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Lothar Birk, University of New Orleans, USA
Bridging the information gap between fluid mechanics and ship hydrodynamics
Fundamentals of Ship Hydrodynamics is designed as a textbook for undergraduate education in ship resistance and propulsion. The book provides connections between basic training in calculus and fluid mechanics and the application of hydrodynamics in daily ship design practice. Based on a foundation in fluid mechanics, the origin, use, and limitations of experimental and computational procedures for resistance and propulsion estimates are explained.
The book is subdivided into sixty chapters, providing background material for individual lectures. The unabridged treatment of equations and the extensive use of figures and examples enable students to study details at their own pace.
Key features:
* Covers the range from basic fluid mechanics to applied ship hydrodynamics.
* Subdivided into 60 succinct chapters.
* In-depth coverage of material enables self-study.
* Around 250 figures and tables.
Fundamentals of Ship Hydrodynamics is essential reading for students and staff of naval architecture, ocean engineering, and applied physics. The book is also useful for practicing naval architects and engineers who wish to brush up on the basics, prepare for a licensing exam, or expand their knowledge.
Lothar Birk, University of New Orleans, USA
Bridging the information gap between fluid mechanics and ship hydrodynamics
Fundamentals of Ship Hydrodynamics is designed as a textbook for undergraduate education in ship resistance and propulsion. The book provides connections between basic training in calculus and fluid mechanics and the application of hydrodynamics in daily ship design practice. Based on a foundation in fluid mechanics, the origin, use, and limitations of experimental and computational procedures for resistance and propulsion estimates are explained.
The book is subdivided into sixty chapters, providing background material for individual lectures. The unabridged treatment of equations and the extensive use of figures and examples enable students to study details at their own pace.
Key features:
* Covers the range from basic fluid mechanics to applied ship hydrodynamics.
* Subdivided into 60 succinct chapters.
* In-depth coverage of material enables self-study.
* Around 250 figures and tables.
Fundamentals of Ship Hydrodynamics is essential reading for students and staff of naval architecture, ocean engineering, and applied physics. The book is also useful for practicing naval architects and engineers who wish to brush up on the basics, prepare for a licensing exam, or expand their knowledge.
LOTHAR BIRK has more than two decades of experience teaching ship and offshore hydrodynamics, first at the Technische Universität Berlin and now at the University of New Orleans (UNO). Fascinated by the world of boats and ships, he studied naval architecture at Technische Universität Berlin (TUB) in Germany. After graduation he worked at TUB as a research scientist completing projects and teaching classes related to hydrodynamics and optimization of ship and offshore structures. In 2004, he joined the faculty of the School of Naval Architecture and Marine Engineering at UNO where he teaches classes in ship resistance and propulsion, propeller hydrodynamics, experimental, numerical and offshore hydrodynamics as well as computer aided design and optimization. His passion for teaching has earned him several awards by student organizations.
