Calculating the gauge pressure?

AI Thread Summary
To calculate the gauge pressure in the lower pipe, the flow speed must first be determined using the flow rate and the area of the pipes. The equation of continuity is then applied to find the velocity in the lower pipe. The gauge pressure is derived from the difference between pressures, factoring in the height difference and the velocities of both pipes. Since the pressure in the upper pipe is atmospheric, it simplifies the calculation for gauge pressure. The approach outlined is correct, and atmospheric pressure can be treated as zero for gauge pressure calculations.
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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.
 
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