Relative Roughness of pipes - Solving a Three Reservoir Problem

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SUMMARY

The discussion centers on solving a three-reservoir problem involving the calculation of relative roughness, Reynolds number, and friction factor. The provided data includes reservoir water levels, pipeline coefficients, lengths, diameters, and roughness values. A critical point raised is that the relative roughness must be less than 0.05, which was initially miscalculated due to incorrect unit usage for pipe diameter. The resolution involved correcting the units from meters to millimeters, allowing for accurate calculations of discharge and flow directions.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically the Reynolds number and friction factor calculations.
  • Familiarity with the Moody Diagram for determining flow characteristics based on relative roughness.
  • Knowledge of unit conversions, particularly between meters and millimeters in engineering contexts.
  • Proficiency in solving systems of equations related to fluid flow, such as discharge equations.
NEXT STEPS
  • Study the calculation of Reynolds number using the formula: Re = (Density * Velocity * Diameter) / Viscosity.
  • Learn how to interpret and utilize the Moody Diagram for various flow regimes.
  • Research the impact of relative roughness on flow resistance in pipelines.
  • Explore methods for solving complex fluid flow systems, including the use of computational fluid dynamics (CFD) software.
USEFUL FOR

Engineers, fluid mechanics students, and professionals involved in hydraulic design and analysis, particularly those working with pipeline systems and fluid flow calculations.

xaan
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Relative Roughness of pipes!

Homework Statement



Here is the Data:

Reservoir Water Entry Pipeline Pipeline Pipeline
Number Level Coeff. Length Diameter Roughness
m [AHD] [m] [m] [mm]
0 20.665 0.814 432.453 1.222 0.089
1 17.787 0.544 111.972 1.361 0.147
2 11.166 0.583 201.258 1.171 0.076


Homework Equations


I need to solve this three reservoir problem, but I'm stuck in finding the Reynold's number and Friction factor from Relative densities. Relative roughness is just (Pipeline Roughness/Pipe Diameter). From Moody Diagram, the highest Relative roughness is 0.05 and I can't see anything higher than that, but the values I get are all higher than 0.05 for relative roughness.


The Attempt at a Solution


Is there a solution to this?
 
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Hello Xaan, you're relative roughnesses are smaller than 0.05. Look at the unit of relative roughness and the ones you are given in the table. That should clarify one of your problems. The one for calculating the Reynolds number is something else. Do you know the formula for this? Can you give some more information on how this system looks like? It is a bit unclear for me to understand.
 
coomast said:
Hello Xaan, you're relative roughnesses are smaller than 0.05. Look at the unit of relative roughness and the ones you are given in the table. That should clarify one of your problems. The one for calculating the Reynolds number is something else. Do you know the formula for this? Can you give some more information on how this system looks like? It is a bit unclear for me to understand.

Yes I realized that relative roughnesses have to be smaller than 0.05. I had to go back and double check it from where I got the info from, and they told me the units they used was wrong. Instead of mm, they put m for pipe diameter. lol so I solved it and I go all the dischages and their directions:

Q1 + Q2 = Q3

*cheerz!*
 

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