List of Figures xvii
List of Tables xxvii
Preface xxxi
Acknowledgments xxxv
About the Companion Website xxxvii
1 Ship Hydrodynamics 1
1.1 Calm Water Hydrodynamics 1
1.2 Ship Hydrodynamics and Ship Design 6
1.3 Available Tools 7
2 Ship Resistance 10
2.1 Total Resistance 10
2.2 Phenomenological Subdivision 11
2.3 Practical Subdivision 12
2.3.1 Froude's hypothesis 14
2.3.2 ITTC's method 15
2.4 Physical Subdivision 17
2.4.1 Body forces 18
2.4.2 Surface forces 18
2.5 Major Resistance Components 20
3 Fluid and Flow Properties 26
3.1 A Word on Notation 26
3.2 Fluid Properties 29
3.2.1 Properties of water 29
3.2.2 Properties of air 31
3.2.3 Acceleration of free fall 32
3.3 Modeling and Visualizing Flow 32
3.4 Pressure 35
4 Fluid Mechanics and Calculus 41
4.1 Substantial Derivative 41
4.2 Nabla Operator and Its Applications 44
4.2.1 Gradient 44
4.2.2 Divergence 45
4.2.3 Rotation 47
4.2.4 Laplace operator 48
5 Continuity Equation 50
5.1 Mathematical Models of Flow 50
5.2 Infinitesimal Fluid Element Fixed in Space 51
5.3 Finite Control Volume Fixed in Space 54
5.4 Infinitesimal Element Moving With the Fluid 55
5.5 Finite Control Volume Moving With the Fluid 55
5.6 Summary 56
6 Navier-Stokes Equations 59
6.1 Momentum 59
6.2 Conservation of Momentum 60
6.2.1 Time rate of change of momentum 60
6.2.2 Momentum flux over boundary 60
6.2.3 External forces 63
6.2.4 Conservation of momentum equations 65
6.3 Stokes' Hypothesis 66
6.4 Navier-Stokes Equations for a Newtonian Fluid 67
7 Special Cases of the Navier-Stokes Equations 71
7.1 Incompressible Fluid of Constant Temperature 71
7.2 Dimensionless Navier-Stokes Equations 75
8 Reynolds Averaged Navier-Stokes Equations (RANSE) 82
8.1 Mean and Turbulent Velocity 82
8.2 Time Averaged Continuity Equation 84
8.3 Time Averaged Navier-Stokes Equations 87
8.4 Reynolds Stresses and Turbulence Modeling 89
9 Application of the Conservation Principles 94
9.1 Body in a Wind Tunnel 94
9.2 Submerged Vessel in an Unbounded Fluid 99
9.2.1 Conservation of mass 100
9.2.2 Conservation of momentum 102
10 Boundary Layer Theory 106
10.1 Boundary Layer 106
10.1.1 Boundary layer thickness 107
10.1.2 Laminar and turbulent flow 108
10.1.3 Flow separation 110
10.2 Simplifying Assumptions 111
10.3 Boundary Layer Equations 115
11 Wall Shear Stress in the Boundary L Wall Shear Stress in the Boundary Layer 118
11.1 Control Volume Selection 118
11.2 Conservation of Mass in the Boundary Layer 119
11.3 Conservation of Momentum in the Boundary Layer 121
11.3.1 Momentum flux over boundary of control volume 122
11.3.2 Surface forces acting on control volume 124
11.3.3 Displacement thickness 130
11.3.4 Momentum thickness 131
11.4 Wall Shear Stress
12 Boundary Layer of a Flat Plate 132
12.1 Boundary Layer Equations for a Flat Plate 132
12.2 Dimensionless Velocity Profiles 134
12.3 Boundary Layer Thickness 136
12.4 Wall Shear Stress 140
12.5 Displacement Thickness 141
12.6 Momentum Thickness 142
12.7 Friction Force and Coefficients 143
13 Frictional Resistance 146
13.1 Turbulent Boundary Layers 146
13.2 Shear Stress in Turbulent Flow 152
13.3 Friction Coefficients for Turbulent Flow 153
13.4 Model-Ship Correlation Lines 155
13.5 Effect of Surface Roughness 157
13.6 Effect of Form 160
13.7 Estimating Frictional Resistance 161
14 Inviscid Flow 165
14.1 Euler Equations for Incompressible Flow 165
14.2 Bernoulli Equation 166
14.3 Rotation, Vorticity, and Circulation 171
15 Potential Flow 177
15.1 Velocity Potential 177
15.2 Circulation and Velocity Potential 182
15.3 Laplace Equation 184
15.4 Bernoulli Equation for Potential Flow 187
16 Basic Solutions of the Laplace Equation 191
