Firefigting nozzle pressure and reaction

[Chris314]

A ladder pipe with a 2" tip at 80 psi nozzle pressure will have approximately ____ pounds of nozzle reaction.
Now I've been out of college and out of practice with my math and physics skills for quite a while. With studying my firefighting materials for operations, a lot of the statements by these books do not add up. The answer given to the above question is 502.4 pounds of reaction force. Newton's third law of motion states to every action; equal and opposite reaction. Pi*r^2 to find the area of the nozzle would give me 3.1416 square inches of surface area and when multiplied by 80 pounds per square inch I arrive at 251.33 pounds of reaction force from the nozzle. So why would the book answer be approximately twice my answer?

 

[Drakkith]

Hmm... according to this site the reaction force is given by NR = 1.57 D²NP.
So in your case it would be NR = 1.57 (4)(80) which equals 502.4 lbs of reaction force.

I'm not sure why the formula is different from Pi x r².