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Question

An incompressible fluid of density ρ flows through a horizontal pipe of radius r and then passes through a constriction of radius r2 . If the fluid has pressure Po and velocity Vo before the constriction, pressure in the constriction is Po3α2ρV2o. Here α is an integer. Find α .

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Solution

By equation of continuity,
πr2Vo=πr24V
V=4Vo
By Bernoulli's equation,
Po+12ρV2o=P+12ρV2
Po+12ρV2o=P+1216ρV2o;
P=Po152ρV2o

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