16.1 Uniform Parallel Flow 191
16.2 Sources and Sinks 192
16.3 Vortex 196
16.4 Combinations of Singularities 198
16.4.1 Rankine oval 198
16.4.2 Dipole 202
16.5 Singularity Distributions 204
17 Ideal Flow Around A Long Cylinder 207
17.1 Boundary Value Problem 207
17.1.1 Moving cylinder in fluid at rest 208
17.1.2 Cylinder at rest in parallel flow 210
17.2 Solution and Velocity Potential 211
17.3 Velocity and Pressure Field 214
17.3.1 Velocity field 215
17.3.2 Pressure field 216
17.4 D'Alembert's Paradox 218
17.5 Added Mass 219
18 Viscous Pressure Resistance 223
18.1 Displacement Effect of Boundary Layer 223
18.2 Flow Separation 226
19 Waves and Ship Wave Patterns 230
19.1 Wave Length, Period, and Height 230
19.2 Fundamental Observations 233
19.3 Kelvin Wave Pattern 235
20 Wave Theory 239
20.1 Overview 239
20.2 Mathematical Model for Long-crested Waves 240
20.2.1 Ocean bottom boundary condition 241
20.2.2 Free surface boundary conditions 242
20.2.3 Far field condition 246
20.2.4 Nonlinear boundary value problem 247
20.3 Linearized Boundary Value Problem 248
21 Linearization of Free Surface Boundary Conditions 250
21.1 Perturbation Approach 250
21.2 Kinematic Free Surface Condition 252
21.3 Dynamic Free Surface Condition 254
21.4 Linearized Free Surface Conditions for Waves 256
22 Linear Wave Theory 259
22.1 Solution of Linear Boundary Value Problem 259
22.2 Far Field Condition Revisited 265
22.3 Dispersion Relation 265
22.4 Deep Water Approximation 267
23 Wave Properties 271
23.1 Linear Wave Theory Results 271
23.2 Wave Number 272
23.3 Water Particle Velocity and Acceleration 275
23.4 Dynamic Pressure 279
23.5 Water Particle Motions 280
24 Wave Energy and Wave Propagation 284
24.1 Wave Propagation 284
24.2 Wave Energy 287
24.2.1 Kinetic wave energy 287
24.2.2 Potential wave energy 290
24.2.3 Total wave energy density 292
24.3 Energy Transport and Group Velocity 293
25 Ship Wave Resistance 299
25.1 Physics of Wave Resistance 299
25.2 Wave Superposition 301
25.3 Michell's Integral 310
25.4 Panel Methods 312
26 Ship Model Testing 316
26.1 Testing Facilities 316
26.1.1 Towing Lank 317
26.1.2 Cavitation tunnel 320
26.2 Ship and Propeller Models 321
26.2.1 Turbulence generation 322
26.2.2 Loading condition 323
26.2.3 Propeller models 324
26.3 Model Basins 324
27 Dimensional Analysis 327
27.1 Purpose of Dimensional Analysis 327
27.2 Buckingham -Theorem 328
27.3 Dimensional Analysis of Ship Resistance 328
28 Laws of Similitude 332
28.1 Similarities 332
28.1.1 Geometric similarity 333
28.1.2 Kinematic similarity 333
28.1.3 Dynamic similarity 334
28.1.4 Summary 340
28.2 Partial Dynamic Similarity 340
28.2.1 Hypothetical case: full dynamic similarity 340
28.2.2 Real world: partial dynamic similarity 342
28.2.3 Froude's hypothesis revisited 343
29 Resistance Test 345
29.1 Test Procedure 345
29.2 Reduction of Resistance Test Data 348
29.3 Form Factor k 351
29.4 Wave Resistance Coefficient Cw 354
29.5 Skin Friction Correction Force FD 355
30 Full Scale Resistance Prediction 357
30.1 Model Test Results 357
30.2 Corrections and Additional Resistance Components 358
30.3 Total Resistance and Effective Power 359
30.4 Example Resistance Prediction 360
31 Resistance Estimates - Guldhammer and Harvald's Method 367
31.1 Historical Development 367
31.2 Guldhammer and Harvald's Method 369
31.2.1 Applicability 369
31.2.2 Required input 369
31.2.3 Resistance estimate 372
31.3 Extended Resistance Estimate Example 378
31.3.1 Completion of input parameters 379
31.3.2 Range of speeds 380
31.3.3 Residuary resistance coefficient 380
31.3.4 Frictional resistance coefficient 383
31.3.5 Additional resistance coefficients 383
