# Mechanical Agitator Power Requirements for Liquid Batches

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 PDHonline Course K103 (2 PDH) Mechanical Agitator Power Requirements for Liquid Batches Instructor: John Frank Pietranski, P.E., Ph.D PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA Phone & Fax: An Approved Continuing Education Provider

3 be described by radial and tangential velocity components. If we assume that the tangential liquid velocity is some fraction k, of the blade-tip velocity then: V u2 = k * u 2 = k * π * D * N ( 1 ) where: V u2 = tangential component velocity of the liquid leaving the blade tip. u 2 = velocity of the impeller blade tip. D = diameter of the impeller, feet. N = rotational speed of the impeller. The volumetric flow rate through the radial sweep of the impeller, see Figure 6, is expressed as: where: q = V r2 * A p ( 2 ) V r2 = radial component velocity of the liquid leaving the blade tip. A p = area of the cylinder swept out by the impeller blade tips, sq. ft. By definition: where: A p = π * D * W ( 3 ) q = volumetric flow rate through the impeller, cu. ft/sec. Page 2 of 23

4 W = width of the impeller blades, ft. By defining the angle at which the fluid leaves the impeller as β 2, it can be shown that: V r2 = ( u 2 - V u2 ) * tan β 2 ( 4 ) substituting equations (1), (2), and (3) into equation (4) and rearranging yields: q = π 2 * D 2 * N * W * ( 1 k ) * tan β 2 ( 5 ) For geometrically similar impellers W is proportional to D. For given k and β 2 values the flow can be expressed as: q α N * D 3 ( 6 ) The ratio of equations (5) and (6) is defined as the Flow Number, N Q, and written as: N Q = q / ( N * D 3 ) (7) For marine propellers β 2 values can be considered constant. For turbines β 2 values are a function of the relative impeller and tank diameter size. Typically the design of agitated baffled vessels uses the Flow Number to be: For marine propellers: N Q = 0.5 For six bladed- turbines: N Q = 0.93 * T / D Page 3 of 23

5 where : T = diameter of the vessel or tank. The power input to a frictionless impeller is derived in detail from a Bernoulli energy balance equation, in reference 1 page 190. This relationship is where: P Delivered * g c = m * ω * r 2 * V u2 (8) P Delivered = Power delivered in ft-lb f /sec. g c = Newton s-law proportionality factor, 32.2 ft-lb m /lb f - sec 2. m = mass flow rate in lb./sec. ω = angular velocity in radians/sec. r 2 = radius of impeller The right hand side of equation (8) can be re-written as equation (9) by substituting for ω = 2 * π * N, and r 2 = D/2: P Delivered * g c = m * π * D * N * V u2 (9) Substituting equation (1) and m = ρ B * q into equation (9) yields: where: P Delivered * g c = π 2 * ρ B * q * k * D 2 * N 2 (10) Page 4 of 23

6 ρ B = batch liquid density at the average batch temperature, lb./cu. ft. Substituting equation (5) into equation (10) and rearranging into dimensionless form yields: (P Delivered * g c ) / ( N 3 * D 5 * ρ B ) = π 4 * ( W / D ) * ( 1 k ) * tan β 2 (10) The left-hand side of equation (10) is called the power number, N P : N P = (P Delivered * g c ) / ( N 3 * D 5 * ρ B ) (11) P Delivered = N P * ( N 3 * D 5 * ρ B ) / g c (12) The right-hand side of equation (10) indicates that the power number, N P, depends on the ratio of width of the impeller blades to impeller diameter, W / D, as well as k and β 2. The values of k and β 2 vary with many parameters of the system and cannot be predicted theoretically. They must be found by experiment. As a side note, the power number, flow number and k are related by dividing equation (10) by the term ( ρ B * D 5 * N 3 ) and using the definitions of equations (7) and (11) to result in: k = π 2 * ( N P / N Q ) (13) Calculation of Agitated Liquid Batch Power Numbers To determine the power delivered to a given fluid at a set rotational speed, several other variables are also required. These variables relate to the vessel geometry and other shape parameters. A number of benchmark studies were done by J. H. Rushton, Reference # 10, in the 1950 s to correlate power number with know vessel Page 5 of 23

