Fundamentals of ship hydrodynamics  fluid mechnics, ship resistance and propulsion

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Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page i — # Fundamentals of Ship Hydrodynamics j j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page i — # Fundamentals of Ship Hydrodynamics Fluid Mechanics, Ship Resistance and Propulsion Lothar Birk School of Naval Architecture and Marine Engineering The University of New Orleans New Orleans, LA United States j j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page ii — # This edition first published  ©  John Wiley & Sons Ltd All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions The right of Lothar Birk to be identified as the author of this work has been asserted in accordance with law Registered Offices John Wiley & Sons, Inc.,  River Street, Hoboken, NJ , USA John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO SQ, UK Editorial Office The Atrium, Southern Gate, Chichester, West Sussex, PO SQ, UK For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com Wiley also publishes its books in a variety of electronic formats and by print-on-demand Some content that appears in standard print versions of this book may not be available in other formats j Limit of Liability/Disclaimer of Warranty In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make This work is sold with the understanding that the publisher is not engaged in rendering professional services The advice and strategies contained herein may not be suitable for your situation You should consult with a specialist where appropriate Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages Library of Congress Cataloging-in-Publication Data Names: Birk, Lothar, - author Title: Fundamentals of ship hydrodynamics : fluid mechanics, ship resistance and propulsion / Lothar Birk, University of New Orleans Description: Hoboken, NJ : John Wiley & Sons, Ltd, [] | Includes bibliographical references and index Identifiers: LCCN | ISBN  (hardcover) | ISBN  (epub) Subjects: LCSH: Ships–Hydrodynamics Classification: LCC VM B  | DDC ./–dc LC record available at https://lccn.loc.gov/ Cover Design: Wiley Cover Image: © zennie / Getty Images Set in pt Warnock Pro Regular by Lothar Birk Printed in Great Britain by TJ International Ltd, Padstow, Cornwall           j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page iii — # v To My Family They make everything worthwhile! j j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page v — # vii Contents List of Figures xvii List of Tables xxvii Preface xxxi Acknowledgments xxxv About the Companion Website xxxvii j . . . Ship Hydrodynamics  Calm Water Hydrodynamics  Ship Hydrodynamics and Ship Design  Available Tools  . . . .. .. . .. .. . Ship Resistance  Total Resistance  Phenomenological Subdivision  Practical Subdivision  Froude’s hypothesis  ITTC’s method  Physical Subdivision  Body forces  Surface forces  Major Resistance Components  . . .. .. .. . . Fluid and Flow Properties  A Word on Notation  Fluid Properties  Properties of water  Properties of air  Acceleration of free fall  Modeling and Visualizing Flow  Pressure  . . .. .. .. .. Fluid Mechanics and Calculus  Substantial Derivative  Nabla Operator and Its Applications  Gradient  Divergence  Rotation  Laplace operator  . . Continuity Equation  Mathematical Models of Flow  Infinitesimal Fluid Element Fixed in Space  j j Trim Size: mm × mm Single Column Tight viii j j Birk — “fshy” — // — : — page vi — # Contents . . . . Finite Control Volume Fixed in Space  Infinitesimal Element Moving With the Fluid  Finite Control Volume Moving With the Fluid  Summary  . . .. .. .. .. . . Navier-Stokes Equations  Momentum  Conservation of Momentum  Time rate of change of momentum  Momentum flux over boundary  External forces  Conservation of momentum equations  Stokes’ Hypothesis  Navier-Stokes Equations for a Newtonian Fluid  . . Special Cases of the Navier-Stokes Equations  Incompressible Fluid of Constant Temperature  Dimensionless Navier-Stokes