31.3.6 Total resistance coefficient 384
31.3.7 Total resistance and effective power 384
32 Introduction to Ship Propulsion 389
32.1 Propulsion Task 389
32.2 Propulsion Systems 391
32.2.1 Marine propeller 391
32.2.2 Water jet propulsion 392
32.2.3 Voith Schneider propeller (VSP) 393
32.3 Efficiencies in Ship Propulsion 394
33 Momentum Theory of the Propeller 398
33.1 Thrust, Axial Momentum, and Mass Flow 398
33.2 Ideal Efficiency and ^rust Loading Coefficient 403
34 Hull-Propeller Interaction 408
34.1 Wake- Fraction 408
34.2 ^rust Deduction Fraction 414
34.3 Relative Rotative Efficiency 417
35 Propeller Geometry 420
35.1 Propeller Parts 420
35.2 Principal Propeller Characteristics 422
35.3 Other Geometric Propeller Characteristics 431
36 Lifting Foils 435
36.1 Foil Geometry and Flow Patterns 435
36.2 Lift and...
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Fertigungstechnik |
| Genre: | Importe, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | 704 S. |
| ISBN-13: | 9781118855485 |
| ISBN-10: | 1118855485 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Birk, Lothar |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Wiley-VCH GmbH, Boschstr. 12, D-69469 Weinheim, product-safety@wiley.com |
| Maße: | 255 x 187 x 42 mm |
| Von/Mit: | Lothar Birk |
| Erscheinungsdatum: | 10.06.2019 |
| Gewicht: | 1,468 kg |
LOTHAR BIRK has more than two decades of experience teaching ship and offshore hydrodynamics, first at the Technische Universität Berlin and now at the University of New Orleans (UNO). Fascinated by the world of boats and ships, he studied naval architecture at Technische Universität Berlin (TUB) in Germany. After graduation he worked at TUB as a research scientist completing projects and teaching classes related to hydrodynamics and optimization of ship and offshore structures. In 2004, he joined the faculty of the School of Naval Architecture and Marine Engineering at UNO where he teaches classes in ship resistance and propulsion, propeller hydrodynamics, experimental, numerical and offshore hydrodynamics as well as computer aided design and optimization. His passion for teaching has earned him several awards by student organizations.
List of Figures xvii
List of Tables xxvii
Preface xxxi
Acknowledgments xxxv
About the Companion Website xxxvii
1 Ship Hydrodynamics 1
1.1 Calm Water Hydrodynamics 1
1.2 Ship Hydrodynamics and Ship Design 6
1.3 Available Tools 7
2 Ship Resistance 10
2.1 Total Resistance 10
2.2 Phenomenological Subdivision 11
2.3 Practical Subdivision 12
2.3.1 Froude's hypothesis 14
2.3.2 ITTC's method 15
2.4 Physical Subdivision 17
2.4.1 Body forces 18
2.4.2 Surface forces 18
2.5 Major Resistance Components 20
3 Fluid and Flow Properties 26
3.1 A Word on Notation 26
3.2 Fluid Properties 29
3.2.1 Properties of water 29
3.2.2 Properties of air 31
3.2.3 Acceleration of free fall 32
3.3 Modeling and Visualizing Flow 32
3.4 Pressure 35
4 Fluid Mechanics and Calculus 41
4.1 Substantial Derivative 41
4.2 Nabla Operator and Its Applications 44
4.2.1 Gradient 44
4.2.2 Divergence 45
4.2.3 Rotation 47
4.2.4 Laplace operator 48
5 Continuity Equation 50
5.1 Mathematical Models of Flow 50
5.2 Infinitesimal Fluid Element Fixed in Space 51
5.3 Finite Control Volume Fixed in Space 54
5.4 Infinitesimal Element Moving With the Fluid 55
5.5 Finite Control Volume Moving With the Fluid 55
5.6 Summary 56
6 Navier-Stokes Equations 59
6.1 Momentum 59
6.2 Conservation of Momentum 60
6.2.1 Time rate of change of momentum 60
6.2.2 Momentum flux over boundary 60
6.2.3 External forces 63
6.2.4 Conservation of momentum equations 65
6.3 Stokes' Hypothesis 66
