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B Bernoulli's equation, Venturi effect, hydraulic head, nozzle

  1. Jun 5, 2017 #1
    Hi, I have this problem:

    I have a vertical tube 1 meter D, in the bottom end there is a nozzle with 0,5 m D. The tube is full of water. the tube lenght is 10 meters and the nozzle lenght is 2 meters. I need to calculate the power of this by this equation:

    W = Q * g * h * p

    where W is watt, Q is the volumetric flow rate, g is 9.81,h is the head and p is the density (1000 kg/m3 for the water.

    The issue is the velocity in the nozzle: for the Venturi effect, in the nozzle the velocity increases. So in the velocity Torricelli's equation: sqrt(2 * g * h) = v the h value changes in h = (v^2) / 2 * g that is greater then the real h value (12 meters). So in the power equations I use this second h value. Is it right?

    There is an explaination: https://en.wikipedia.org/wiki/Pelton_wheel#Power but I'm not understanding it.
  2. jcsd
  3. Jun 5, 2017 #2

    jack action

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    I'm guessing the velocity in the tube ##v_t## is not zero. This is why the velocity in the nozzle ##v_n## gives a head ##h_n## greater than the physical height of the tube ##h_t##. The relation between the two should be:
    $$\rho g h_t + \frac{\rho v_t^2}{2} = \frac{\rho v_n^2}{2} \equiv \rho g h_n$$
    Of course, the velocity of the fluid in the tube does translate into energy in the nozzle, so ##h_n## should be considered in such a case.
  4. Jun 5, 2017 #3
    Thank you!
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