Equations  . . . . Reynolds Averaged Navier-Stokes Equations (RANSE)  Mean and Turbulent Velocity  Time Averaged Continuity Equation  Time Averaged Navier-Stokes Equations  Reynolds Stresses and Turbulence Modeling  . . .. .. Application of the Conservation Principles  Body in a Wind Tunnel  Submerged Vessel in an Unbounded Fluid  Conservation of mass  Conservation of momentum  10 . .. .. .. . . Boundary Layer Theory  Boundary Layer  Boundary layer thickness  Laminar and turbulent flow  Flow separation  Simplifying Assumptions  Boundary Layer Equations  11 . . . .. .. .. .. . Wall Shear Stress in the Boundary Layer  Control Volume Selection  Conservation of Mass in the Boundary Layer  Conservation of Momentum in the Boundary Layer  Momentum flux over boundary of control volume  Surface forces acting on control volume  Displacement thickness  Momentum thickness  Wall Shear Stress  j j Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page vii — # j Contents j 12 . . . . . . . Boundary Layer of a Flat Plate  Boundary Layer Equations for a Flat Plate  Dimensionless Velocity Profiles  Boundary Layer Thickness  Wall Shear Stress  Displacement Thickness  Momentum Thickness  Friction Force and Coefficients  13 . . . . . . . Frictional Resistance  Turbulent Boundary Layers  Shear Stress in Turbulent Flow  Friction Coefficients for Turbulent Flow Model–Ship Correlation Lines  Effect of Surface Roughness  Effect of Form  Estimating Frictional Resistance  14 . . . Inviscid Flow  Euler Equations for Incompressible Flow  Bernoulli Equation  Rotation, Vorticity, and Circulation  15 . . . . Potential Flow  Velocity Potential  Circulation and Velocity Potential  Laplace Equation  Bernoulli Equation for Potential Flow  16 . . . . .. .. . Basic Solutions of the Laplace Equation  Uniform Parallel Flow  Sources and Sinks  Vortex  Combinations of Singularities  Rankine oval  Dipole  Singularity Distributions  17 . .. .. . . .. .. . . Ideal Flow Around A Long Cylinder  Boundary Value Problem  Moving cylinder in fluid at rest  Cylinder at rest in parallel flow  Solution and Velocity Potential  Velocity and Pressure Field  Velocity field  Pressure field  D’Alembert’s Paradox  Added Mass  j ix  j Trim Size: mm × mm Single Column Tight x j j Birk — “fshy” — // — : — page viii — # Contents 18 . . Viscous Pressure Resistance  Displacement Effect of Boundary Layer  Flow Separation  19 . . . Waves and Ship Wave Patterns  Wave Length, Period, and Height  Fundamental Observations  Kelvin Wave Pattern  20 . . .. .. .. .. . Wave Theory  Overview  Mathematical Model for Long-crested Waves  Ocean bottom boundary condition  Free surface boundary conditions  Far field condition  Nonlinear boundary value problem  Linearized Boundary Value Problem  21 . . . . Linearization of Free Surface Boundary Conditions  Perturbation Approach  Kinematic Free Surface Condition  Dynamic Free Surface Condition  Linearized Free Surface Conditions for Waves  22 . . . . Linear Wave Theory  Solution of Linear Boundary Value Problem  Far Field Condition Revisited  Dispersion Relation  Deep Water Approximation  23 . . . . . Wave Properties  Linear Wave Theory Results  Wave Number  Water Particle Velocity and Acceleration  Dynamic Pressure  Water Particle Motions  24 . . .. .. .. . Wave Energy and Wave Propagation  Wave Propagation  Wave Energy  Kinetic wave energy  Potential wave energy  Total wave energy density  Energy Transport and Group Velocity  25 . . . Ship Wave Resistance  Physics of Wave Resistance  Wave Superposition  Michell’s Integral  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page ix — # Contents j . Panel Methods  26 . .. .. . .. .. .. . Ship Model Testing  Testing Facilities  Towing tank  Cavitation tunnel  Ship and Propeller Models  Turbulence generation  Loading condition  Propeller models  Model Basins  27 . . . Dimensional Analysis  Purpose of Dimensional Analysis  Buckingham 𝜋-Theorem  Dimensional Analysis of Ship Resistance  28 . .. .. .. .. . .. .. .. Laws of Similitude  Similarities  Geometric similarity  Kinematic similarity  