7 geometry and shape parameters. The basis for the power correlations was done using a modified Reynolds number that was specific for agitated liquid batches. The agitated liquid batch Reynolds number indicates the flow of momentum associated with the bulk motion of the fluid. The Reynolds number is defined for agitated batch liquids as: N Re = ( D 2 * N * ρ B / μ B B ) (14) μ B = viscosity of the batch liquid at the average batch liquid temperature, lb./hr-ft. D = agitator cross sectional diameter measured tip to tip, ft. N = agitator speed, revolutions per hour. Figure 4 is a typical power correlation curve for agitated liquid batches. Both of the axes are defined in logarithmic scale. The x-axis is the Reynolds number as calculated by equation (14). The y-axis is the experimentally determined power number. The plot indicates that at various stages of flow regimes; laminar, transitional, and turbulent, the power number varies with the Reynolds number. It can be seen from the plot, which as the Reynolds number is increased from early stages of turbulence to increasingly larger Reynolds numbers, the power number becomes constant. This course will focus on the mechanical power requirements for liquid batches in the turbulent flow regime, as defined as: N Re > 10,000 (15) All power numbers reported within this course will deal with correlation results in the turbulent flow regime and be reported as a constant. Power number constants are listed in Table 2 for the various impeller types shown in Figure 3. Figure 5 and Table 1 are references for the various shape parameters that impact the power number. The example that follows will demonstrate how to determine motor power requirements for agitated liquid batches. Page 6 of 23

8 The selection of an electric motor required to deliver the design power to an application consists of two additional steps after the power delivered has been calculated from equations (12) and (14). N Re = ( D 2 * N * ρ B / μ B B ) (14) P Delivered = N P * ( N 3 * D 5 * ρ B ) / g c (12) Given known values for fluid properties, impeller diameter, and rotational speed, along with the power number from the appropriate correlation, the first step is an adjustment for friction losses. These losses are from the loss of usable energy in the form of work though the motor, shaft gearing, and bearings. P Motor = P Delivered / ( 100 %Losses ) (16) The second step round up motor horsepower to closest higher standard size. Table 4, Three-Phase Electric Motor Sizes, is provided for the student s use. P Design = P Motor (17) A rule of thumb that has been utilized as a rough guide for quickly estimating mechanical agitator power requirements for water is given in Table 5. Page 7 of 23

9 Application Equations Mechanical agitator power requirements for liquid batches are calculated by determining the power number, N P, for a given system and correcting for motor, gearing and bearing losses. Design specification of the motor is then determined by selecting the closest higher standard size. The system turbulence is checked by calculating the Reynolds number for the agitation system. Adequate turbulence is defined at Reynolds numbers greater than 10,000. Shape factors S1 through S9 are calculated using the mixing vessel geometry as defined in Table 1 and shown in Figure 5. A power number is then obtained by comparing the shape factor results with published power correlations. Table 2 is provided for six types of typical agitator impellers. N Re = ( D 2 * N * ρ B / μ B B ) (14) P Delivered = N P * ( N 3 * D 5 * ρ B ) / g c (12) P Motor = P Delivered / ( 100 %Losses ) (16) P Design = P Motor (17) Page 8 of 23

10 Table 1. Shape Factor Descriptions and Definitions. For use with Table 2 and Figure 5. Shape Factor Ratio Description S1 T/D Tank Diameter/Impeller Diameter S2 Z/D Height of Impeller above vessel floor/impeller Diameter S3 L/D Length of impeller blade/impeller Diameter S4 D/W Impeller Diameter/Width of blade S5 T/B Tank Diameter/Baffle width S6 H/D Liquid depth in vessel/impeller Diameter S7 # Number of impeller blades S8 degrees pitch/angle S9 # Number of baffles Page 9 of 23

11 Table 2. Power Numbers, N P, for Various Impeller Types and Shape Parameters Impeller Type Ref # S1 S2 S3 S4 S5 S6 S7 S8 S9 Power Number, PO = constant. N Re >10,000 Propeller ND ND pitch=d Propeller ND ND pitch=2d Pitched blade turbine 4 ND ND ND 8 12 ND 6 45 deg Straight full blade turbine 4 ND ND ND 8 12 ND 6 0 deg 4 3 Curved full blade turbine 8 ND ND ND 8 ND ND ND 0 deg ND 2.7 Flat blade turbine Flat blade turbine Flat blade turbine deg deg deg 4 4 Flat paddle deg ND= No Data. Page 10 of 23

12 Table 3. Physical Property Data COMPOUND PHYSICAL PROPERTY REF Water Temperature = 80 deg F Liquid Density = 8.56 lbs./gal 5 Liquid Viscosity = centipoise 5 Page 11 of 23

