$8\mathrm{.}4\mathrm{.}21$ WP To conserve water and energy, a "flow reducer" is installed in the shower head as shown in Fig. P$8\mathrm{.}4\mathrm{.}21.$ If the pressure at point $(1)$ remains constant and all losses except for that in the flow reducer are neglected, determine the value of the loss coefficient $($based on the velocity in the pipe$)$ of the flow reducer if its presence is to reduce the flowrate by a factor of $2.$ Neglect gravity.

FIGURE P$8\mathrm{.}4\mathrm{.}21$