# Pipe Flow Calculations

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Pipe Flow Calculation R. Shankar Subramanian epartment o Chemical and Biomolecular Engineering Clarkon Univerity We begin with ome reult that we hall ue when making riction lo calculation or teady, ully developed, incompreible, Newtonian low through a traight circular pipe. π Volumetric low rate Q= V where i the pipe diameter, and V i the average velocity. V ρ V Q m Reynold Number: Re = = = = where ρ i the denity o the µ ν π ν π µ luid, µ i it dynamic vicoity, and ν = µ / ρ i the kinematic vicoity. The preure drop P i related to the lo in the Engineering Bernoulli Equation, or equivalently, the rictional head lo h, through P= ρ lo = γ h Here, the peciic weight γ = ρ g, where g i the magnitude o the acceleration due to gravity. Power The power required to overcome riction i related to the preure drop through Power = PQ or we can relate it to the head lo due to pipe riction via Power = γ h Q Head o/preure rop The head lo h i related to the Fanning riction actor through h V = g = or alternatively we can write the preure drop a P ( ρ V ) Friction Factor 16 In laminar low, =. Re In turbulent low we can ue either the Colebrook or the Zigrang-Sylveter Equation, depending on the problem. Both give equivalent reult well within experimental uncertainty. In thee equation, ε i the average roughne o the interior urace o the pipe. A table o roughne 1

2 value recommended or commercial pipe given in a textbook on Fluid Mechanic by F.M. White i provided at the end o thee note. Colebrook Equation 1 ε / 1.6 =.0 log +.7 Re Zigrang-Sylveter Equation 1 ε / 5.0 ε / 1 =.0 log log +.7 Re.7 Re Non-Circular Conduit Not all low conduit are circular pipe. An example o a non-circular cro-ection in heat exchanger application i an annulu, which i the region between two circular pipe. Another i a rectangular duct, ued in HVAC (Heating, Ventilation, and Air-Conditioning) application. e common are duct o triangular or elliptical cro-ection, but they are ued on occaion. In all thee cae, when the low i turbulent, we ue the ame riction actor correlation that are ued or circular pipe, ubtituting an equivalent diameter or the pipe diameter. The equivalent diameter, which i et equal to our time the Hydraulic Radiu, R i deined a ollow. e h e Cro - Sectional Area = Rh = Wetted Perimeter In thi deinition, the term wetted perimeter i ued to deignate the perimeter o the croection that i in contact with the lowing luid. Thi applie to a liquid that occupie part o a conduit, a in ewer line carrying wate-water, or a creek or river. I a ga low through a conduit, the entire perimeter i wetted. Uing the above deinition, we arrive at the ollowing reult or the equivalent diameter or two common cro-ection. We aume that the entire perimeter i wetted. Rectangular uct b For the duct hown in the ketch, the cro-ectional area i ab, while the perimeter i ( a+ b) o that the equivalent diameter i written a ollow. a

3 e ab = = ( a+ b) a b I the low i laminar, a reult imilar to that or circular tube i available or the riction actor, which can be written a = C/ Re, where C i a contant that depend on the apect ratio a/ b, and the Reynold number i deined uing the equivalent diameter. A ew value o the contant C or elected value o the apect ratio are given in the Table below (Source: F.M. White, Fluid Mechanic, 7 th Edition). For other apect ratio, you can ue interpolation. a/ b C a/ b C Annulu a b The cro-ectional area o the annulu hown i ( a b ) π ( a+ b). Thereore, the equivalent diameter i obtained a ( a b ) π e = = a b π ( a+ b) π, while the wetted perimeter i Again, or laminar low, we ind that = C/ Re, where C i a contant that depend on the apect ratio a/ b, and the Reynold number i deined uing the equivalent diameter. A with the rectangular cro-ection, a ew value contant C or elected value o the apect ratio are given in the Table that ollow (Source: F.M. White, Fluid Mechanic, 7 th Edition). For other apect ratio, you can ue interpolation.