13 Table 4. Three-Phase Electric Motor Horsepower Sizes MOTOR HP REF #11 Page 12 of 23

14 Table 5. Rule of Thumb Power Ratios for Water AGITATION POWER RATIO HP/1000 GALS Mild Vigorous 2-3 Intensive 4-10 Reference #1 Page 13 of 23

15 Example #1 It is proposed to mix a batch of water at 80 deg F in an agitated vessel similar to the one shown in Figure 1. Calculate the power required, in horse power, for an agitation speed of 60 rpm. Use an approximate loss of efficiency of 20% for the motor, gearbox, and bearings. Can the mixing be considered intensive under these conditions? Equipment details are given below: Equipment Data: Vessel Diameter (T) = 9.0 ft. Impeller Diameter (D) = 3.0 ft. Impeller type = Flat blade turbine. # of blades = 6 Blade width (W) =7 inches. Blade length (L) = 9 inches. Number of Baffles = 4; equally spaced. Baffle width (B) = 11 inches. Liquid Depth (H) = 9.0 feet. Impeller height above vessel bottom (Z) = 3 feet. Step #1.1: Determine the agitated batch liquid physical properties: a. From Table 3. the physical properties of the batch liquid at 80 deg F are: ρ B = Liquid Density = 8.56 lbs./gal μ B = Liquid Viscosity = centipoise Converting liquid density to lbs./cu. ft. requires multiplying the density from Table 3 by 7.48 and results in a liquid density of ρ B = 64.0 lbs./cu. ft. Converting viscosity to lb./hr-ft units requires multiplying the viscosity from Table 3 by 2.42 and results in a liquid viscosity of μ B = 2.12 lb./hr-ft. Page 14 of 23

16 Step #1.2: Determine the agitator speed in appropriate units for Reynolds number calculation: N = revolutions per hour (rph). The agitation speed is given in the example as 60 revolutions per minute, which when multiplied by 60 minutes/hr yields: N = 60 rpm * 60 = 3,600 rph Step #1.3: Determine the agitated batch liquid Reynolds number using equation (14): N Re = Reynolds number for agitated liquids = ( D 2 * N * ρ B / μ B ). N Re = ( * 3,600 * 64.0 / 2.12 ) N Re = 977,035. This exceeds requirement for equation (15) N Re > 10,000 (15) Step #1.4 Determine the values for the shape factors S1 through S9. Using Table 1 and Figure 5 along with the information given in the example yields: S1 = T/D = 9/3 = 3 S2 = Z/D = 3/3 = 1 S3 = L/D = (9/12)/3 = 0.25 S4 = D/W = 3/(7/12) = 5 S5 = T/B = 9/(11/12) = 9.8 S6 = H/D = 9/3 = 3 S7 = 6 S8 = 0 Degrees, no pitch S9 = 4 Page 15 of 23

17 Step #1.5: Determine the appropriate power number N P from the three flat blade turbine impellers listed in Table 2. The flat blade impeller that most closely resembles the shape factors is the second one listed. Its power number N P is: N P = 6 Step #1.6: Determine the agitator speed in appropriate units for power calculation: N = revolutions per sec (rps). The agitation speed is given in the example as 60 revolutions per minute, which when divided by 60 seconds/minute yields: N = 60 rpm / 60 = 1 rps Step #1.7: Determine Power Number from the appropriate correlation, and calculate the uncorrected Power required. The correlations calculate the delivered Power to the fluid. This must be corrected back to the agitator motor and account for efficiency losses in the motor, gearbox, and bearings. P Delivered = ( N P ρ B * N 3 * D A 5 )/ G C P Delivered = 6 * 64 * 1 3 * 3 5 / 32.2 P Delivered = 2,898 ft-lb./sec or using 550 ft-lb./sec per Hp, P Delivered = 5.3 Hp Page 16 of 23

18 Step #1.8: Determine the motor Power required using estimated losses at 30%: P Motor = P Delivered / ( 1 Losses ) P Motor = 5.3 / ( ) P Motor = 6.6 Hp Step #1.9: Round up motor horsepower to closest higher standard size from Table 4: P Motor = 7.5 Hp. Step #1.10: Determine power to volume ratio: P Motor = 7.5 Hp Volume = 5,500 gallons or 5.5 thousand gallons Power Ratio = 7.5 Hp/ 5.5 Power Ratio = 1.4 Can the mixing be considered intensive under these conditions? No. From Table 5 the agitation is between mild and vigorous. Page 17 of 23