Dynamic similarity  Summary  Partial Dynamic Similarity  Hypothetical case: full dynamic similarity  Real world: partial dynamic similarity  Froude’s hypothesis revisited  29 . . . . . Resistance Test  Test Procedure  Reduction of Resistance Test Data  Form Factor 𝑘  Wave Resistance Coefficient 𝐶𝑊  Skin Friction Correction Force 𝐹𝐷  30 . . . . Full Scale Resistance Prediction  Model Test Results  Corrections and Additional Resistance Components  Total Resistance and Effective Power  Example Resistance Prediction  31 . . .. .. .. . .. Resistance Estimates – Guldhammer and Harvald’s Method  Historical Development  Guldhammer and Harvald’s Method  Applicability  Required input  Resistance estimate  Extended Resistance Estimate Example  Completion of input parameters  j xi j Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page  — # j 51.4 Resistance and Propulsion Estimate Example Table 51.14 𝑣𝑆 [kn] 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 𝑣𝑆 [m∕s] 7.717 7.974 8.231 8.488 8.746 9.003 9.260 9.517 9.774 647 Self propulsion point based on mean resistance curve 𝐹𝑟 [−] 0.2019 0.2086 0.2153 0.2221 0.2288 0.2355 0.2422 0.2490 0.2557 𝑤𝑇𝑆 [−] 0.3028 0.3030 0.3031 0.3032 0.3033 0.3035 0.3036 0.3037 0.3038 𝑣𝐴 [m∕s] 5.380 5.558 5.736 5.914 6.093 6.271 6.449 6.627 6.805 𝐶𝑆 [−] 0.59864 0.60852 0.61995 0.63291 0.64741 0.66345 0.68103 0.70014 0.72078 𝐽𝑇𝑆 [−] 0.6163 0.6133 0.6099 0.6061 0.6019 0.5973 0.5925 0.5874 0.5820 𝐾𝑇𝑆 10𝐾𝑄𝑇𝑆 [−] [−] 0.2274 0.3754 0.2289 0.3774 0.2306 0.3796 0.2325 0.3821 0.2345 0.3848 0.2367 0.3878 0.2391 0.3909 0.2416 0.3942 0.2442 0.3976 Table 51.15 Prediction of rate of revolution and delivered power for trial condition based on mean resistance curve j 𝑣𝑆 [kn] 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 𝑣𝑆 [m∕s] 7.717 7.974 8.231 8.488 8.746 9.003 9.260 9.517 9.774 Table 51.16 𝑣 [kn] 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 𝐹𝑟 [−] 0.2019 0.2086 0.2153 0.2221 0.2288 0.2355 0.2422 0.2490 0.2557 𝑇 [kN] 426.80 463.08 502.52 545.40 592.02 642.69 697.73 757.48 822.28 𝑄 [kNm] 342.15 370.76 401.76 435.36 471.78 511.23 553.96 600.22 650.25 𝑛 [1∕s] 1.781 1.849 1.919 1.992 2.066 2.142 2.221 2.302 2.386 𝑛 [rpm] 106.877 110.964 115.169 119.497 123.955 128.546 133.276 138.149 143.170 𝑃𝐷 [kW] 3829.36 4308.25 4845.40 5447.98 6123.89 6881.85 7731.49 8683.37 9749.06 Predicted efficiencies based on mean resistance curve 𝑣 [m/s] 7.717 7.974 8.231 8.488 8.746 9.003 9.260 9.517 9.774 𝐹𝑟 [−] 0.2019 0.2086 0.2153 0.2221 0.2288 0.2355 0.2422 0.2490 0.2557 𝜂𝑂 [−] 0.5942 0.5921 0.5896 0.5868 0.5837 0.5804 0.5768 0.5729 0.5689 𝜂𝐵 [−] 0.5996 0.5974 0.5949 0.5921 0.5890 0.5856 0.5820 0.5781 0.5740 𝜂𝐻 [−] 1.1619 1.1621 1.1623 1.1625 1.1627 1.1629 1.1631 1.1633 1.1634 𝜂𝐷 [−] 0.6967 0.6942 0.6915 0.6883 0.6848 0.6810 0.6769 0.6725 0.6678 efficiency of .% is achieved at the design speed of . kn This could possibly be improved by designing a wake adapted propeller using lifting line theory and other methods j j Trim Size: mm × mm Single Column Tight Birk — “fshy” — // — : — page  — # j 51 Hollenbach’s Method 648 Comparison of predicted rate of revolution and delivered power Table 51.17 Guldhammer and Harvald Hollenbach 𝑣𝑆 𝑛min 𝑃𝐷min 𝑛mean 𝑃𝐷mean 𝑛max 𝑃𝐷max 𝑛 𝑃𝐷 [kn] 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 [rpm] 101.84 105.81 109.91 114.14 118.52 123.04 127.71 132.53 137.52 [kW] 3134.85 3540.31 3998.65 4516.78 5102.39 5764.01 6511.05 7353.89 8303.96 [rpm] 106.88 110.96 115.17 119.50 123.96 128.55 133.28 138.15 143.17 [kW] 3829.36 4308.25 4845.40 5447.98 6123.89 6881.85 7731.49 8683.37 9749.06 [rpm] 113.18 117.54 122.03 126.66 131.44 136.36 141.44 146.68 152.08 [kW] 4816.33 5420.96 6099.78 6861.99 7717.78 8678.38 9756.18 10964.81 12319.22 [rpm] 111.81 115.88 120.05 124.34 128.79 133.42 138.31 143.86 150.28 [kW] 4067.26 4545.39 5077.00 5671.91 6343.20 7108.52 7992.05 9121.81 10598.40 Holtrop and Mennen Table . 