4 a/ b C a/ b C , Minor oe Minor loe i a term ued to decribe loe that occur in itting, expanion, contraction, and the like. Fitting commonly ued in the indutry include bend, tee, elbow, union, and o coure, valve ued to control low. Even though thee loe are called minor, they can be ubtantial compared to thoe or low through hort traight pipe egment. oe are V / g. Thereore, we can write commonly reported in velocity head. A velocity head i minor loe a h m V = K, where K i called the lo coeicient. g Typical value o K or ome common itting are given below. Uually, the value depend upon the nominal pipe diameter, the Reynold number, and the manner in which the valve i intalled (crewed or langed). Manuacturer data hould be ued wherever poible. Globe Valve (ully open): Gate Valve (ully open): Swing Check Valve (ully open): Standard 5 o Elbow: ong radiu 5 o Elbow: Standard 90 o Elbow: ong radiu 90 o Elbow: Tee: When olving homework problem, ue the value given in Table 1.1 in the textbook by Welty et al. Sudden Expanion and Sudden Contraction A udden expanion in a pipe i one o the ew cae where the loe can be obtained rom the baic balance. The expreion or K i given by K d = 1

5 Here, d and repreent the diameter o the maller and larger pipe, repectively. For a udden contraction, we can ue the ame reult i d / For maller value o d / we can ue the empirical relation K = 0. 1 d /. In both cae, we hould multiply K by the velocity head in the pipe egment o diameter d. The loe would be maller i the expanion or contraction i gradual. When a pipe emptie into a reervoir, all the kinetic energy in the luid coming in i diipated, o that you can treat thi a a udden expanion with the ratio d / = 0, yielding K = 1. Typical Pipe Flow Problem In typical pipe low problem, we know the nature o the luid that will low through the pipe, and the temperature. Thereore, we can ind the relevant phyical propertie immediately. They are the denity ρ and the dynamic vicoity µ. Knowing thee propertie, we alo can calculate the kinematic vicoity ν = µ / ρ. The length o the pipe can be etimated rom proce equipment layout conideration. The nature o the luid to be pumped will dictate corroion contraint on the pipe material. Other conideration are cot and eae o procurement. Baed on thee, we can elect the material o the pipe to be ued, and once we do, the roughne ε can be peciied. Thi leave u with three unpeciied parameter, namely the head lo h or equivalently, the preure drop required to pump the luid p, the volumetric low rate Q (or equivalently the ma low rate), and the pipe diameter. Unle we plan to alo optimize the cot, two o thee mut be peciied, leaving only a ingle parameter to be calculated. Thu, pipe low problem that do not involve cot optimization will all into three broad categorie. 1. Given and Q, ind the head lo h. Given and h, ind the volumetric low rate Q. Given Q and h, ind the diameter Each o thee three type o problem i illutrated next with a numerical example. 5

6 Example 1 Find the head lo due to the low o 1,500 gpm o oil ( ν = 1.15 t / ) through 1,600 eet o 8" diameter cat iron pipe. I the denity o the oil ρ = 1.75 lug / t, what i the power to be upplied by a pump to the luid? Find the BHP o the pump i it eiciency i Solution We have the ollowing inormation. ρ = 1.75 lug / t ν = 1.15 t / = t Thereore, the cro-ectional area i A = π / = π t / = 0.9 t 1 t / t Q = 1500 ( gpm) =. 8.8 ( gpm) Thereore, the average velocity through the pipe i V We can calculate the Reynold number. ( t ) ( t ) = Q. / A = 0.9 = 9.58 t ( t) ( t ) V / Re = = = 5.55 ν ( t ) 1.15 / Thereore, the low i turbulent. For cat iron, ε = 8.5 t. Thereore, the relative roughne i ( t) ( t) ε 8.5 = = Becaue we have the value o both the Reynold number and the relative roughne, it i eicient to ue the Zigrang-Sylveter equation or a once-through calculation o the turbulent low riction actor. 1 ε / 5.0 ε / 1 =.0 log log +.7 Re.7 Re =.0 log log = which yield =

7 The head lo i obtained by uing ( t) ( t ) V 1, / h = = = 8.7 t g t. t / The ma low rate i m = ρ Q= = 5.85 The power upplied to the luid i calculated rom lug t lug t lug t t lb Power to Fluid = m h g = ( t). = 1.58 t lb We know that 1 HorePower = 550. Thereore, Power to Fluid = 8.7 hp The eiciency o the pump η = Thereore, 8.7 ( hp) Power to Fluid Brake Hore Power = = =.7 hp η 0.85 Example Water at 15 C low through a 5 cm diameter riveted teel pipe o length 50 m and roughne ε =. mm. The head lo i known to be 7.0 m. Find the volumetric low rate o water in the pipe. Solution For water at 15 C, ρ = 999 kg / m 6 calculated a ν = µ / ρ = 1.16 m / µ = 1.16 Pa o that the kinematic vicoity can be The pipe diameter i given a = 0.5 m, o that the cro-ectional area i A= π / = π 0.5 m / =.91 m The length o the pipe i given a = 50 m We do not know the velocity o water in the pipe, but we can expre the Reynold number in term o the unknown velocity. ( m) V 0.5 V 5 Re = = =.16 V ν ( m ) / where V mut be in m/. At thi point, we do not know whether the low i laminar or turbulent. Given the ize o the pipe and the head lo, it i reaonable to aume turbulent low and proceed. In the end, we need to check whether thi aumption i correct. 7