19 Figure 1. Agitated Liquid Batch Vessel Data: Volume= 5,500 gals Diameter = 9 feet Baffles: 4 equally spaced Baffle width = 11 inches Agitator Motor Speed = 60 rpm Liquid Level = 9 feet Liquid Volume = 5,000 gals Fluid = Water Viscosity = cp. Density = 8.56 lbs./gal Temperature = 80 F Baffles Baffles John F. Pietranski, PhD, PE December 2002 Impeller Data: Flat Blade Turbine Six (6) Blades Diameter = 3.0 feet Blade width = 7 inches Blade length = 9 inches Impeller height = 3 feet Page 18 of 23

20 Figure 2. Agitated Liquid Batch Flow Patterns Axial Flow Pattern for Marine Impeller Radial Flow Pattern for Flat Blade Turbine Impeller John F. Pietranski, PhD, PE December 2002 Reference #9. Page 19 of 23

21 Figure 3. Impeller Types A. Marine Propeller, Ref #4. B. CurvedFull Blade Turbine, Ref #4. C. Pitched Blade Turbine, Ref #4. D. Flat Bade Turbine, Ref #4. E. Straight Full Blade Turbine, F. Flat Paddle, Ref #6. Ref #1. John F. Pietranski, PhD, PE December 2002 Page 20 of 23

22 Figure 4. Typical Power Curve for Agitator Impellers Np Np Np Np Reference #9. John F. Pietranski, PhD, PE December 2002 Page 21 of 23

23 Figure 5. Agitated Liquid Batch Shape Parameters Baffle width, B Blade Length, L Liquid Height, H Blade Width, W Impeller Diameter, D Impeller Depth, Tank Diameter, T Reference #9. John F. Pietranski, PhD, PE December 2002 Page 22 of 23

24 Page 23 of 23

### Over-all Heat Transfer Coefficients in Agitated Vessels

PDHonline Course K102 (4 PDH) Over-all Heat Transfer Coefficients in Agitated Vessels Instructor: John Frank Pietranski, P.E., Ph.D. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658

### Mixing in the process industry: Chemicals Food Pharmaceuticals Paper Polymers Minerals Environmental. Chemical Industry:

Mixing Notes: Chapter 19 Robert P. Hesketh Mixing in the process industry: Chemicals Food Pharmaceuticals Paper Polymers Minerals Environmental Chemical Industry: Paints and Coatings Synthetic Rubbers

### 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

### 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

### 5.1-Angles and Their Measure

5.1-Angles and Their Measure Objectives: 1. Find the degree or radian measure of co-terminal angles. 2. Convert between degrees minutes and seconds and decimal degrees. 3. Convert between degrees and radians.

### Civil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes

Civil Engineering Hydraulics Mechanics of Fluids Flow in Pipes 2 Now we will move from the purely theoretical discussion of nondimensional parameters to a topic with a bit more that you can see and feel

### FLUID FLOW AND MIXING IN BIOREACTORS (Part 2 of 2)

FLUID FLOW AND MIXING IN BIOREACTORS (Part 2 of 2) Overview Power requirements for mixing Newtonian and non-newtonian liquids Ungassed and gassed systems Scale-up issues, scale-down approach Adapting bioreactor

### Understanding Pump and Suction Specific Speeds

PDHonline Course M136 (2 PDH) Understanding Pump and Suction Specific Speeds Instructor: Randall W. Whitesides, PE 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax:

### AGITATION AND MIXING OF FLUIDS

AGITATION AND MIXING OF FLUIDS Purpose of agitation: intensification of transport processes in agitated batch (heat and mass transfer) preparation of materials of required properties (suspension, emulsion)

### CENTRIFUGAL PUMP SELECTION, SIZING, AND INTERPRETATION OF PERFORMANCE CURVES

CENTRIFUGAL PUMP SELECTION, SIZING, AND INTERPRETATION OF PERFORMANCE CURVES 4.0 PUMP CLASSES Pumps may be classified in two general types, dynamic and positive displacement. Positive displacement pumps

### 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

### Module 9: Basics of Pumps and Hydraulics Instructor Guide

Module 9: Basics of Pumps and Hydraulics Instructor Guide Activities for Unit 1 Basic Hydraulics Activity 1.1: Convert 45 psi to feet of head. 45 psis x 1 ft. = 103.8 ft 0.433 psi Activity 1.2: Determine

