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Flow in a streamtube



Previously we found that the resultant work effected on the amount of fluid under consideration in order to realise the displacement under consideration is given by

ΔW1 - ΔW2 = P1×ΔV1 - P2×ΔV2 = (P1 - P2)×ΔV


Hence, if the difference in work effected on the amount of fluid is converted into kinetic energy, then

(P1 - P2)×ΔV = ρfluid ΔV (v22 -v12)/2


which, by dividing out ΔV, turns into

P1 - P2 = ρfluid  (v22 -v12)/2
or equivalently

P1 + ρfluid v12/2 = P2 + ρfluid v22/2


This is the principle of Bernoulli.




streamtube