6.4 Navier-Stokes Equations for a Newtonian Fluid 67
7 Special Cases of the Navier-Stokes Equations 71
7.1 Incompressible Fluid of Constant Temperature 71
7.2 Dimensionless Navier-Stokes Equations 75
8 Reynolds Averaged Navier-Stokes Equations (RANSE) 82
8.1 Mean and Turbulent Velocity 82
8.2 Time Averaged Continuity Equation 84
8.3 Time Averaged Navier-Stokes Equations 87
8.4 Reynolds Stresses and Turbulence Modeling 89
9 Application of the Conservation Principles 94
9.1 Body in a Wind Tunnel 94
9.2 Submerged Vessel in an Unbounded Fluid 99
9.2.1 Conservation of mass 100
9.2.2 Conservation of momentum 102
10 Boundary Layer Theory 106
10.1 Boundary Layer 106
10.1.1 Boundary layer thickness 107
10.1.2 Laminar and turbulent flow 108
10.1.3 Flow separation 110
10.2 Simplifying Assumptions 111
10.3 Boundary Layer Equations 115
11 Wall Shear Stress in the Boundary L Wall Shear Stress in the Boundary Layer 118
11.1 Control Volume Selection 118
11.2 Conservation of Mass in the Boundary Layer 119
11.3 Conservation of Momentum in the Boundary Layer 121
11.3.1 Momentum flux over boundary of control volume 122
11.3.2 Surface forces acting on control volume 124
11.3.3 Displacement thickness 130
11.3.4 Momentum thickness 131
11.4 Wall Shear Stress
12 Boundary Layer of a Flat Plate 132
12.1 Boundary Layer Equations for a Flat Plate 132
12.2 Dimensionless Velocity Profiles 134
12.3 Boundary Layer Thickness 136
12.4 Wall Shear Stress 140
12.5 Displacement Thickness 141
12.6 Momentum Thickness 142
12.7 Friction Force and Coefficients 143
13 Frictional Resistance 146
13.1 Turbulent Boundary Layers 146
13.2 Shear Stress in Turbulent Flow 152
13.3 Friction Coefficients for Turbulent Flow 153
13.4 Model-Ship Correlation Lines 155
13.5 Effect of Surface Roughness 157
13.6 Effect of Form 160
13.7 Estimating Frictional Resistance 161
14 Inviscid Flow 165
14.1 Euler Equations for Incompressible Flow 165
14.2 Bernoulli Equation 166
14.3 Rotation, Vorticity, and Circulation 171
15 Potential Flow 177
15.1 Velocity Potential 177
15.2 Circulation and Velocity Potential 182
15.3 Laplace Equation 184
15.4 Bernoulli Equation for Potential Flow 187
16 Basic Solutions of the Laplace Equation 191
16.1 Uniform Parallel Flow 191
16.2 Sources and Sinks 192
16.3 Vortex 196
16.4 Combinations of Singularities 198
16.4.1 Rankine oval 198
16.4.2 Dipole 202
16.5 Singularity Distributions 204
17 Ideal Flow Around A Long Cylinder 207
17.1 Boundary Value Problem 207
17.1.1 Moving cylinder in fluid at rest 208
17.1.2 Cylinder at rest in parallel flow 210
17.2 Solution and Velocity Potential 211
17.3 Velocity and Pressure Field 214
17.3.1 Velocity field 215
17.3.2 Pressure field 216
17.4 D'Alembert's Paradox 218
17.5 Added Mass 219
18 Viscous Pressure Resistance 223
18.1 Displacement Effect of Boundary Layer 223
18.2 Flow Separation 226
19 Waves and Ship Wave Patterns 230
19.1 Wave Length, Period, and Height 230
19.2 Fundamental Observations 233
19.3 Kelvin Wave Pattern 235
20 Wave Theory 239
20.1 Overview 239
20.2 Mathematical Model for Long-crested Waves 240
20.2.1 Ocean bottom boundary condition 241
20.2.2 Free surface boundary conditions 242
20.2.3 Far field condition 246
20.2.4 Nonlinear boundary value problem 247
20.3 Linearized Boundary Value Problem 248
21 Linearization of Free Surface Boundary Conditions 250
21.1 Perturbation Approach 250
21.2 Kinematic Free Surface Condition 252
21.3 Dynamic Free Surface Condition 254
21.4 Linearized Free Surface Conditions for Waves 256
22 Linear Wave Theory 259
22.1 Solution of Linear Boundary Value Problem 259
22.2 Far Field Condition Revisited 265
22.3 Dispersion Relation 265