### TANKJKT. Heat Transfer Calculations for Jacketed Tanks SCREEN SHOTS. Copyright 2015. By chemengsoftware.com

TANKJKT Heat Transfer Calculations for Jacketed Tanks SCREEN SHOTS Copyright 2015 By chemengsoftware.com Visit http://www.pipesizingsoftware.com/ for further information and ordering The following page

### Induction Motor Theory

PDHonline Course E176 (3 PDH) Induction Motor Theory Instructor: Jerry R. Bednarczyk, P.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org

### Hydrodynamics for Ocean Engineers Prof. A.H. Techet Fall 2004

13.012 Hydrodynamics for Ocean Engineers Prof. A.H. Techet Fall 2004 Marine Propellers Today, conventional marine propellers remain the standard propulsion mechanism for surface ships and underwater vehicles.

### 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

### 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

### Selecting a Vertical Turbine Pump (Information required from client)

Selecting a Vertical Turbine Pump (Information required from client) 1. Liquid to be pumped: (Note: If liquid is not clear water, the following must also be ascertained). a. Foreign material present in

### FILTRATION. Introduction. Batch Filtration (Small Scale) Controlling parameters: Pressure drop, time for filtration, concentration of slurry

FILTRATION Introduction Separation of solids from liquids is a common operation that requires empirical data to make predictions of performance. These data are usually obtained from experiments performed

### AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL

14 th European Conference on Mixing Warszawa, 10-13 September 2012 AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL Joanna Karcz, Lukasz Kacperski

### FILTRATION. Introduction

FILTRATION Introduction Separation of solids from liquids is a common operation that requires empirical data to make predictions of performance. These data are usually obtained from experiments performed

### Pipe Flow-Friction Factor Calculations with Excel

Pipe Flow-Friction Factor Calculations with Excel Course No: C03-022 Credit: 3 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980

### Tips For Selecting DC Motors For Your Mobile Robot

Tips For Selecting DC Motors For Your Mobile Robot By AJ Neal When building a mobile robot, selecting the drive motors is one of the most important decisions you will make. It is a perfect example of an

### 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

### International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015

International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):2278-5299 EXPERIMENTAL STUDY

### Chapter 3.5: Fans and Blowers

Part I: Objective type questions and answers Chapter 3.5: Fans and Blowers 1. The parameter used by ASME to define fans, blowers and compressors is a) Fan ration b) Specific ratio c) Blade ratio d) Twist

### Propeller Efficiency. Rule of Thumb. David F. Rogers, PhD, ATP

Propeller Efficiency Rule of Thumb David F. Rogers, PhD, ATP Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller. Here, think the Osprey or helicopters.

### Centripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.

Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.

### 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

### Direct Conversion of Wind Energy into Heat Using Joule Machine

International Conference on Environmental and Computer Science ICBEE vol.9() () IACSI ress, Singapore Direct Conversion of Wind Energy into Heat Using Joule Machine Roustiam Chakirov, and Yuriy Vagapov

### HEAVY OIL FLOW MEASUREMENT CHALLENGES

HEAVY OIL FLOW MEASUREMENT CHALLENGES 1 INTRODUCTION The vast majority of the world s remaining oil reserves are categorised as heavy / unconventional oils (high viscosity). Due to diminishing conventional

### Pressure Effect on Turbine Meter Gas Flow Measurement

Pressure Effect on Turbine Meter Gas Flow Measurement Paul W. Tang, M.Sc.,P.Eng. Fortis BC Energy 16705 Fraser Highway Surrey, B.C. V4N0E8 Canada Abstract: Pressure sensitivity of turbine gas meters is

### Electric Motors and Drives

EML 2322L MAE Design and Manufacturing Laboratory Electric Motors and Drives To calculate the peak power and torque produced by an electric motor, you will need to know the following: Motor supply voltage,

### Pumps: Convert mechanical energy (often developed from electrical source) into hydraulic energy (position, pressure and kinetic energy).

