Water is traveling through a horizontal pipe with a speed of 1.7 m/s and at a pressure of 205 kPa. This pipe is reduced to a new pipe which

Question

Water is traveling through a horizontal pipe with a speed of 1.7 m/s and at a pressure of 205 kPa. This pipe is reduced to a new pipe which has a diameter half that of the first section of pipe. Determine the speed and pressure of the water in the new, reduced in size pipe.

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Sigridomena 5 years 2021-08-26T23:19:51+00:00 1 Answers 12 views 0

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  1. nguyetanh
    0
    2021-08-26T23:21:00+00:00
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    Answer:

    The velocity is  v_2 = 6.8 \ m/s

    The pressure is  P_2 = 204978 Pa

    Explanation:

    From the question we are told that

     The speed at which water is travelling through is  v = 1.7 \ m/s

      The pressure is  P_1 = 205 k Pa = 205 *10^{3} \ Pa

       The diameter of the new pipe is d = \frac{D}{2}

    Where D is the diameter of first pipe

       

    According to the principal of continuity we have that

           A_1 v_1 = A_2 v_2    

    Now  A_1 is the area of the first pipe which is mathematically represented as

           A_1 = \pi \frac{D^2}{4}

    and  A_2 is the area of the second pipe which is mathematically represented as  

           A_2 = \pi \frac{d^2}{4}

    Recall   d = \frac{D}{2}

            A_2 = \pi \frac{[ D^2]}{4 *4}

            A_2 = \frac{A_1}{4}

    So    A_1 v_1 = \frac{A_1}{4} v_2

    substituting value

            1.7 = \frac{1}{4} * v_2    

            v_2 = 4 * 1.7    

           v_2 = 6.8 \ m/s

       

    According to Bernoulli’s equation  we have that

         P_1 + \rho \frac{v_1 ^2}{2} = P_2 + \rho \frac{v_2 ^2}{2}

    substituting values

         205 *10^{3 }+ \frac{1.7 ^2}{2} = P_2 + \frac{6.8 ^2}{2}

         P_2 = 204978 Pa

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