Develop an expression for the pressure at location 1 in terms of the velocity at location 1

To conserve water and energy, a "flow reducer" is installed in the shower head as shown in Fig. P8.57. 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.

Minor head loss depends on loss coefficient and velocity.

1) With location 1 as the reference height, what are the terms in the Bernoulli equation at location 1 (Write the equation in terms of specific weight and gravity)?

2) With location 2 at the position after the flow has passed through the nozzles, what is the pressure at location 2?

p2 =

3) For location 2, what are the terms in the Bernoulli equation at location 2?

4) What is the velocity at position 2 in terms of that at location 1?

V2 = × V1

5) What is the expression for the pressure at location 1 in terms of the velocity at location 1? (Round the value to 2 decimal places)

p1/γ =