HYDRAULIC MACHINES Used to convert between hydraulic and mechanical energies. Pumps: Convert mechanical energy (often developed from electrical source) into hydraulic energy (position, pressure and kinetic

### Chapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.

Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems

### Solution: Angular velocity in consistent units (Table 8.1): 753.8. Velocity of a point on the disk: Rate at which bits pass by the read/write head:

Problem P8: The disk in a computer hard drive spins at 7200 rpm At the radius of 0 mm, a stream of data is magnetically written on the disk, and the spacing between data bits is 25 μm Determine the number

### GEAROLOGY 4-1 WORMS AND WORM GEARS WORMS AND WORM GEARS

GEAROLOGY 4-1 4 4-2 GEAROLOGY COMMON APPLICATIONS: Worm and worm gear sets are used in many, everyday products including: electrical mixers, hubometers, right Now that you have an understanding of two

### CHARGE TO MASS RATIO OF THE ELECTRON

CHARGE TO MASS RATIO OF THE ELECTRON In solving many physics problems, it is necessary to use the value of one or more physical constants. Examples are the velocity of light, c, and mass of the electron,

### 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

### Calculating Motor Start Time

Calculating Motor Start Time Timothy L. O'Hearn, P.E. Course Outline In this course, a method is described to approximate the motor starting time using the characteristics provided by the manufacturer.

### 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

### 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

### Working Math Formulas, Units, Conversions

Working Math Formulas, Units, Conversions This presentation has been adapted from Math for Subsurface Operators given at the North Carolina Subsurface Operator School Math will be used to Determine a flow

### Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher

Higher Technological Institute Civil Engineering Department Lectures of Fluid Mechanics Dr. Amir M. Mobasher 1/14/2013 Fluid Mechanics Dr. Amir Mobasher Department of Civil Engineering Faculty of Engineering

### 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

### WebAssign Lesson 3-3 Applications (Homework)

WebAssign Lesson 3-3 Applications (Homework) Current Score : / 27 Due : Tuesday, July 15 2014 11:00 AM MDT Jaimos Skriletz Math 175, section 31, Summer 2 2014 Instructor: Jaimos Skriletz 1. /3 points A

### Pump ED 101. Positive Displacement Pumps. Part I Reciprocating Pumps

Pump ED 101 Positive Displacement Pumps Part I Reciprocating Pumps Joe Evans, Ph.D http://www.pumped101.com There are many pump designs that fall into the positive displacement category but, for the most

### For Water to Move a driving force is needed

RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

### Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

### What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation)

OPEN CHANNEL FLOW 1 3 Question What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation) Typical open channel shapes Figure

### Experiment (13): Flow channel

Introduction: An open channel is a duct in which the liquid flows with a free surface exposed to atmospheric pressure. Along the length of the duct, the pressure at the surface is therefore constant and

### A Guide to Calculate Convection Coefficients for Thermal Problems Application Note

A Guide to Calculate Convection Coefficients for Thermal Problems Application Note Keywords: Thermal analysis, convection coefficients, computational fluid dynamics, free convection, forced convection.

### Pfaudler Mixing Systems. Reduce processing times and save costs

Pfaudler Mixing Systems Reduce processing times and save costs R E A C T O R S Y S T E M S Reduce processing times and save costs with Pfaudler Mixing Systems PFAUDLER-BALFOUR - a worldwide leader in the

### 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

### Module 2: Review of Fluid Mechanics Basic Principles for Water Resources Engineering. Basic Definitions. Basic Definitions.

Module : Review of Fluid Mechanics Basic Principles for Water Resources Engineering Robert Pitt University of Alabama and Shirley Clark Penn State - Harrisburg Mass quantity of matter that a substance

### Technical Bulletin TB8102 Rupture Disc Sizing

Technical Bulletin TB8102 Rupture Disc Sizing The objective of this bulletin is to provide detailed guidance for sizing rupture discs using standard methodologies found in ASME Section VIII Div. 1, API

### Chapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations

Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.

### Question 1. Problem statement. Problem solution

TP III Fluid Mechanics Problem Sheet 5: Two-phase Flows in Pipes 1 Prof. Omar K. Matar, Department of Chemical Engineering, Imperial College London, ACEX 517, o.matar@imperial.ac.uk. Question 1 Problem

### 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,

### Open Channel Flow Measurement Weirs and Flumes

Open Channel Flow Measurement Weirs and Flumes by Harlan H. Bengtson, PhD, P.E. 1. Introduction Your Course Title Here Measuring the flow rate of water in an open channel typically involves some type of

### GEAROLOGY 2-1 SPUR GEARS SPUR GEARS

GEAROLOGY 2-1 2 2-2 GEAROLOGY COMMON APPLICATIONS: Spur gears are used to Now that you ve been introduced to both Boston Gear and some of the basics of our Gearology course which we like to call Power