𝑛 𝑃𝐷 [rpm] 112.99 117.28 121.70 126.27 130.95 135.70 140.54 145.52 150.75 [kW] 4637.23 5208.37 5850.65 6573.49 7378.31 8263.98 9239.76 10328.13 11573.40 14000 mean PD Hollenbach PD Guldhammer and Harvald 12000 delivered power PD [kW] j PD Holtrop and Mennen j PDmin − PDmax range Hollenbach 10000 8000 6000 results for design speed 17.5 kn 4000 2000 100 110 120 130 rate of revolution n 140 150 160 [rpm] Figure 51.2 Comparison of predicted rate of revolution and delivered power for the methods by Hollenbach, Guldhammer and Harvald, and Holtrop and Mennen Comparison Table . and Figure . present a comparison of the estimated rate of revolution and delivered power for the prediction methods discussed in this book Although the curves are close together there are differences, especially in the predicted rate of revolution j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # 51.4 Resistance and Propulsion Estimate Example 649 for each speed Circles mark the values predicted for the design speed Holtrop and Mennen’s method predicts the highest delivered power of 𝑃𝐷 = 9414.4 kW at a rate of revolution of 𝑛 = 170.53 rpm Hollenbach’s estimate is the most optimistic with a delivered power of . kW at . rpm An engine may be selected based on the powering prediction The delivered power is converted into the engine brake power 𝑃𝐵 via Equations (.) and (.) Proper sea and engine margins have to be added to the brake power predicted for trial conditions The final combination of rate of revolution and brake power is matched with the engine layout diagram This is a marine engineering rather than a hydrodynamic problem The reader can find details in the engine selection guides published by engine manufacturers Engine selection The spread of the predicted power values is an indication of the uncertainty intrinsic to resistance and propulsion estimates used in early design phases Better results can hardly be expected since only a few form parameters are used to describe the hull shape Too much of the flow patterns depends on details of the hull geometry, which will not be known until the lines plan is completed Once the lines are faired, a model may be manufactured and tested The hull geometry may also serve as the starting point for a CFD analysis if computational resources and expertise are available Conclusion References j Andersen, P and Guldhammer, H () A computer-oriented power prediction procedure In Proc of Int Conf on Computer Aided Design, Manufacture, and Operation in the Marine and Offshore Industries (CADMO ’), Washington, DC, USA Hollenbach, K () Verfahren zur Abschätzung von Widerstand und Propulsion von Ein- und Zweischraubenschiffen im Vorentwurf In Jahrbuch der Schiffbautechnischen Gesellschaft, volume , pages – Schiffbautechnische Gesellschaft (STG) Hollenbach, K (a) Beitrag zur Abschätzung von Widerstand und Propulsion von Ein- und Zweischraubenschiffen im Vorentwurf PhD thesis, Institut für Schiffbau, Universität Hamburg, Hamburg, Germany Hollenbach, K (b) Beitrag zur Abschätzung von Widerstand und Propulsion von Ein- und Zweischraubenschiffen im Vorentwurf IfS Report , Institut für Schiffbau, Universität Hamburg, Hamburg, Germany Hollenbach, K (a) Estimating resistance and propulsion for single-screw and twin-screw ships Schiffstechnik/Ship Technology Research, ():– Hollenbach, K (b) Weiterentwicklung eines verfahrens zur Abschätzung von Widerstand und Propulsion von Ein- und Zweischraubenschiffen im Vorentwurf In Jahrbuch der Schiffbautechnischen Gesellschaft, volume , pages – Berlin Hollenbach, K () Estimating resistance and propulsion for single-screw and twinscrew ships in the preliminary design In Proc of th Int Conference on Computer Applications in Shipbuilding (ICCAS ’) Holtrop, J () A statistical re-analysis of resistance and propulsion data International Shipbuilding Progress, ():– j j Trim Size: mm × mm Single Column Tight 650 j Birk — “fshy” — // — : — page  — # 51 Hollenbach’s Method Holtrop, J () A statistical resistance prediction method with a speed dependent form factor In Scientific and Methodological Seminar on Ship Hydrodynamics (SMSSH ’), Varna, Bulgaria Holtrop, J and Mennen, G () An approximate power prediction method International Shipbuilding Progress, ():– ITTC ()  ITTC performance prediction method International Towing Tank Conference, Recommended Procedures and Guidelines .