Question

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).

Answer 1

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

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

           $v_n =14.09 \ m/s$