Water is flowing in a pipe as depicted in the figure. What pressure is indicated

Question

Water is flowing in a pipe as depicted in the figure. What pressure is indicated on the upper pressure gauge? (Take d1 = 4.0 cm, v1 = 3.1 m/s, and h = 1.1 m. The density of water is 1000 kg/m3.

Explanation / Answer

Let the velocity at 2nd point is v2 m/s,By the law of continuity of flow:- =>Q = A1v1 = A2v2 =>1/4 x p x d1^2 x v1 = 1/4 x p x d2^2 x v2 =>v2 = (d1/d2)^2 x v1 =>v2 = (3.9/3)^2 x 3.4 =>v2 = 5.75 m/s By the Bernoulli theorem:- =>P1 + 1/2?v1^2 + ?gh1 = P2 + 1/2?v2^2 + ?gh2 =>100 x 10^3 + 1/2 x 1000 x (3.4)^2 + 1000 x 9.8 x 0 = P2 + 1/2 x 1000 x (5.75)^2 + 1000 x 9.8 x 1.2 =>P2 = 10^5 + 1/2 x 1000 x [11.56 - 33.06 - 23.52] =>P2 = 10^5 - 22510 =>P2 = 77490 Pa =>P2 = 77.49 kPa

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