8 Now, we are given the head lo h. et u write the reult or h in term o the riction actor. V h = Subtitute the value o known entitie in thi equation. g 50 ( m) V 7.0 ( m) = 0.5 ( m) Thi can be rearranged to yield 9.81 ( m/ ) V m = 1.99 where V mut be in m/. Taking the quare root, we ind 0.11 = V We can ee that the product Re can be calculated, even though we do not know the velocity V. Re =.16 V =.05 V Given ε =. mm, the relative roughne i ε. ( m) = = m Thereore, the entire right ide in the Colebrook Equation or the riction actor i known. We can ue the Colebrook Equation to evaluate the riction actor in an once-through calculation. ε =.0 log + =.0 log = Re / Thereore, the riction actor i = Uing =, we can evaluate the velocity a V 0.11 ( m/ ) 0.11 ( m/ ) V = = = 1.9 m/ o that the volumetric low rate i obtained a 0. Q = VA = 1.9 m /.91 m = We mut check the Reynold number. Re =.16 V =.00. Thi i well over,000 o that we can conclude that the aumption o turbulent low i correct. m 8

9 Example etermine the ize o mooth 1-gage BWG copper tubing needed to convey gpm o a 5 proce liquid o kinematic vicoity ν =.0 t / over a ditance o 1 t at ground level uing a torage tank at an elevation o 0 t. You can aume minor loe rom itting in the line to account or 5 t o head. In thi problem, we are aked to calculate the diameter o the tube. We are given = 150 t 1 t / t and Q = gpm =.. Given that the torage tank i located at an 8.8( gpm) elevation o 0 t above ground, we can iner that the available head lo or riction in the low h = 0 5 t = 15 t. through the tube i The diameter appear in both the Reynold number and the reult or the head lo in term o the riction actor. et u begin with the head lo and write it in term o the volumetric low rate, which i known. ( Q π ) / V Q h = = = g g π g Subtituting known entitie in thi equation, we obtain 5. ( t / ) 1 t. t / 15 t = = π where mut be in eet. 5 o that =.6 5 The Reynold number can be written a ( t ) Q. / 1.18 Re = = = 5 πν π.0 t / 9 where mut be in eet. We can make urther progre i we aume the type o low, o that we can ue a correlation or the riction actor. It i reaonable in proce ituation with thi low rate to aume turbulent low. So, we hall proceed with that aumption, to be veriied later when we can calculate the Reynold number. It doe not matter which correlation we ue, becaue we mut olve an implicit equation or the diameter in either cae. So, let u ue the Colebrook equation becaue it i impler. For a mooth tube, the roughne, ε = 0, o that we can et the relative roughne ε / = 0 in the Colebrook equation to obtain

10 1 1.6 =.0 log Re In thi equation, ubtitute or both the riction actor and the Reynold number in term o the diameter, to obtain 5.0 log 5/.0 log / = = 5/ 7.5 ( 1.18 / ) ( 7.5 ) or = 190 log.5 5/ 5 / Solving thi equation, we obtain " = t = A table o tandard tubing dimenion or peciied nominal diameter and Birmingham Wire Gage (BWG) value can be ound in many place. The textbook by Welty et al. provide it a Appendix N. From the table, we ind that or 1-gage tubing with an outide diameter o 1", the 1 inide diameter i 0.8. The next higher outide diameter available i 1 inch, and or thi O, 1-gage tubing come with an inide diameter o Thereore, we mut elect one o thee two tube. I we want to be ure to obtain the deired low rate, we mut chooe the value that i larger than You may wonder why. Here i an approximate anwer. In turbulent low, the riction actor V a, where 0 a < 1. In laminar low, V 1. In b both cae, we can write V V where b > 0. Thereore, the head lo rom pipe low b riction h = V V V g For a ixed volumetric low rate, a the diameter i increaed, V b decreae and 1/ alo decreae. Thereore, the head lo decreae or a given volumetric low rate a the diameter i increaed. Thi mean that with a ixed head lo available, we can comortably achieve the deired low rate uing a uitable valve. On the other hand, i we chooe a diameter that i maller than the calculated value, we would need a larger head available or driving the low than i available. Now, let u ue the actual inide diameter o the elected tube, evaluate the Reynold number o the low. = 1.08" = 9.0 t to

