Calculating the gauge pressure?

[miamirulz29]

Homework Statement

Water flows through a .259m radius pipe at the rate of .125m^3/s. The pressure in the pipe is atmospheric. The pipe slants downhill and feeds into a second pipe with a radius of .190m, positioned .796m lower. What is the gauge pressure in the lower pipe? The acceleration of gravity is 9.81 m/s^2. Answer in the units of Pa.

Homework Equations

A1V1 = A2V2
flow speed = flow rate / area
P1 + [(Rho)(g)(h1)] + [(1/2)(rho)(V1^2)] = P2 + [(Rho)(g)(h2)] + [(1/2)(rho)(V2^2)]

The Attempt at a Solution

Calculating the flow speed gives me V1. Then I can find V2 using the equation of continuity.
Also, because we are looking for gauge pressure, I am look for P1- P2. Therefore:

P1-P2 = [(rho)(g)(delta H)] + [(1/2)(rho)(V2^2)] - [(1/2)(rho)(V1^2)]

Is this correct? Also, do I need to do anything for P1 if that pressure is atmospheric in the pipe? Thanks in advance.

 

[miamirulz29]

Anybody? Just tell me if what I am doing is correct.