Bournalli's Equation homework problem

[jan2905]

A fluid of density (rho) flows through a horizontal pipe with negligible viscosity. The flow is streamline with constant flow rate. The diameter of the pipe at Point 1 is d and the flow speed is v. If the diameter of the pipe at Point 2 is d/3, then the pressure at Point 2 is?



Bournalli's Equation (sp). I ended up getting P2=P1 - 40(rho)v^2. Correct?

 

[nvn]

jan2905: That is correct; p2 = p1 - 40*rho*v^2.

 

[jan2905]

would this mean that if i were hit with the liquid at the respective points...

p1 would hurt more than p2? that would mean that a large mouth waterhose has more force than a small mouth... that is not correct though.

 

[nvn]

jan2905: I think water exiting a small-mouth water hose at point 2 would probably hurt more, because it has a much higher velocity than the water at point 1. Both streams would be at atmospheric pressure immediately upon exit from the nozzle.

 

[jan2905]

but we deduced that p1 would have more pressure therefore hurting more. this math seems to be counterintuitive.