Itt. FLO OF FLUIDS - waterlinefountains.com

1 :;-3 .. ;:,::J ,~~::Itt. ,~ ~ ~ ~ ~ ~ ~ ~ ~ :z::::t .:::=:t .. ~ --:.:=) .~" ~ . ;::::) ~:::::) .=:,) :::::) :::::::) .=::.:) :::::l ::::::l ~ ::::') FLO OF FLUIDS THROUGH VALVES, FITTINGS, AND PIPE By the Engineering Division Copyright, 1969-Crane Co; All rights reserved: This publication is fully protected by copyright and nothing that appears in it may be re-printed, either wholly or in part. without special permission . CRANE CO. Executive Office 300 Park Avenue New York, 10022 Direct inquiries to 4100 S. Kechi. Aven'ue Chicago, Illinois 60632 Technical Paper No. 410 Price $ PR1~TED IN U. S. A. ~"" (rw~lfth ) ;f"~". 10 .. -" '-~""-:l . I TablE~ of Contents -----CHAPTER Theory of Flow in Pipe page Introduction.

2 _ .. _ .. _ .. _ .. _ .. 1-1 Physical Properties of Fluids_ .. _ .. _ .. __ .. __ .. _. __ .. 1-2 Viscosity .. '" .. _ .. _. __ .. _ .. _ .. 1-2 VV' eigh t density .. _ .. 1-3 Specific volume .. _ .. 1-3 Sped fic gra \' ity .. _ .. __ .. 1-3 Nature of Flow in Pipe-Laminar and TurbulenL .. _ .. _ .. _ .. ___ ._ .. _ .. _. 1-4 IIIean velocity of flow .. _ .. _ .. _ .. 1-4 Reynolds number .. _ .. _ .. ___ .. _ .. 1-4 Hydraulic radius .. _ .. 1-4 General Energy Equation-Bernoulli's Theorem .. 1-5 Measurement of Pressure .. _ .. 1-5 Darcy's Formula-General Equation for Flow of FLUIDS .. _ .. 1-6 Friction factor _ .. _ .. 1-6 Effect of age and use on pipe friction .. 1-7 Principles of Co:npressible Flow in Pipe.

3 _ .. 1-7 Complete isothermal equation .. _ .. 1-8 Simplifiedcornpressible flow-gas pipe line formula .. _ .. _ .. 1-8 Other commonly used formulas for compressib:.e flow in long pipe lines .. _ .. 1-8 Comparison of formulas for compressible flow in pipe lines .. _ .. 1-8 Limiting flow of gases and vapors .. _ .. 1-9 Steam-General Discussion ._ .. _ .. _ .. 1-10 ------CHAPTER 3 Formulas cmd Nomographs for Flow Through Valves, Fittings, and Pipe page Introduction .. _ .. _ .. _ .. _ .. _ 3-1 Summary of Formulas .. _ .. _ .. 3-2 to 3-5 Formulas and Nomographs for Liquid Flow V e10ci ty .. _ .. _ .. 3-6 Reynolds number; friction factor for clean steel and wrought iron pipe .. 3-8 Pressure drop for turbulent flow.

4 _.: .. 3-10 Pressure drop for laminar flow .. _ .. 3-12 Flow through nozzles and orifices .. _ .. 3-14 Formulas and Nomographs for Compressible Flow Velocity .. _ .. 3-16 Reynolds number; friction factor for clean steel and wrought iron pipe .. 3-18 Pressure drop .. _. 3-20 Simplified flow .. 3-22 Flow through nozzles and orifices .. 3-24 CHAPTER 2 _ .. --__ . flow of fluid :$ Through Valves and Fittings Introduction .. __ .. _ .. Types of Valves and Fittings Used in Pipe Systems .. _ .. _ .. __ .. _ .. 2-2 Pressure Drop Chargeable to Val ves and Fittings .. _ .. '" 2-2 Crane Flow Tests .. _ .. _ .. ; 2-3 Relationship of Pressure Drop to Velocity of Flow .. _ .. _ .. _ .. _ .. 2-7 Resistance Coefficient K, EquivalentLength LID, and Cv - 2-8 Relationship of Equivalent Length LID and Resistance Coefficient K to the.