---. Revision  Self Study Problems  Discuss the principal differences and similarities between the resistance estimates based on Guldhammer and Harvald’s method, Holtrop and Mennen’s method, and Hollenbach’s method  For a ship design project the following data is provided Ship data j length between perpendiculars length in waterline molded beam molded draft block coefficient (based on 𝐿𝑃𝑃 ) prismatic coefficient (based on 𝐿𝑃𝑃 ) 𝐿𝑃𝑃 𝐿𝑊𝐿 𝐵 𝑇 𝐶𝐵 𝐶𝑃 = . m = . m = . m = . m = . = . Compute the input values for block coefficient 𝐶𝐵 and prismatic coefficient 𝐶𝑃 for Hollenbach’s method Compare the results with the values from the corresponding problem at the end of Chapter   Implement Hollenbach’s resistance and propulsion estimate as a program in Python, Matlab, or similar, and test it with the data presented in the last section j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # 651 Index A j Actuator disk  Added mass  Admiralty coefficient  Advance coefficient , , , , –,  Airy, Sir George Biddell  American Towing Tank Conference see ATTC Angle of attack , , , , ,  effective  ideal –,  induced  zero lift ,  Appendage  Archimedes  Archimedes’ principle , , , ,  ATTC  Averaging  B Behind condition , , , , , , ,  adjustment  Bernoulli equation , , –, , , ,  linearized , , , ,  potential flow –, , , ,  steady flow , , ,  unsteady flow , ,  Bertrand, Joseph  Bilge keels  Biot, Jean-Baptiste  Biot–Savart law – Blade see Propeller, blade Blockage  correction , ,  factor  Schuster’s correction  Tamura’s correction  Boiling point  Bollard pull  Boundary condition  body , , , , , , , , ,  Dirichlet  far field , , ,  free surface see Free surface kinematic , ,  mixed  Neumann ,  ocean bottom  Boundary layer , , , ,  buffer layer  equations  inner law  inner scaling  laminar  log–wake law  logarithmic overlap law  modified log–wake law  no slip condition  outer scaling  overlap layer ,  separation  thickness , , ,  turbulent , –,  viscous sublayer , ,  wall layer  wall shear stress  Boundary layer theory , – assumptions  Boundary value problem  cylinder  j j Trim Size: mm × mm Single Column Tight 652 j Index Chord length , , , ,  Circulation , , ,  bound ,  free  Coefficient block , , , , , , , , , , , ,  midship section  prismatic , , , , ,  waterplane area  Collocation point  Computational Fluid Dynamics see CFD Condition behind , , ,  calm water , ,  loading , ,  open water , , , , , , , , , , ,  service ,  trial , ,  Conformal mapping  Conservation of mass , , , , , , , ,  of momentum –, , , , , ,  integral form  Conservative  Continuity equation –, , , , ,  differential, conservative ,  differential, nonconservative  incompressible, steady flow ,  integral form  integral, nonconservative  integral, conservative  Contraction nozzle ,  Control volume  differential ,  fixed  moving  finite see Control volume, displacement flow (thin foil) ,  lifting flow (thin foil) ,  linear wave theory  moving cylinder ,  thin foil  Boussinesq’s eddy viscosity hypothesis  Boussinesq, Joseph V  British method see Propulsion test, load variation Buckingham 𝜋-theorem  Buckingham, Edgar  Bulbous bow , , , ,  resistance ,  Burrill % back cavitation criterion , , ,  cavitation chart ,  Burrill, Lennard Constantine  j Birk — “fshy” — // — : — page  — # C Camber , , ,  maximum  Cauchy principal value integral –,  Cauchy, Augustin-Louis  Cavitation ,  bubble ,  cloud  effects – face  hub vortex  inception  prevention – propeller–hull  sheet  test  tip vortex  tunnel  Cavitation criterion see Burrill Cavitation number  free stream  propeller ,  CFD , , , , ,  Chapman, Fredrik H af  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # Index integral infinitesimally small see Control volume, differential integral , ,  fixed  moving  Coordinate system Cartesian xvii, ,  cylindrical  polar ,  spherical  Correlation lines  Cupping see Propeller blade, cupping D j d’Alembert’s paradox , , ,  