Calculating the gauge pressure?

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SUMMARY

The discussion focuses on calculating the gauge pressure in a lower pipe connected to an upper pipe with a specified flow rate and dimensions. The problem involves using the principle of conservation of mass and Bernoulli's equation to relate pressures and velocities in the two pipes. The user correctly identifies the need to calculate flow speeds using the equation of continuity and applies Bernoulli's equation to find the difference in pressure. The atmospheric pressure in the upper pipe is acknowledged as a reference point for gauge pressure calculations.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Knowledge of the equation of continuity in fluid flow.
  • Familiarity with gauge pressure and its relation to atmospheric pressure.
  • Basic skills in algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Study Bernoulli's equation in detail, focusing on its applications in fluid mechanics.
  • Learn about the equation of continuity and its implications for varying pipe diameters.
  • Explore the concept of gauge pressure versus absolute pressure in fluid systems.
  • Practice solving fluid dynamics problems involving multiple pipes and varying heights.
USEFUL FOR

Students in physics or engineering courses, particularly those studying fluid mechanics, as well as professionals involved in hydraulic systems and fluid flow analysis.

miamirulz29
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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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Anybody? Just tell me if what I am doing is correct.
 

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