MEC-E2001 Ship Hydrodynamics. Prof. Z. Zong Room 213a, K3, Puumiehenkuja 5A, Espoo
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1 MEC-E2001 Ship Hydrodynamics Prof. Z. Zong Room 213a, K3, Puumiehenkuja 5A, Espoo
2 Teacher: Prof. Z. Zong, Room 213a, K3, Puumiehenkuja 5A, Espoo Teaching assistant: Ms Yan Dongni, Room 213a, K3, Puumiehenkuja 5A, Espoo Lecture: , 2017, 8:15-10, Tue & Thur, R008/202 Exercises: ,2017, 10:15-12:00 Thur, R008/202 Model tests at VTT ( , & ) Examinations: 12.12,2017, 9:00-12:00 Tue, R008/202
3 0. Introduction
4 Small is big Dimensional Analysis for Model Testing
5 References Additional Readings: J. N Newman, Marine Hydrodynamics, MIT Press, 1977 L I Sedov, Similarity and Dimensional Methods in Mechanics, Tenth Edition, CRC, 1993
6 Model testing Similitude I am here
7 Invariance Similarity ratio
8 Invariance What else remains unchanged? (Froude ) Kinetic similarity-same flow patterns Dynamic similarity Forces: impossible to be same Reduced forces: possible to be same How to keep kinetic and dynamic similarities?
9 Example 1: A free-falling ball in vacuum One of most famous experiment in history Observations: (1) unit-free constant (½) is unchanged. Constants (invariants) are unchanged between a model testing and a full-size test. These constants are similarity parameters.
10 Example 1: A free-falling ball in vacuum One of most famous experiment in history Observations: (2) unit-free constant represents a combination of some quantities such that it does not have unit of measurement dimensionless.
11 Example 1: A free-falling ball in vacuum One of most famous experiment in history dimension: a quantity to measure other physical quantities, e.g. length, mass Unit: value assigned to a dimension e.g., m, sec, kg Observations: (3) Dimensional homogeneity. Any physically meaningful equation will have the same dimensions on the right and left sides of an equation or an inequality.
12 Example 1: A free-falling ball in vacuum One of most famous experiment in history Observations: (4) Buckingham P theorem. If there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n k dimensionless parameters π 1, π 2,..., π p constructed from the original variables
13 Example 1: A free-falling ball in vacuum One of most famous experiment in history Fundamental dimensions Observations: (5) Nondimensiolization. Finding invariant C is equal to making every quantities dimensionless
14 Dimensional Analysis (Maxwell) In summary 1: Dimensional Equation 2: Fundamental Dimensions 3: Dimensionless Quantities 4: Dimensionless Equation 5: Model testing to determine the dimensionless equation
15 Example 2: Again free-falling ball 1: Dimensional Equation 2: Fundamental quantities 3: Dimensionless Quantities 4: Dimensionless Equation 5: Experimental test Test no Observations
16 Example 3: Water Wave 1: Dimensional Equation 2: Fundamental quantities 3: Dimensionless Quantities 4: Dimensionless Equation Special cases
17 Example 3: Water Wave (Continued) Dispersion relationship (1) Longer waves travel faster (2) The speed of a (displacement) ship cannot exceed the wave speed produced by it, that is,, therefore where L is ship length and U is speed (3) Froude Law: displacement ship
18 Example 4: Drag on a sphere (Rayleigh) 1: Dimensional Equation D f ( d, U,, ). 2: Fundamental quantities 3: Dimensionless Quantities 4: Dimensionless Equation 5: The same is true of a circular cylinder
19 Example 4: Drag on a sphere (continued) Parameters Kinetic similarity Qualitative behaviors of fluid flow depends to a large extent on Reynolds number; similar flow patterns often appear when the shape and Reynolds number is matched, although other parameters like surface roughness have a big effect Dynamic similarity The drag coefficient (commonly denoted as: c d, c x or c w ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less hydrodynamic drag.
20 Example 5: Drag on a plate 1: Dimensional Equation D f ( d, U,, ). 2: Fundamental quantities 3: Dimensionless Quantities 4: Dimensionless Equation
21 Example 6: Resistance of a ship 1: Dimensional Equation 2: Fundamental quantities 3: Dimensionless Quantities 4: Dimensionless Equation 5: Froude decomposition and ITTC-57 formula
22 Example 6: Resistance of a ship 2: The real ship 3: Resistance of the real ship CDs t Fr
23 Example 6: Resistance of a ship I am here
24 Highlights of the lecture 1: Invariance and invariants Geometric, kinematic and dynamic similarities Drag coefficient 2: Buckingham P theorem It may reduce n physical unknowns to n-3 unknowns 3: Four-steps dimensional analysis Approach to find invariants in a model testing 4: Design test to determine the coefficients A well-designed test talks. Small is big
25 Homework Problems 1. Problems 1-3, Marine Hydrodynamics, Due: 1 week Think: 1. How to determine the number of unknowns in a physically-meaningful equation as in the first step of the dimensional analysis. Think further: 1. How can we know a very hot planet faraway from us (1400 ly, to say) is suitable for life?
MEC-E2001 Ship Hydrodynamics. Prof. Z. Zong Room 213a, K3, Puumiehenkuja 5A, Espoo
MEC-E2001 Ship Hydrodynamics Prof. Z. Zong zhi.zong@aalto.fi Room 213a, K3, Puumiehenkuja 5A, 02510 Espoo Teacher: Prof. Z. Zong, zhi.zong@aalto.fi Room 213a, K3, Puumiehenkuja 5A, 02510 Espoo Teaching
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![Fig. 2.1 I =... A [2] Suggest why it would be impossible for overhead cables carrying an alternating current to float in the Earth s magnetic field.](/thumbs/78/78653113.jpg "Fig. 2.1 I =... A [2] Suggest why it would be impossible for overhead cables carrying an alternating current to float in the Earth s magnetic field.")
1 (a) Fig. 2.1 shows a horizontal current-carrying wire placed in a uniform magnetic field. I region of uniform magnetic field wire Fig. 2.1 The magnetic field of flux density 0.070 T is at right angles
Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.
Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 7 Reading Assignment R1. Read the section Common Dimensionless Groups