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https://www.chegg.com/homework-help/questions-and-answers/derive-expression-area- velocity-relationship-compressible-fluid-form-frac-d-frac-d-v-v-lef-q
The condition of fluid before entering the passage is stand still. Apply steady flow energy equation at stand still condition to a section where velocity is V, area is A.
From equation (ii), it is clear that as velocity increases, pressure decreases or vice versa.