22.4 Deep Water Approximation 267
23 Wave Properties 271
23.1 Linear Wave Theory Results 271
23.2 Wave Number 272
23.3 Water Particle Velocity and Acceleration 275
23.4 Dynamic Pressure 279
23.5 Water Particle Motions 280
24 Wave Energy and Wave Propagation 284
24.1 Wave Propagation 284
24.2 Wave Energy 287
24.2.1 Kinetic wave energy 287
24.2.2 Potential wave energy 290
24.2.3 Total wave energy density 292
24.3 Energy Transport and Group Velocity 293
25 Ship Wave Resistance 299
25.1 Physics of Wave Resistance 299
25.2 Wave Superposition 301
25.3 Michell's Integral 310
25.4 Panel Methods 312
26 Ship Model Testing 316
26.1 Testing Facilities 316
26.1.1 Towing Lank 317
26.1.2 Cavitation tunnel 320
26.2 Ship and Propeller Models 321
26.2.1 Turbulence generation 322
26.2.2 Loading condition 323
26.2.3 Propeller models 324
26.3 Model Basins 324
27 Dimensional Analysis 327
27.1 Purpose of Dimensional Analysis 327
27.2 Buckingham -Theorem 328
27.3 Dimensional Analysis of Ship Resistance 328
28 Laws of Similitude 332
28.1 Similarities 332
28.1.1 Geometric similarity 333
28.1.2 Kinematic similarity 333
28.1.3 Dynamic similarity 334
28.1.4 Summary 340
28.2 Partial Dynamic Similarity 340
28.2.1 Hypothetical case: full dynamic similarity 340
28.2.2 Real world: partial dynamic similarity 342
28.2.3 Froude's hypothesis revisited 343
29 Resistance Test 345
29.1 Test Procedure 345
29.2 Reduction of Resistance Test Data 348
29.3 Form Factor k 351
29.4 Wave Resistance Coefficient Cw 354
29.5 Skin Friction Correction Force FD 355
30 Full Scale Resistance Prediction 357
30.1 Model Test Results 357
30.2 Corrections and Additional Resistance Components 358
30.3 Total Resistance and Effective Power 359
30.4 Example Resistance Prediction 360
31 Resistance Estimates - Guldhammer and Harvald's Method 367
31.1 Historical Development 367
31.2 Guldhammer and Harvald's Method 369
31.2.1 Applicability 369
31.2.2 Required input 369
31.2.3 Resistance estimate 372
31.3 Extended Resistance Estimate Example 378
31.3.1 Completion of input parameters 379
31.3.2 Range of speeds 380
31.3.3 Residuary resistance coefficient 380
31.3.4 Frictional resistance coefficient 383
31.3.5 Additional resistance coefficients 383
31.3.6 Total resistance coefficient 384
31.3.7 Total resistance and effective power 384
32 Introduction to Ship Propulsion 389
32.1 Propulsion Task 389
32.2 Propulsion Systems 391
32.2.1 Marine propeller 391
32.2.2 Water jet propulsion 392
32.2.3 Voith Schneider propeller (VSP) 393
32.3 Efficiencies in Ship Propulsion 394
33 Momentum Theory of the Propeller 398
33.1 Thrust, Axial Momentum, and Mass Flow 398
33.2 Ideal Efficiency and ^rust Loading Coefficient 403
34 Hull-Propeller Interaction 408
34.1 Wake- Fraction 408
34.2 ^rust Deduction Fraction 414
34.3 Relative Rotative Efficiency 417
35 Propeller Geometry 420
35.1 Propeller Parts 420
35.2 Principal Propeller Characteristics 422
35.3 Other Geometric Propeller Characteristics 431
36 Lifting Foils 435
36.1 Foil Geometry and Flow Patterns 435
36.2 Lift and...
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Fertigungstechnik |
| Genre: | Importe, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | 704 S. |
| ISBN-13: | 9781118855485 |
| ISBN-10: | 1118855485 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Birk, Lothar |
| Hersteller: | Wiley |
| Verantwortliche Person für die EU: | Wiley-VCH GmbH, Boschstr. 12, D-69469 Weinheim, product-safety@wiley.com |
| Maße: | 255 x 187 x 42 mm |
| Von/Mit: | Lothar Birk |
| Erscheinungsdatum: | 10.06.2019 |
| Gewicht: | 1,468 kg |
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