You work at a small consulting firm whose client is planning

You work at a small consulting firm whose client is planning to enter the nozzle market for fire protection. Your supervisor has asked you to do a preliminary design computation. He wants you to provide the required internal diameter for the exit of a nozzle for the following conditions.

• required flow rate of 100 gal/min

• hydrant pressure of 100 psi

• fire hose internal diameter of 3 inches

• fire hose length of 50 m

• fire personnel standoff distance of 25 m.

• the water jet emanating from the nozzle must reach at least to the top of a 5 story building (a story is 3m).

The head loss for the nozzle is:

h_n = 1*V²/2g (1)

and the head loss for the fire hose is:

h_f = k₂*(V²/2g)*(L/D) (2)

where L is the length of the fire hose, D is the diameter of the fire hose, 1 = 0.5 and 2 = 0.02. Your job is to provide a value for d, the diameter of the nozzle exit. You may assume that there are no other losses. There are other assumptions that you may wish to make; be sure that they are clearly stated.

A problem like this may be over-constrained or under-constrained. Over-constrained means that there is no nozzle diameter that will give you the required volumetric flow rate and the required elevation of the water jet. Under-constrained means that there is more than one diameter that will meet these requirements. If the problem is over-constrained, state this and provide a recommendation of possible ways to meet these conditions via minimal changes in the problem statement. If the problem is under-constrained, point out the extra capability that you have with your nozzle design. Use the SI system in all of your calculations.

Present your design in three pages or less. Points will be deducted for any material in excess of three pages. Also imagine that you are presenting this to someone such as your boss who might not have your engineering background so keep that in mind in the presentation of your problem.