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Water flows at 12 m/s in a horizontal pipe with a pressure of 3.0 104 n/m2. if the pipe widens to twice its original radius, what is the pressure in the wider section?

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Aliwohaish12

Total pressure is constant and PT = P = 1/2ρv^2

So p1 + 1/2ρv1^2 = p2 + 1/2ρv2^2 and from continuity we have ρA1v1 = ρA2v2

So v2 = v1A1/A2 since r2 = 2r1 then A2 = 4A1

so v2 = v1/4

Now from above p2 = p1 + 1/2ρv1^2 - 1/2ρv2^2 = p1 + 1/2ρv1^2 - 1/2ρv1^2/4^2

So p2 = 3.0x10^4Pa + 1/21000kg/m^3(12m/s)^2 - 1/21000kg/m^3*12^2/16

= 9.75x10^4Pa = 9.8x10^4Pa

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