d’Alembert, Jean-Baptiste le Rond ,  Density  of air  of fresh water  of seawater  Derivative convective  directional  local  normal see Normal derivative partial  substantial ,  Differential equation ordinary , ,  partial , , , , , ,  Differential equations partial  Dimensional analysis –,  Dipole  Direct numerical simulation (DNS) ,  Dispersion relation , ,  Displacement effect , , , , ,  thickness , , ,  volumetric ,  653 Divergence –, , , , , ,  theorem ,  Downwash , ,  Drag , , ,  coefficient , , , , , ,  induced  E Efficiency  behind ,  gearing  hull , , ,  ideal , ,  open water , , , –, , , , ,  quasi-propulsive ,  relative rotative , , –, , , ,  shafting  total propulsive  Energy kinetic , ,  potential  Entrance  half angle of  Euler equations ,  formula ,  number ,  Euler, Leonard , ,  Eulerian formulation ,  Expanded area  Expanded area ratio , ,  required , ,  F Field point see Collocation point theory  Flat plate friction coefficient ATTC, Schoenherr  Grigson  ITTC  see ITTC,  model–ship correlation line Prandtl–Schlichting  White  j j Trim Size: mm × mm Single Column Tight 654 j Birk — “fshy” — // — : — page  — # j Index Flow cylinder ,  displacement , , ,  exterior , ,  interior  irrotational  laminar ,  lifting , , ,  parallel , –, , , , ,  Rankine oval  source  steady , , , , ,  turbulent ,  unsteady , , , , , ,  viscous , , , , , ,  vortex  wave ,  Fluid  ideal , ,  incompressible , ,  isotropic  Newtonian , ,  viscous , , , ,  Flux mass , , , , ,  momentum , , , , , ,  Foil see Lifting foil Foil section , ,  camber see Camber chord length see Chord length geometry  thickness  Force body , , ,  conservative  external , , ,  friction  gravity  inertia , ,  pressure , , , , ,  surface , ,  viscous  Form factor , , , ,  appendage  Granville  Grigson  Holtrop and Mennen  Prohaskas’s method  Watanabe  Free surface , , ,  dynamic boundary condition , ,  elevation  generalized boundary condition ,  kinematic boundary condition , , ,  Froude depth number  number , , , , ,  similarity  Froude’s hypothesis , ,  law of similarity  method ,  Froude, William , , , ,  G Gas  Gauss’ integral theorem  Glauert integral , ,  series , , , ,  Glauert, Hermann  Gradient  Gravitational acceleration ,  function of latitude  local  standard value  Group velocity , ,  Guldhammer, H.E  H Harvald, Svend Aage  Helmholtz’s theorems , , , ,  Helmholtz, Hermann von  Hollenbach, Uwe  Holtrop, Jan  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # Index Hooke’s law  Hooke, Robert  Hot wire anemometer  Hull–propeller interaction  Hydraulically actuated  smooth ,  Hydrometer  Hydrostatic equilibrium  Hydrostatics basic theorem of  I j IAPWS  Interaction hull–propeller , ,  Intermittency factor  International Association for the Properties of Water and Steam see IAPWS International Towing Tank Conference see ITTC ITTC xvii, , , , , , , , , , , ,   model–ship correlation line , , , , , , , , , , , , , , , , , , ,   performance prediction method , , ,   performance prediction procedure  J Jet efficiency see Efficiency, ideal Joukowsky, Nikolay Yegorovich  K Keller’s formula , ,  Keller, J auf ’m  Kelvin angle  wave pattern – Kelvin, Lord  Kinematic  Kinetic  Kutta condition ,  Kutta, Martin Wilhelm  655 Kutta-Joukowsky’s lift theorem , , , , ,  L Lagrange, Joseph-Louis  Lagrangian formulation  Landau’s symbol  Laplace equation , –, , , , , , , , , , , , ,  cylindrical coordinates  polar coordinates ,  spherical coordinates  Laplace operator , ,  dimensionless  Laplace, Pierre-Simon ,  Leading edge ,  suction  Length characteristic  computation  in waterline  over wetted surface  Length–displacement ratio  Lift , , , ,  Lift coefficient , , , ,  Lift force  Lift–drag ratio ,  Lifting foil , –,  Lifting line  Lifting line theory ,  Liquid  Load variation test  M Margin engine  service , ,  Mass transport (in waves)  Mass flow rate see Flux, mass Mass flux see Flux, mass Mathematical models ,  Matrix  multiplication  Maximum continuous rating  Mean line , ,  j j Trim Size: mm × mm Single Column Tight 656 Index NACA 𝑎 = 0.8  