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Wave Velocity

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Laplace’s equation in the Polar Coordinate System

www.math.ucdavis.edu

represent the heat and wave equations in the polar coordinate system. For the heat equation, the solution u(x,y t)˘ r µ satisfies ut ˘k(uxx ¯uyy)˘k µ urr ¯ 1 r ur ¯ 1 r2 uµµ ¶, k ¨0: diffusivity, whereas for the wave equation, we have utt ˘c 2(u xx ¯uyy)˘c 2 µ urr ¯ 1 r ur ¯ 1 r2 uµµ ¶ c ¨0: wave velocity. 3

  System, Coordinates, Equations, Waves, Velocity, Polar, Wave velocity, Equation in the polar coordinate system, In the polar coordinate system

DERIVATION AND ANALYSIS OF SOME WAVE EQUATIONS

www.colorado.edu

4.3. WATERWAVES 5 Wavetype Cause Period Velocity Sound Sealife,ships 10 −1−10 5s 1.52km/s Capillaryripples Wind <10−1s 0.2-0.5m/s Gravitywaves Wind 1-25s 2-40m/s Sieches Earthquakes,storms minutestohours standingwaves

  Waves, Velocity

Chapter 13 OPEN-CHANNEL FLOW - Ira A. Fulton College of ...

www2.et.byu.edu

The Froude number is also the ratio of the flow speed to wave speed, Fr = V /co. Discussion The Froude number is the most important parameter in open-channel flow. 13-11 Solution A single wave is initiated in a sea by a strong jolt during an earthquake. The speed of the resulting wave is to be determined. Assumptions The depth of water is constant,

  Open, Chapter, Flows, Waves, Channel, Chapter 13 open channel flow

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