More information

Chapter 16 Electric Forces and Fields

Chapter 16 Electric Forces and Fields Chapter 16 Electric Forces and Fields 2. How many electrons does it take to make one coulomb of negative charge? A. 1.00 10 9 B. 6.25 10 18 C. 6.02 10 23 D. 1.66 10 18 E. 2.24 10 4 10. Two equal point

More information

Torque Analyses of a Sliding Ladder

Torque Analyses of a Sliding Ladder Torque Analyses of a Sliding Ladder 1 Problem Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (May 6, 2007) The problem of a ladder that slides without friction while

More information

NEWTON S LAWS OF MOTION

NEWTON S LAWS OF MOTION NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied

More information

STEAM TURBINE 1 CONTENT. Chapter Description Page. V. Steam Process in Steam Turbine 6. VI. Exhaust Steam Conditions, Extraction and Admission 7

STEAM TURBINE 1 CONTENT. Chapter Description Page. V. Steam Process in Steam Turbine 6. VI. Exhaust Steam Conditions, Extraction and Admission 7 STEAM TURBINE 1 CONTENT Chapter Description Page I Purpose 2 II Steam Turbine Types 2 2.1. Impulse Turbine 2 2.2. Reaction Turbine 2 III Steam Turbine Operating Range 2 3.1. Curtis 2 3.2. Rateau 2 3.3.

More information

Hooke s Law and Simple Harmonic Motion

Hooke s Law and Simple Harmonic Motion Hooke s Law and Simple Harmonic Motion OBJECTIVE to measure the spring constant of the springs using Hooke s Law to explore the static properties of springy objects and springs, connected in series and

More information

So if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.

So if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold. Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,

More information

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.

Magnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise. Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.

More information

A Magnetic Linear Accelerator

A Magnetic Linear Accelerator 1 Problem A Magnetic Linear Accelerator Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (March, 200) A delightful science toy, sold by Scitoys.com [1] is shown in

More information

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide.

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide. Fluid Mechanics FE Review Carrie (CJ) McClelland, P.E. cmcclell@mines.edu Fluid Mechanics FE Review These slides contain some notes, thoughts about what to study, and some practice problems. The answers

More information

Hydro power plants. Inlet gate Surge shaft. Air inlet. Penstock. Tunnel Sand trap Trash rack Self closing valve. Tail water. Main valve Turbine

Hydro power plants. Inlet gate Surge shaft. Air inlet. Penstock. Tunnel Sand trap Trash rack Self closing valve. Tail water. Main valve Turbine Hydro power plants Hydro power plants Air inlet Inlet gate Surge shaft Penstock Tail water Tunnel Sand trap Trash rack Self closing valve Draft tube Draft tube gate Main valve Turbine The principle the

More information

6.1: Angle Measure in degrees

6.1: Angle Measure in degrees 6.1: Angle Measure in degrees How to measure angles Numbers on protractor = angle measure in degrees 1 full rotation = 360 degrees = 360 half rotation = quarter rotation = 1/8 rotation = 1 = Right angle

More information