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A water jet that leaves a nozzle at 78 m/s at a flow rate of 120 kg/s is to be used to generate power by striking the buckets located on the perimeter of a wheel. Determine the power generation potential of this water jet. Assume that the water jet flows steadily at the specified speed and flow rate. (Round the final answer to two decimal places.) The power generation potential is kW.

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okpalawalter8

Answer:

The  value is [tex]E = 365040 J/s [/tex]

Explanation:

From the question we are told that

   The  speed of the water jet is  [tex]v = 78 \ m/s[/tex]

    The  flow rate of the water jet is  [tex]\r m = 120 \ kg /s[/tex]

Generally the mechanically energy possessed by a water flow is mathematically represented as

           [tex]E = \r m * e[/tex]

Here here e  is the specific mechanical energy generated which is mathematically represented as

          [tex]e[KJ/kg] = FE + KE + PE[/tex]

Here  

     FE - flow  energy

    KE  - kinetic energy

    PE  -  potential energy

Generally give that we are only considering the power generation due to the kinetic energy of the water we have that

       [tex]E = \r m * KE [/tex]

Here  

     [tex]KE = \frac{v^2}{2}[/tex]

    [tex]E  =  \r m  * \frac{v^2}{2} [/tex]

=>    [tex]E  = 120  * \frac{78^2}{2} [/tex]

=>    [tex]E  = 365040 J/s [/tex]