parabolic  Mennen, G.G.J  Michell’s integral – Michell, John Henry  Model basin ,  test  testing – Moment pitch  Momentum  flux see Flux, momentum thickness , , , , ,  Moody chart  Motion steady  unsteady  Normal vector , , , , , , , , , , , –, , , , , , , , , , ,  Normal velocity see Velocity, normal O Open water condition see Condition, open water Open water diagram , , , , , , , ,  Open water efficiency see Efficiency, open water Open water test –, , , , , ,  P Paint flow test  Panel methods  Pathline  Performance prediction , , , , – Perturbation  Phase velocity , , ,  deep water  Pitch , ,  angle , ,  constant  effective  variable , ,  Pitch–diameter ratio , , , ,  optimum ,  Pitot, Henri  Pitot-static tube ,  Potential see also Velocity potential,  of gravity  Potential flow , , –, , , , ,  Potential theory , , , ,  Power brake ,  delivered , , , , ,  effective , , ,  shaft  thrust , , ,  N j Birk — “fshy” — // — : — page  — # j Nabla operator ,  dimensionless  NACA  NASA  Naval architect  Navier, Claude L.M.H  Navier, Claude Louis Marie Henri  Navier-Stokes equations –, , ,  conservative, differential  dimensionless  incompressible flow  incompressible, steady flow  Navier-Stokes equations, Reynolds averaged see RANSE Newton’s first law  laws of motion  second law , , , , ,  Newton, Sir Isaac , ,  Newton-Raphson method  Newtonian fluid see Fluid, Newtonian Nomenclature xvii Nonconservative  Normal derivative , ,  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # Index j Power law  Powering estimate  comparison  example , – Hollenbach – Holtrop and Mennen – Prandtl, Ludwig , , ,  Pressure ,  atmospheric ,  coefficient , , , , , , , , , , ,  difference  shock  vapor , , ,  Preturbulence , ,  Propeller  azimuthing  clearance  controllable pitch , ,  developed area  diameter , , ,  ducted  expanded area ratio see Expanded area ratio fixed pitch ,  high skew  left-handed  lightly loaded  loading see Thrust loading number of blades ,  pitch–diameter ratio see Pitch–diameter ratio podded  projected area ,  rake see Rake right-handed  skew see Skew slip ,  stock  Voith Schneider  warp  wheel effect  Propeller blade back  cupping  expanded  face  leading edge  radius  tip  trailing edge  Propeller boat see Propeller dynamometer Propeller design constant , ,  task  –, – task   task   task  , – Propeller design chart – 𝐵𝑃1 -chart ,  𝐵𝑃2 -chart  𝐵𝑈1 -chart  𝐵𝑈2 -chart ,  logarithmic chart  Propeller dynamometer , ,  Propeller hub  radius ,  vortex  Propeller selection optimum diameter –, – optimum rate of revolution –, – Propeller series – controllable pitch  ducted  Gawn  KCA  Newton–Rader  skew  Wageningen B-Series – Propulsion test – continental method ,  load variation  Propulsor , , , , ,  R Rake ,  angle  skew induced  Rankine oval , ,  source ,  j 657 j Trim Size: mm × mm Single Column Tight 658 j Birk — “fshy” — // — : — page  — # j Index residuary , , , , ,  steering  total , , , ,  wave , , ,  Resistance estimate  comparison  example –, –, – Guldhammer and Harvald – Hollenbach – Holtrop and Mennen – Reynolds averaging  stress tensor , , – stresses  Reynolds number , , , , , , , ,  at radius 𝑥 = 0.75 ,  local ,  Reynolds, Osborne , , ,  Rheology  Roughness equivalent sand ,  propeller  technical  Roughness allowance see Resistance, roughness allowance Run , , ,  length of , ,  Rankine, William J.M  RANSE , , – Rate of revolution , , , , ,  Reech, Ferdinand ,  Region multiply connected  simply connected  Relaminarization  Resistance – air ,  appendage , , , , ,  bow thruster  bow thruster tunnel ,  bulbous bow  components ,  correlation allowance  eddy  frictional , –, , –, ,  hollows ,  humps ,  induced  residuary , , ,  roughness allowance , ,  shape factors  spray  steering  total , , , , , , , , , ,  transom ,  viscous , , , , ,  viscous pressure , , ,  wave , , , , , , , , –, , – wave breaking ,  wave pattern ,  Resistance coefficient  air , ,  appendage  bow thruster tunnel  correlation allowance , , ,  environmental  frictional , , , ,  S Sagitta  Salinity  Savart, Félix  Scale acceleration  