11 ( t ) Q. / Re = = = πν π.0 t / 9.0 t turbulent a aumed. Thereore, the low i The actual riction actor can be calculated rom the Zigrang-Sylveter equation. 1 ε / 5.0 ε / 1 =.0 log log +.7 Re.7 Re =.0 log 0 log = yielding = The actual head lo or the deired volumetric low rate will be ( t) ( t ) Q 1. / h = = = 8.0 t 5 π g 5 π. t / 9.0 t which i le than available head o 15 t. Thereore, we mut peciy 1-gage, 1 1 inch tubing or thi application. 11

12 Roughne value or Commercial Pipe Thee roughne value are given in Table 6.1 rom a textbook by White (1). Becaue o the variation in roughne in thee material depending on the ource, the roughne value reported here have uncertaintie ranging rom ± 0 % or new wrought Iron to ± 70 % or riveted teel. A typical uncertainty in the roughne value can be aumed to be in the range ± 0 50 %. Material Condition t mm Steel Sheet metal, new Stainle, new 6 7 Commercial, new Riveted 1.0 Ruted 7.0 Iron Cat, new Wrought, new Galvanized, new Aphalted, cat 1. 1 Bra rawn, new 6 7 Platic rawn tubing Gla Smooth Smooth Concrete Smoothed 1. Rough 7.0 Rubber Smoothed 5. 1 Wood Stave Reerence 1. F.M. White, Fluid Mechanic, 7 th Edition, McGraw-Hill, New York,

### Heat transfer to or from a fluid flowing through a tube

Heat tranfer to or from a fluid flowing through a tube R. Shankar Subramanian A common ituation encountered by the chemical engineer i heat tranfer to fluid flowing through a tube. Thi can occur in heat

### Engineering Bernoulli Equation

Engineering Bernoulli Equation R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkon Univerity The Engineering Bernoulli equation can be derived from the principle of conervation

### 6. Friction, Experiment and Theory

6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal

### ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts

ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr

### FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES

FLUID MECHANICS TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES In thi tutorial you will continue the work on laminar flow and develop Poieuille' equation to the form known a the Carman - Kozeny equation. Thi

### σ m using Equation 8.1 given that σ

8. Etimate the theoretical fracture trength of a brittle material if it i known that fracture occur by the propagation of an elliptically haped urface crack of length 0.8 mm and having a tip radiu of curvature

### 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

### Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

### Forced Convection Heat Transfer

Forced onvection Heat raner onvection i the mechanim o heat traner through a luid in the preence o bul luid motion. onvection i claiied a natural (or ree) and orced convection depending on how the luid

### Hydraulic losses in pipes

Hydraulic losses in pipes Henryk Kudela Contents 1 Viscous flows in pipes 1 1.1 Moody Chart.................................... 2 1.2 Types of Fluid Flow Problems........................... 5 1.3 Minor

### EXPERIMENT 11 CONSOLIDATION TEST

119 EXPERIMENT 11 CONSOLIDATION TEST Purpoe: Thi tet i performed to determine the magnitude and rate of volume decreae that a laterally confined oil pecimen undergoe when ubjected to different vertical

### Turbulent Mixing and Chemical Reaction in Stirred Tanks

Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational

### Darcy Friction Factor Formulae in Turbulent Pipe Flow

Darcy Friction Factor Formulae in Turbulent Pipe Flow Jukka Kiijärvi Lunowa Fluid Mechanics Paper 110727 July 29, 2011 Abstract The Darcy riction actor in turbulent pipe low must be solved rom the Colebrook

### Unit 11 Using Linear Regression to Describe Relationships

Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory

### v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t

Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement

### FLUID FLOW Introduction General Description

FLUID FLOW Introduction Fluid flow is an important part of many processes, including transporting materials from one point to another, mixing of materials, and chemical reactions. In this experiment, you

### MECH 2110 - Statics & Dynamics

Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11 - Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic - Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight

### Newton s Laws. A force is simply a push or a pull. Forces are vectors; they have both size and direction.

Newton Law Newton firt law: An object will tay at ret or in a tate of uniform motion with contant velocity, in a traight line, unle acted upon by an external force. In other word, the bodie reit any change

