Segment I of a pipe has a cross section area of A_1 = 9.0x 10^3 m^2 and a water

Question

Segment I of a pipe has a cross section area of A_1 = 9.0x 10^3 m^2 and a water flow speed of = 1.50 m/s. Segments 2 and 3 of the pipe narrow to A_2 = A_3 = 2.5 x 10^3 m^2. Segment 3 is a height h above segments 1 and 2. What is the fluid flow speed v_2 in segment 2? Given the fluid pressure in segment I, write the appropriate equation and solve algebraically for the pressure P_3 in segment 3. All terms used in the equation must be the ones given above or defined on the diagram. No numbers allowed.

Explanation / Answer

Bernoulli's theorem
P + (rho)v^2/2 + (rho)gh = constant

Continuity equation
AV = const

so, v2 = A1v1/A2 = 9*1.5/2.5 = 5.625m/s = v3
P1 + (rho)(v1)^2 = P3 + (rho)v3^2/2 + (rho)gh
P3 = P1 + rho([v1]^2 - 2gh - [v3]^2)/2

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