Physics...............?
water flows horizontally through a garden hose of radius 1.0cm at speed of 1.4 m/s. the water shoots horizontally out of a nozzle radius of .25cm. what is the gauge pressure of the water inside the hose?
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By the law of continuity of flow:-
=>Q = A1v1 = A2v2
=>v2 = v1 x (A1/A2)
=>v2 = v1 x (r1/r2)^2
=>v2 = 1.4 x (1/0.25)^2
=>v2 = 22.4 m/s
By Bernoulli's theorem:-
=>P1 + 1/2dv1^2 + dgh1 = P2 + 1/2dv2^2 + dgh2
=>as h1 = h2
=>P1-P2 = 1/2d(v2^2 - v1^2)
=>P1 - P2 = 1/2 x 1000 x [(22.4)^2 - (1.4)^2]
=>P1 - P2 = 2.5 x 10^5 Pa
=>∆P = 2.5 x 10^5 Pa
Bernoulli principle :
p1 + (1/2)ρ*v1^2 = p2 + (1/2)ρ*v2^2
Δp = (1/2) * ρ (v2^2 - v1^2) = (1/2) * 1000 * 1.4^2(16^2- 1) = 2.50 x 10^5 Pa
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