### PDHonline Course S151A (1 PDH) Steel Sheet Piling. Instructor: Matthew Stuart, PE, SE. PDH Online PDH Center

PDHonline Course S151A (1 PDH) Steel Sheet Piling Instructor: Matthew Stuart, PE, SE 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088 www.pdhonline.org

### Pump Formulas Imperial and SI Units

Pump Formulas Imperial and Pressure to Head H = head, ft P = pressure, psi H = head, m P = pressure, bar Mass Flow to Volumetric Flow ṁ = mass flow, lbm/h ρ = fluid density, lbm/ft 3 ṁ = mass flow, kg/h

### Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

### International Journal of TechnoChem Research. Eldho Abraham

International Journal of TechnoChem Research ISSN: 2395-4248 www.technochemsai.com Vol.01, No.01, pp 25-34, 2015 Study on Gas Induction and Comparison of Power Consumption of Gas Inducing Mechanically

### 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

### Selecting a Centrifugal Pump to Handle a Viscous Liquid

Copyright 2002, 2005, 2008 Randall W. Whitesides, P.E. Introduction This course provides the student with an understanding of fluid viscosity and its effects on the performance of centrifugal pump operation.

### STUDY OF MIXING BEHAVIOR OF CSTR USING CFD

Brazilian Journal of Chemical Engineering ISSN 0104-6632 Printed in Brazil www.abeq.org.br/bjche Vol. 31, No. 01, pp. 119-129, January - March, 2014 STUDY OF MIXING BEHAVIOR OF CSTR USING CFD D. Rajavathsavai,

### DRAFTING MANUAL. Gears (Bevel and Hypoid) Drafting Practice

Page 1 1.0 General This section provides the basis for uniformity in engineering gears drawings and their technical data for gears with intersecting axes (bevel gears), and nonparallel, nonintersecting

### Pacific Pump and Power

Pacific Pump and Power 91-503 Nukuawa Street Kapolei, Hawaii 96707 Phone: (808) 672-8198 or (800) 975-5112 Fax: (866) 424-0953 Email: sales@pacificpumpandpower.com Web: www.pacificpumpandpower.com Table

### Understanding Plastics Engineering Calculations

Natti S. Rao Nick R. Schott Understanding Plastics Engineering Calculations Hands-on Examples and Case Studies Sample Pages from Chapters 4 and 6 ISBNs 978--56990-509-8-56990-509-6 HANSER Hanser Publishers,

### HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS

HEAT TRANSFER AUGMENTATION THROUGH DIFFERENT PASSIVE INTENSIFIER METHODS P.R.Hatwar 1, Bhojraj N. Kale 2 1, 2 Department of Mechanical Engineering Dr. Babasaheb Ambedkar College of Engineering & Research,

### 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

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### An Attempt towards Performance Optimization. Presented By : Kripal lakhi Singh Chemical Engineering IIT Madras

An Attempt towards Performance Optimization Presented By : Kripal lakhi Singh Chemical Engineering IIT Madras A cooling tower in its most generic sense,is a heat rejection device, which extracts waste

### INTERIM UNITS OF MEASURE As suggested by Federal Standard 376B January 27, 1993. hectare (ha) Hundred for traffic buttons.

SI - The Metrics International System of Units The International System of Units (SI) is a modernized version of the metric system established by international agreement. The metric system of measurement

### Battery Thermal Management System Design Modeling

Battery Thermal Management System Design Modeling Gi-Heon Kim, Ph.D Ahmad Pesaran, Ph.D (ahmad_pesaran@nrel.gov) National Renewable Energy Laboratory, Golden, Colorado, U.S.A. EVS October -8, 8, 006 Yokohama,

### Foundations and Mathematical Application of the Water Rocket

Foundations and Mathematical Application of the Water Rocket Students Utilize 2-Liter Bottle Rocket Launcher will help students to explore the science of rocketry. Students build &propel 2-liter bottle

### ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates

### Drill Bit Nozzle Pressure Loss

AADE-10-DF-HO-26 Drill Bit Nozzle Pressure Loss [EXPLOITATION OF FINAGLE FACTOR TECHNOLOGY] Leon Robinson, Retired Copyright 2010, AADE This paper was prepared for presentation at the 2010 AADE Fluids

### Hydraulic Jumps and Non-uniform Open Channel Flow, Course #507. Presented by: PDH Enterprises, LLC PO Box 942 Morrisville, NC 27560 www.pdhsite.