### Pressure drop in pipes...

Pressure drop in pipes... PRESSURE DROP CALCULATIONS Pressure drop or head loss, occurs in all piping systems because of elevation changes, turbulence caused by abrupt changes in direction, and friction

### Applied Fluid Mechanics

Applied Fluid Mechanics Sixth Edition Robert L. Mott University of Dayton PEARSON Prentkv Pearson Education International CHAPTER 1 THE NATURE OF FLUIDS AND THE STUDY OF FLUID MECHANICS 1.1 The Big Picture

### Transient turbulent flow in a pipe

Tranient turbulent flow in a pipe M. S. Ghidaoui A. A. Kolyhkin Rémi Vaillancourt CRM-3176 January 25 Thi work wa upported in part by the Latvian Council of Science, project 4.1239, the Natural Science

### 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

### 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) When two objects slide against one another, the magnitude of the frictional force is always equal to μ

Phyic 100 Homewor 5 Chapter 6 Contact Force Introduced ) When two object lide againt one another, the magnitude of the frictional force i alway equal to μ B) When two object are in contact with no relative

### Polyethylene (PE) pipes Dimensions

DEUTSCHE NORM Augut 1999 Polyethylene (PE) pipe Dimenion { 8074 ICS 23.040.20 Rohre au Polyethylen (PE) PE 63, PE 80, PE 100, PE HD Maße Superede September 1987 edition. In keeping with current practice

### 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

### hose-to-hose coupling pump-to-hose coupling

pipe_02 A homeowner plans to pump water from a stream in their backyard to water their lawn. A schematic of the pipe system is shown in the figure. 3 m 1 m inlet pipe-to-pump coupling stream re-entrant

### Chapter 10 Stocks and Their Valuation ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter Stoc and Their Valuation ANSWERS TO EN-OF-CHAPTER QUESTIONS - a. A proxy i a document giving one peron the authority to act for another, typically the power to vote hare of common toc. If earning

### 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 7. General Energy Equation

### Linear Momentum and Collisions

Chapter 7 Linear Momentum and Colliion 7.1 The Important Stuff 7.1.1 Linear Momentum The linear momentum of a particle with ma m moving with velocity v i defined a p = mv (7.1) Linear momentum i a vector.

Section 3.4 Pre-Activity Preparation Quadrilateral Intereting geometric hape and pattern are all around u when we tart looking for them. Examine a row of fencing or the tiling deign at the wimming pool.

### Bob York. Simple FET DC Bias Circuits

Bob York Simple FET DC Bia Circuit Loa-Line an Q-point Conier the effect of a rain reitor in the comnon-ource configuration: Smaller + g D out KL: Thi i the equation of a line that can be uperimpoe on

### Fluid Mechanics Definitions

Definitions 9-1a1 Fluids Substances in either the liquid or gas phase Cannot support shear Density Mass per unit volume Specific Volume Specific Weight % " = lim g#m ( ' * = +g #V \$0& #V ) Specific Gravity

### Three Phase Theory - Professor J R Lucas

Three Phae Theory - Profeor J Luca A you are aware, to tranit power with ingle phae alternating current, we need two wire live wire and neutral. However you would have een that ditribution line uually

### A note on profit maximization and monotonicity for inbound call centers

A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an

### Senior Thesis. Horse Play. Optimal Wagers and the Kelly Criterion. Author: Courtney Kempton. Supervisor: Professor Jim Morrow

Senior Thei Hore Play Optimal Wager and the Kelly Criterion Author: Courtney Kempton Supervior: Profeor Jim Morrow June 7, 20 Introduction The fundamental problem in gambling i to find betting opportunitie

### 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

### 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

### Figure 2.1. a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsystems

Figure. a. Block diagram repreentation o a ytem; b. block diagram repreentation o an interconnection o ubytem REVIEW OF THE LAPLACE TRANSFORM Table. Laplace tranorm table Table. Laplace tranorm theorem

### Mathematical Modeling of Molten Slag Granulation Using a Spinning Disk Atomizer (SDA)

Mathematical Modeling of Molten Slag Granulation Uing a Spinning Dik Atomizer (SDA) Hadi Purwanto and Tomohiro Akiyama Center for Advanced Reearch of Energy Converion Material, Hokkaido Univerity Kita

### ME 24-221 THERMODYNAMICS I

Solution to extra problem in chapter 8 Noember 9, 000 Fall 000 J. Murthy ME 4- HERMODYNAMICS I 8.5 Water i ued a the working fluid in a Carnot cycle heat engine, where it change from aturated liquid to

