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Elanso [62]
3 years ago
9

Water is flowing in a fire hose with a velocity of 1.0 m/s and a pressure of 200000 Pa. At the nozzle the pressure decreases to

atmospheric pressure (101300 Pa), there is no change in height. Use the Bernoulli equation to calculate the velocity of the water exiting the nozzle. The velocity of the water exiting the nozzle is_______m/s. (Hint: The density of water is 1000 kg/m3).
Physics
1 answer:
jeka57 [31]3 years ago
6 0

Answer:

The velocity is v_n  =14.09 \ m/s

Explanation:

From the question we are told that

    The velocity of the water in the pipe is  v_i =  1.0 \ m/s

     The pressure inside the pipe  is  P_i  = 200000 \ Pa

      The pressure at the nozzle is  P_n  =  101300 \ Pa

       The density of water is  \rho  =  1000 \ kg / m^3

      For the height h_1 = h_2 = h

where  h_1 is height of water in the pipe

  and  h_2 is height of water at the nozzle

Generally Bernoulli equation is represented as

       \frac{1}{2} \rho * v_i ^2 + \rho * g * h_1 +  P_i =  \frac{1}{2} \rho v_n ^2 + \rho * g* h_2 + P_n

=>   \frac{1}{2} \rho * v_i ^2 + \rho * g * h +  P_1 =  \frac{1}{2} \rho v_n ^2 + \rho * g* h + P_2

Where v_n is the velocity of the water at the nozzle

Now  making  v_n  the subject

            v_n  =  \sqrt{\frac{2}{\rho} [ P_i - Pn + \frac{1}{2} \rho v_i^2}

substituting values

            v_n  =  \sqrt{\frac{2}{1000} [ 200000 - 101300 + \frac{1}{2} (1000 * (1.0)^2)}

           v_n  =14.09 \ m/s

     

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