Surface tension, of constant value o, causes the pressure at the water surface to be different from that in the atmosphere by an amount proportional to the curvature of the surface by introducing an additional restoring force directed towards the undis- turbed horizontal water surface (z = 0). The fluid pressure at the surface for small waves is thus p = Pa – 0- i. Show that the phase speed, c = w/k, of waves when surface tension is present is given by c? = g/k + (o/p)k. ii. Does surface tension cause a given wave to travel faster or slower and why should this be so? iii. Which waves are most affected by surface tension and why should this be so?
Surface tension, of constant value o, causes the pressure at the water surface to be different from that in the atmosphere by an amount proportional to the curvature of the surface by introducing an additional restoring force directed towards the undis- turbed horizontal water surface (z = 0). The fluid pressure at the surface for small waves is thus p = Pa – 0- i. Show that the phase speed, c = w/k, of waves when surface tension is present is given by c? = g/k + (o/p)k. ii. Does surface tension cause a given wave to travel faster or slower and why should this be so? iii. Which waves are most affected by surface tension and why should this be so?
Sustainable Energy
2nd Edition
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:DUNLAP, Richard A.
Chapter12: Wave Energy
Section: Chapter Questions
Problem 9P
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Transcribed Image Text:Surface tension, of constant value o, causes the pressure at the water surface to be
different from that in the atmosphere by an amount proportional to the curvature of
the surface by introducing an additional restoring force directed towards the undis-
turbed horizontal water surface (z = 0). The fluid pressure at the surface for small
waves is thus
p = Pa – o
i. Show that the phase speed, c = w/k, of waves when surface tension is present
is given by
c? = g/k + (0/p)k.
ii. Does surface tension cause a given wave to travel faster or slower and why should
this be so?
iii. Which waves are most affected by surface tension and why should this be so?
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