### Drill Bit Hydraulics

Drill it Hyraulic Aumtion ) Change o reure ue to eleation i negligible. ) Velocity utream i negligible comare to nozzle. 3) reure ue to riction i negligible. Δ Δ 8.075E 4ρ n reure ro acro bit, 0 n nozzle

### Pipe Loss Experimental Apparatus

Pipe Loss Experimental Apparatus Kathleen Lifer, Ryan Oberst, Benjamin Wibberley Ohio Northern University Ada, OH 45810 Email: b-wibberley@onu.edu Abstract The objective of this project was to develop

### Practice Problems on Pumps. Answer(s): Q 2 = 1850 gpm H 2 = 41.7 ft W = 24.1 hp. C. Wassgren, Purdue University Page 1 of 16 Last Updated: 2010 Oct 29

_02 A centrifugal with a 12 in. diameter impeller requires a power input of 60 hp when the flowrate is 3200 gpm against a 60 ft head. The impeller is changed to one with a 10 in. diameter. Determine the

### A technical guide to 2014 key stage 2 to key stage 4 value added measures

A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool

### Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test

Report 4668-1b Meaurement report Sylomer - field tet Report 4668-1b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of

### Queueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems,

MANAGEMENT SCIENCE Vol. 54, No. 3, March 28, pp. 565 572 in 25-199 ein 1526-551 8 543 565 inform doi 1.1287/mnc.17.82 28 INFORMS Scheduling Arrival to Queue: A Single-Server Model with No-Show INFORMS

### 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

### Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power

Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,

### Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur

Module 8 Three-phae Induction Motor Verion EE IIT, Kharagpur Leon 33 Different Type of Starter for Induction Motor (IM Verion EE IIT, Kharagpur Inructional Objective Need of uing arter for Induction motor

### Physics 111. Exam #1. January 24, 2014

Phyic 111 Exam #1 January 24, 2014 Name Pleae read and follow thee intruction carefully: Read all problem carefully before attempting to olve them. Your work mut be legible, and the organization clear.

### MSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents

MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................

### STUDY ON THE EFFECT OF COOLING WATER TEMPERATURE RISE ON LOSS FACTOR AND EFFICIENCY OF A CONDENSER FOR A 210 MW THERMAL POWER UNIT

International Journal of Emerging Technology and Advanced Engineering Volume 3, Special Iue 3: ICERTSD 2013, Feb 2013, page 485-489 An ISO 9001:2008 certified Int. Journal, ISSN 2250-2459, available online

### Experiment 3. Filters II Filter Design with MATLAB

Experiment 3 Filter II Filter Deign with MATLAB The objective o thi experiment i to gain ome experience in deigning ilter with deired peciication. You will work with a number o tool helping you in deigning

### Table 1 Mechanical Properties of Pipe Table 2 Section Properties of Pipe and Reinforcing Dowel The Fitting with the Rib

Table 1 Mechanical Properties o Pipe Material Minimum Minimum Allowable Modulus Tensile Yield Yield o trength trength trength* Elasticity (psi) (psi) (psi) (ksi) Aluminum 6063-T6 Pipe ATM429 30,000 25,000

### Pipe flow with friction losses solutions using HP and TI calculators By Gilberto E. Urroz, October 2005

Pipe low with riction losses solutions using HP and TI calculators By Gilberto E. Urroz, October 005 1. arcy-weisbach Equation and riction actor The basic equation governing riction losses in a pipeline

### 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

### Heat transfer in Flow Through Conduits

Heat transfer in Flow Through Conduits R. Shankar Suramanian Department of Chemical and Biomolecular Engineering Clarkson University A common situation encountered y the chemical engineer is heat transfer

### 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

### Calibration and Uncertainties of Pipe Roughness Height

9 th IWA/IAHR Conerence on Urban Drainage Modelling Calibration and Uncertainties o Pipe Roughness Height Kailin Yang, Yongxin Guo, Xinlei Guo,Hui Fu and Tao Wang China Institute o Water Resources and

### Solution of the Heat Equation for transient conduction by LaPlace Transform

Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame

### Piping Hydraulic Line Design and Sizing Software KLM Technology Group

Piping Hydraulic Line Design and Sizing Software KLM Technology Group Practical Engineering Guidelines for Processing Plant Solutions #03-12 Block Aronia, Jalan Sri Perkasa 2 Taman Tampoi Utama 81200 Johor

