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Example

tex2html_wrap1439

5sec sinusoidal wave is propagating in deep water. Find the velocity vector and pressure (difference from hydrostatic in the absence of the wave) at a distance tex2html_wrap_inline1389 = 10m from the crest, depth of 1m and the time t=3 sec.

eqnarray306

tex2html_wrap_inline1391

x=10 m, z= -1m, t=3 sec

tex2html_wrap_inline1393

tex2html_wrap_inline1395

tex2html_wrap_inline1397 x10-1.257 x tex2html_wrap_inline1401

tex2html_wrap_inline1403

tex2html_wrap_inline1405 x1.257 x tex2html_wrap_inline1409

Note that tex2html_wrap_inline1411

tex2html_wrap_inline1413 x tex2html_wrap_inline1415

tex2html_wrap_inline1417 x tex2html_wrap_inline1419

tex2html_wrap1441

Pressure            tex2html_wrap_inline1421

We are asking for tex2html_wrap_inline1423 1,025 x 9.81 x tex2html_wrap_inline1425 x (-0.5565) x 0.85 = -475.6 Pa

Note that tex2html_wrap_inline1427 1,025 x 9.81 x tex2html_wrap_inline1425 x 0.85 =  854.7 Pa

Q: What if we were asking to find the same quantities tex2html_wrap_inline1431 when the trough of the wave was passing above point A?

A: In this case     tex2html_wrap_inline1433

      tex2html_wrap_inline1435

      tex2html_wrap_inline1437

tex2html_wrap1443


Soon Woong Chang
Wed Oct 27 12:41:46 CDT 1999