5 Inside Diameter of Connecting Pipe .. _ .. Z-lC Valves with Gradually Increased Ports .. _ .. : .. _ .. 2.:..iD Effect of End Connections .. _ .. _ .. _ .. _ .. 2-1C Laminar Flow Conditions .. __ .. _ .. _ .. _ .. _ .. 2'-11 Basis for Design of Charts for Determining Equivalent Length, Resistance CoeffiCient, and Flow Coefficient_ .. _ .. _ .. _ .. 2_11 Resistance of Bends .. _ .. _ .. _ .. ,., 2-12 Other Resistances to Flow .. _ .. ~ .. :_ .. 2-13 Flow Through Nozzles and Orifices_ .. ____ .. 2 .. lJ Liquids, gases, and vapors .. _ .. _Z-1:l Maximum flow of compressible:, FLUIDS in a nozzle .. _ .. _ .. _ .. Flow through short tubes .. _ .. 2-15 Discharge of FLUIDS Through Valves, Fittings, and Pipe Liquid flow.

6 _ .. _ .. _ .. _ .. _ .. _ .. _ .. 2-15' Compressible' flow ._ .. _ .. __ .. _~ .. _. 2~15 1-------CHAPTER 4 Examples of Flow Problems I9';ge Introduction ._ .. _ .. _ .. _ 4'-1 Reynolds Number. and' Friction Factor for Pipe Other than Steel or Wrought Iron .. 4-1 Determination of Valve Resistance in L, . LID, K, and Flow Coefficient C .. _ .. 4-:2 Check Valves-Determination of'Size .. 4--3 Laminar Flow in' Valves, Fittings, and Pipe, .. _ .. 4-4 Pressure Drop and Velocity in Piping Systems .. __ .. ~ Pipe Line Flow Problems .. 4-10 Discharge of FLUIDS from Piping Systems .. 4-:1'2 Flow Through Orifice MeterL .. _ .. 4-15 Application of Hydraulic'Radius to Flow Problems .. 4-:11 Determination of Boiler ~.

7 Apacity .. - .. 4-:18 APPENDIX A ------------~-----------APPENDIX B Physical Properties of FLUIDS and Flow Characteri'stics of Valves, Fitfings, and Pipe page Introduction .. ~ .. A-I Physical Properties of FLUIDS Viscosity of steam .. A-2 Viscosity of \vater .. A-3 Viscosity of liquid petroleum products .. A-3 Viscosity of various liquids .. A-4 Viscosity of gases and hydrocarbon vapors .. A-5 Viscosity of refrigerant vapors .. A-5 Physical properties of .. A-6 Specific gravity-temperature relationship for petroleum oils .. A-7 Weight density and specific gravity of various liquids .. A-7 Physical properties of gases .. A-8 Volumetric composition and specific gravity of gaseous fuels.

8 A-8 Steam-values of k .. A-9 Weight density and specific volume of gases and vapors .. A-lO Properties; saturated steam, saturated water _____ A-12 Properties; superheated steam .. A-16 Properties; superheated steam, compre,osed water .. A-19 Vlow Characteristics of )zzles and Orifices Flow coefficient C for nozzles .. A-20' Flow coefficient C for square edged orifices .. A-20 Net expansion factor Y for compressible flow .. A-21 Critical pressure ratio, r c for compressible flow .. A-21 Flow Characteristics of Pipe, Valves, and Fittings Net expansion factor Y for compressible flow through pipe to a larger flow area .. A-22 Relative roughness of pipe materials and friction factor for complete turbulence.

9 A-23 Friction factors for any type of commercial pipe .. A-24 Friction factors for clean commercial steel and wrought iron pipe .. A-25 Resistance in pipe due to sudden enlargements and A-26 Resistance in pipe due to pipe entrance and .. A-26 Resistance of 90 degree bends .. A-27 Resistance of miter bends .. : .. A-27 Types of valves (sectional ilJustrations) .. A-28 Schedule (thickness) of steel pipe used in obtaining resistance of valves and tittings of various pressure classes .. A-30 Representative equivalent length ( LID) in pipe diameters of valves and tittings .. A-30 Equivalent lengths L and LID and resistance coefficient K .. A-31 Equivalents of resistance coefficient K and flow coefficient C.

10 A-32 Engineering Data page Introduction E-I Equivalent Volume and 'Weight Flow Rates of Compressible FLUIDS .. B.,..2 Equivalents of Viscosity Absolute .. ; .. B-3 Kinematic .. ; .. B-3 Kinematic and Saybolt UniversaL .. : .. B-4 Kinematic and' Saybolt FuroL.. B'-4 Kinematic, Saybolt Universal, . Saybolt Furol, and Absolute .. B-5 Saybolt Universal Viscosity CharL .. B-6 Equivalents of Degrees API, Degrees Baume, Specific Gravity, Weight Density, and Pounds per Gallon .. B-1 Steam Data Boiler capacity .. : .. B-8 Horsepower of an B-8 Ranges in steam consumption by prime movers .. B-8 Power Required for Pumping .. B-9 Equivalents (General) Measure .. :.. B-J 0 vVeight .. :.. B::..! () Velocity.