### Chapter 32. OPTICAL IMAGES 32.1 Mirrors

Chapter 32 OPTICAL IMAGES 32.1 Mirror The point P i called the image or the virtual image of P (light doe not emanate from it) The left-right reveral in the mirror i alo called the depth inverion (the

### International Journal of Heat and Mass Transfer

International Journal of Heat and Ma Tranfer 5 (9) 14 144 Content lit available at ScienceDirect International Journal of Heat and Ma Tranfer journal homepage: www.elevier.com/locate/ijhmt Technical Note

### Project Management Basics

Project Management Baic A Guide to undertanding the baic component of effective project management and the key to ucce 1 Content 1.0 Who hould read thi Guide... 3 1.1 Overview... 3 1.2 Project Management

### FIGURE P8 50E FIGURE P8 62. Minor Losses

8 48 Glycerin at 40 C with r 1252 kg/m 3 and m 0.27 kg/m s is flowing through a 4-cm-diameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe.

### 721.1-192.61 2891.6-192.61 = 0.1958

.5 Conider an ideal team regeneratie cycle in which team enter the turbine at.0 Ma, 00 C, and exhaut to the condener at 0 ka. Steam i extracted from the turbine at 0.8 Ma for an open feedwater heater.

### Profitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations

Proceeding of the 0 Indutrial Engineering Reearch Conference T. Doolen and E. Van Aken, ed. Profitability of Loyalty Program in the Preence of Uncertainty in Cutomer Valuation Amir Gandomi and Saeed Zolfaghari

### NUMERICAL SIMULATION OF WATER CIRCULATION IN A CYLINDRICAL HORIZONTAL THERMAL TANK

NUMERICAL SIMULATION OF WATER CIRCULATION IN A CYLINDRICAL HORIZONTAL THERMAL TANK D. L. Savicki a, and H. A. Vielmo b, a Federal Univerity of Rio Grande Intitute of Mathematic, Statitic and Phyic Av.

### Introduction to the article Degrees of Freedom.

Introduction to the article Degree of Freedom. The article by Walker, H. W. Degree of Freedom. Journal of Educational Pychology. 3(4) (940) 53-69, wa trancribed from the original by Chri Olen, George Wahington

### Office of Tax Analysis U.S. Department of the Treasury. A Dynamic Analysis of Permanent Extension of the President s Tax Relief

Office of Tax Analyi U.S. Department of the Treaury A Dynamic Analyi of Permanent Extenion of the Preident Tax Relief July 25, 2006 Executive Summary Thi Report preent a detailed decription of Treaury

### Chapter 10 Velocity, Acceleration, and Calculus

Chapter 10 Velocity, Acceleration, and Calculu The firt derivative of poition i velocity, and the econd derivative i acceleration. Thee derivative can be viewed in four way: phyically, numerically, ymbolically,

### ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets

ESCI 40 Phyical Meteorology Cloud Phyic Leon 2 Formation of Cloud Droplet Reference: A Short Coure in Cloud Phyic, Roger and Yau Reading: Roger and Yau, Chapter 6 The objective of thi leon are: 1) Undertand

### Design Capacities for Structural Plywood

Deign Capacitie for Structural Plyood Alloale Stre Deign (ASD) The deign value in thi document correpond ith thoe pulihed in the 005 edition of the AF&PA American Wood Council Alloale Stre Deign (ASD)/RFD

### Name: SID: Instructions

CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction - Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/

### TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME

TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic

### CEE 370 Fall 2015. Laboratory #3 Open Channel Flow

CEE 70 Fall 015 Laboratory # Open Channel Flow Objective: The objective of this experiment is to measure the flow of fluid through open channels using a V-notch weir and a hydraulic jump. Introduction:

### Design Capacities for Oriented Strand Board

Deign Capacitie for Oriented Strand Board Alloale Stre Deign (ASD) The deign value in thi document correpond ith thoe pulihed in the 005 edition of the AF&PA American Wood Council Alloale Stre Deign (ASD)/RFD

### 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

### L r = L m /L p. L r = L p /L m

NOTE: In the set of lectures 19/20 I defined the length ratio as L r = L m /L p The textbook by Finnermore & Franzini defines it as L r = L p /L m To avoid confusion let's keep the textbook definition,

### Open Channel Flow. M. Siavashi. School of Mechanical Engineering Iran University of Science and Technology

M. Siavashi School of Mechanical Engineering Iran University of Science and Technology W ebpage: webpages.iust.ac.ir/msiavashi Email: msiavashi@iust.ac.ir Landline: +98 21 77240391 Fall 2013 Introduction