factor  force ,  geometric  length , ,  model  surface ,  time ,  velocity  volume ,  Schlichting, Hermann  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # Index j Schneekluth nozzle  Self propulsion point , , , , , , , , , ,  Self-propelled ,  Separation  laminar flow  point  turbulent flow  Separation of variables ,  Series   Shock free entry  Shortened thrust loading coefficient , ,  Similarity dynamic  Froude  full dynamic  geometric  kinematic  laws of  partial  Singularity ,  Sink  Sinkage aft  dynamic ,  fore  mean , ,  Skew  angle  Skew-back  Skin friction correction  force ,  Source  distribution  point  strength ,  Speed corresponding ,  design  Speed of advance , , , ,  Stagnation point , , , , , , , , ,  Stall  Stokes hypothesis  659 wave theory  Stokes, Sir George Gabriel , , ,  Streakline  Streamline , , ,  dividing ,  Stress apparent  normal  shear ,  tensor  wall shear ,  Strouhal number  Strouhal, Vinzenz  Suction side  Surface free see Free surface fully rough  hydraulically smooth ,  roughness , ,  T Tail–nose line , , , , , ,  Taylor series , , , , ,  series, several variables  series, single variable  Taylor Standard Series  Taylor, Brook  Taylor, David Watson , , ,  TEU , ,  Thickness distribution  elliptical ,  ogival  Thickness ratio  Thin foil theory – Thomson, William see Kelvin, Lord Thrust , , , , , , , , , , , , , , , , ,  available  bearing  blade section  coefficient , , , , , , , ,  coefficient correction  j j Trim Size: mm × mm Single Column Tight 660 j j Birk — “fshy” — // — : — page  — # Index effect of cavitation  identity , , , , , ,  required , , , ,  Thrust deduction ,  Thrust deduction fraction , , –, , –, ,  Guldhammer and Harvald  Hollenbach  Holtrop and Mennen  Thrust loading , , , ,  coefficient , , , , ,  Torque , , , ,  available  blade section  coefficient , , , , , ,  coefficient correction  effect of cavitation  identity ,  Towing carriage  Towing point  Towing tank , , ,  beach  Trailing edge , ,  Trial corrections  Trim  angle , ,  running  Trim tank  Turbulence ,  generation , ,  isotropic ,  longitudinal  mean kinetic energy ,  model ,  transverse  U Updraft dot product  magnitude ,  Vector field irrotational  Velocity attainable  mean ,  normal , , , –, ,  turbulent  wall friction ,  Velocity defect law  Velocity potential , , ,  D dipole  D source  D vortex ,  D dipole  D source  cylinder flow  of deep water wave ,  disturbance , , , , , , , , ,  moving cylinder  parallel flow , ,  Rankine oval  of regular wave ,  Vessel displacement type , , , , , ,  planing type , ,  Viscosity  apparent see Viscosity, eddy dynamic ,  eddy ,  eddy, kinematic  kinematic , , , ,  second  Vortex  bound  distribution  filament  flow  horseshoe  start-up ,  strength , , , , , , ,  tip  Vortex sheet  V Vector  component  cross product  j j Trim Size: mm × mm Single Column Tight j Birk — “fshy” — // — : — page  — # Index roll up  trailing  Vorticity  bound  free ,  W j Wake , , ,  effect of rudder  effective  frictional , ,  nominal  nonuniform  potential ,  wave ,  Wake fraction , –, , , , ,  frictional  full scale  Guldhammer and Harvald  Hollenbach – Holtrop and Mennen  potential  Wake function  Wake hook  Water fresh ,  sea ,  Water jet  Wave  amplitude ,  crest  diffraction  dispersion ,  divergent ,  dynamic pressure  elevation ,  frequency ,  height ,  length , , , ,  long-crested ,  particle acceleration  particle path  particle velocity  pattern ,  period  phase ,  profile  radiation  regular ,  superposition ,  transverse ,  trough  Wave energy  density  kinetic , ,  potential , ,  transport ,  Wave maker ,  Wave number , , ,  deep water ,  Wave theory Airy see Wave theory, linear,  boundary value problem  linear , – linearized boundary value problem  ocean bottom condition  radiation condition  Stokes  Wetted surface ,  appendages  Hollenbach  Holtrop and Mennen  Kristensen and Lützen  Mumford’s formula  Wheel effect  Wigley hull ,  Wind tunnel  Wing finite span  tip  tip vortex  Wingspan  Z Zero lift angle see Angle of attack, zero lift j 661 j