Hydraulic Jumps and Non-uniform Open Channel Flow, Course #507 Presented by: PDH Enterprises, LLC PO Box 942 Morrisville, NC 27560 www.pdhsite.com Many examples of open channel flow can be approximated

### Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN

Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN Contents 7.1 Spur gear tooth force analysis 7.2 Spur gear - tooth stresses 7.3 Tooth bending stress Lewis equation 7.4 Tooth bending stress AGMA procedure

### Objective - Determining characteristic curve of a four-stroke Diesel engine - Calculating thermal efficiency of the engine

Objective - Determining characteristic curve of a four-stroke Diesel engine - Calculating thermal efficiency of the engine Apparatus The experimental setup, shown in Fig. 1, has three main parts: engine,

### Gear Engineering Data. Spur Gear Gear Formulas Drive Selection Horsepower and Torque Tables

Engineering Gear Engineering Data Spur Gear Gear Formulas Drive Selection Horsepower and Torque Tables G-79 Gear Selection Stock Spur Gear Drive Selection When designing a stock gear drive using the horsepower

### Macroscopic Balances for Nonisothermal Systems

Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

### 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

### Diametral Pitch Gear Ratios Herringbone Gears Idler Gear Involute Module Pitch Pitch Diameter Pitch Point. GEARS-IDS Optional Gear Set Straight Edge

105 Webster St. Hanover Massachusetts 02339 Tel. 781 878 1512 Fax 781 878 6708 www.gearseds.com Spur Gear Terms and Concepts Description In order to design, build and discuss gear drive systems it is necessary

### Undergraduate Turbomachine Design Using CFD and 3-D Printing

Undergraduate Turbomachine Design Using CFD and 3-D Printing John Abbitt University of Florida Abstract For the past year, Mechanical & Aerospace Engineering students at the University of Florida have

### The Pressure Velocity (PV) Relationship for Lead Screws

The Pressure Velocity (PV) Relationship for Lead Screws Robert Lipsett, Engineering Manager Thomson Industries, Inc. Wood Dale, IL 540-633-3549 www.thomsonlinear.com The Pressure Velocity (PV) factor is

### Contents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1

Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

### Journal bearings/sliding bearings

Journal bearings/sliding bearings Operating conditions: Advantages: - Vibration damping, impact damping, noise damping - not sensitive for vibrations, low operating noise level - dust tight (if lubricated

### 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:

### A BRIEF INTRODUCTION TO CENTRIFUGAL PUMPS

A BRIEF INTRODUCTION TO CENTRIFUGAL PUMPS figure below is a cross section of a centrifugal pump and shows the two basic parts. Joe Evans, Ph.D IMPELLER This publication is based upon an introductory, half

### Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli 620 015, Tamil Nadu, India

Experimental Thermal and Fluid Science 32 (2007) 92 97 www.elsevier.com/locate/etfs Studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with right

### SIMPLIFIED METHOD FOR ESTIMATING THE FLIGHT PERFORMANCE OF A HOBBY ROCKET

SIMPLIFIED METHOD FOR ESTIMATING THE FLIGHT PERFORMANCE OF A HOBBY ROCKET WWW.NAKKA-ROCKETRY.NET February 007 Rev.1 March 007 1 Introduction As part of the design process for a hobby rocket, it is very

### Pump Selection and Sizing (ENGINEERING DESIGN GUIDELINE)

Guidelines for Processing Plant Page : 1 of 51 Rev 01 Feb 2007 Rev 02 Feb 2009 Rev 03 KLM Technology #03-12 Block Aronia, Jalan Sri Perkasa 2 Taman Tampoi Utama 81200 Johor Bahru. (ENGINEERING DESIGN GUIDELINE)

### Selection Of Centrifugal Pumping Equipment 1

Circular 1048 Selection Of Centrifugal Pumping Equipment 1 Dorota Z. Haman, Fedro S. Zazueta, Forrest T. Izuno 2 INTRODUCTION The pump is an essential component of an irrigation system. Proper selection

### BSM MOTOR DRIVEN CENTRIFUGAL PUMPS

PRINCIPLE OF OPERATION A hydraulically and dynamically balanced impeller with raised vane sections discharges liquid as a result of the centrifugal force developed in rotation. The head developed is entirely