### A Spam Message Filtering Method: focus on run time

, pp.29-33 http://dx.doi.org/10.14257/atl.2014.76.08 A Spam Meage Filtering Method: focu on run time Sin-Eon Kim 1, Jung-Tae Jo 2, Sang-Hyun Choi 3 1 Department of Information Security Management 2 Department

### A Note on Profit Maximization and Monotonicity for Inbound Call Centers

OPERATIONS RESEARCH Vol. 59, No. 5, September October 2011, pp. 1304 1308 in 0030-364X ein 1526-5463 11 5905 1304 http://dx.doi.org/10.1287/opre.1110.0990 2011 INFORMS TECHNICAL NOTE INFORMS hold copyright

### Health Insurance and Social Welfare. Run Liang. China Center for Economic Research, Peking University, Beijing 100871, China,

Health Inurance and Social Welfare Run Liang China Center for Economic Reearch, Peking Univerity, Beijing 100871, China, Email: rliang@ccer.edu.cn and Hao Wang China Center for Economic Reearch, Peking

### cmn_lecture.2 CAD OF DOUBLE PIPE HEAT EXCHANGERS

cmn_lecture.2 CAD OF DOUBLE PIPE HEAT EXCHANGERS A double pipe heat exchanger, in essence, consists of two concentric pipes, one fluid flowing through the inner pipe and the outer fluid flowing countercurrently

### Incline and Friction Examples

Incline and riction Eample Phic 6A Prepared b Vince Zaccone riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC

### DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS

DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS Chritopher V. Kopek Department of Computer Science Wake Foret Univerity Winton-Salem, NC, 2709 Email: kopekcv@gmail.com

### Contents 3 The clever connection 4 The OK coupling explained 6 OKC 100-190 7 OKC 200-400 8 OKC 410-490 8 OKC 500-520 9 OKC 530-1000 10 OKF 100-300 11

OK haft coupling Content 3 The clever connection 4 The OK coupling explained 6 OKC 100-190 7 OKC 200-400 8 OKC 410-490 8 OKC 500-520 9 OKC 530-1000 10 OKF 100-300 11 OKF 310-700 12 OKCS 178-360 13 OKTC

### 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

### 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

### 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

### Pressure Drop in Air Piping Systems Series of Technical White Papers from Ohio Medical Corporation

Pressure Dro in Air Piing Systems Series of Technical White Paers from Ohio Medical Cororation Ohio Medical Cororation Lakeside Drive Gurnee, IL 600 Phone: (800) 448-0770 Fax: (847) 855-604 info@ohiomedical.com

### GUIDELINE FOR FIELD TESTING OF GAS TURBINE AND CENTRIFUGAL COMPRESSOR PERFORMANCE

GUIDELINE FOR FIELD TESTING OF GAS TURBINE AND CENTRIFUGAL COMPRESSOR PERFORMANCE RELEASE.0 Augut 006 Ga Machinery Reearch Council Southwet Reearch Intitute Thi page i intentionally left blank. GUIDELINE

### Exposure Metering Relating Subject Lighting to Film Exposure

Expoure Metering Relating Subject Lighting to Film Expoure By Jeff Conrad A photographic expoure meter meaure ubject lighting and indicate camera etting that nominally reult in the bet expoure of the film.

### 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

### Figure 1. Head losses in a pipe

53:071 Principles of Hydraulics Laboratory Experiment #1 ENERGY AND HYDRAULIC GRADE LINES IN WATER PIPE SYSTEMS Principle The energy of a real fluid decreases as it moves through a pipe. The energy budget

### Bidding for Representative Allocations for Display Advertising

Bidding for Repreentative Allocation for Diplay Advertiing Arpita Ghoh, Preton McAfee, Kihore Papineni, and Sergei Vailvitkii Yahoo! Reearch. {arpita, mcafee, kpapi, ergei}@yahoo-inc.com Abtract. Diplay

### Water hammering in fire fighting installation

Water hammering in fire fighting installation Forward One of major problems raised in the fire fighting network installed at Pioneer company for pharmaceutical industry /Sulaymania was the high water hammering

### Urban Hydraulics. 2.1 Basic Fluid Mechanics

Urban Hydraulics Learning objectives: After completing this section, the student should understand basic concepts of fluid flow and how to analyze conduit flows and free surface flows. They should be able

### 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