Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in figure below, the pressure is P1 = 1.75X104 Pa and the pipe diameter is 6.00 cm. At another point y = 0.250 m higher, the pressure is P2 = 1.20X104 Pa and the pipe diameter is 3.00 cm. Find the speed of flow (A) in the lower section and (B) in the upper section. (C) Find the volume flow rate through the pipe.

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  1. p1 + rho g h1 + (1/2) rho v1^2 = p1 + rho g h1 + (1/2) rho v1^2
    and v2 A2 = v1 A1 = Q , because Q, vol flow, is constant

    density = rho = 10^3 kg/m^3
    g = 9.8

    p1 = 1.75*10^4 N/m^2
    r1 = 0.030 m so A1 = pi (.03)^2 = 2.83*10^-3 m^2
    h1 = 0, select as base height
    p2 = 1.20*10^4
    r2 = 0.015 m so A2 = pi (0.015)^2 = 0.707*10^-3 m^2
    h2 = 0.250 m
    v2 = v1 (A1/A2) = v1 (2.83/.707) = 4 v1
    1.75*10^4 + 0 + 500 v1^2 = 1.2*10^4 + 10^3 * 9.8*0.25 + 500*16v1^2
    solve for v1, then go back for the rest
    v2 = 4 v1
    Q = A1 v1 = A2 v2

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