physics (Urgent)!!!!!!!!!!!!!!!!!!!!!!

A Venturi flow meter is used to measure the the flow velocity of a water main. The water main has a diameter of 40.0 cm, and the constriction has a diameter of 10.0 cm. The two vertical pipes are open at the top, and the difference in water level between them is 4.0 m. Find the velocity, vm (in m/s), and the volumetric flow rate, Q (in m3/s), of the water in the main.

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  1. p + (1/2) rho v^2 = constant
    rho = water density = about 1000 kg/m^3

    p = rho g h
    p big pipe + (1/2) rho vbig^2 = plittle pipe + (1/2)rho vlittle^2

    p big pipe - p little pipe =1000(9.81)(4)
    = 39240 Newtons/m^2 or Pascals
    so
    39240 = (1/2)(1000)(vlittle^2-vbig^2)
    now what can we say about vbig and vlittle?
    Same amount of water per second through both the big pipe and the little pipe
    so
    Vbig(pi Dbig^2/4)=Vlittle(pi*Dlittle^2/4)
    or
    vlittle = Vbig (40^2/10^2) =Vbig(16)
    so now
    2*39.240 = ([16vbig]^2-vbig^2)=255 vbig^2
    so
    vbig = .555 m/s
    Q = .555 * pipe area = .555(pi*.4^2/4)

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    posted by Damon

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