Grade 11Mechanics
A force field is conservative if ![src=data:image/png;base64,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]()
The circle on the integration sign means that the integration is to be taken along a closed curve (a round trip) in the field. A flow is a potential flow (hence irrotational) if ![src=data:image/png;base64,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]()
for every closed path in the field. Using this criterion, show that the fields of (a) Fig. 16-13 and (b) Fig. 16-16 are fields of potential flow.
