What Is the Minimum Diameter of a Duct to Limit Head Loss to 20 Meters?

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Discussion Overview

The discussion revolves around determining the minimum diameter of a circular duct needed to transport heated air while limiting head loss to 20 meters over a distance of 150 meters. The conversation includes aspects of fluid dynamics, specifically focusing on head loss calculations, the application of various equations, and the challenges posed by missing variables such as velocity and friction factor.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant outlines the problem and attempts to use the major head loss equation alongside the flow rate equation, expressing confusion over the calculations involved.
  • Another participant mentions trying the Swamee-Jain formula but notes its inapplicability for smooth pipes, indicating difficulty in finding an alternative method to determine diameter with the given parameters.
  • A suggestion is made to continue with the initial approach, emphasizing the relationship between flow rate and area to find diameter.
  • One participant describes using the Swamee-Jain equation for calculations but acknowledges the need to verify results against the Moody Chart for smooth pipes, indicating a methodical approach involving multiple diameter calculations.
  • Another participant proposes an iterative solution, suggesting assumptions about velocity to calculate Reynolds number and friction factor, then refining the diameter until convergence is achieved.
  • A participant references a specific roughness value for smooth pipes from a textbook, suggesting its use in calculations to derive a diameter.

Areas of Agreement / Disagreement

Participants express varying approaches to the problem, with no consensus on a single method or solution. Disagreement exists regarding the applicability of certain formulas and the necessity of iterative methods.

Contextual Notes

Participants note limitations due to missing variables such as velocity and friction factor, which complicate the calculations. The discussion also highlights dependencies on specific equations and assumptions regarding pipe roughness.

Who May Find This Useful

This discussion may be useful for students or professionals involved in fluid dynamics, particularly those working on duct design and head loss calculations in engineering contexts.

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Homework Statement



Heated air at 1 atmosphere and 35 deg. Celsius is to be transported in a 150 meter long circular plastic duct (smooth) at a rate of 0.35 cubic meters/sec. If the head loss in the pipe is not to exceed 20 meters, determine the minimum diameter of the duct.


Homework Equations



hlt (total head loss) = hl + hlm (major and minor head loss)

there is no minor head loss

hl=f*(L/d)*[(v^2)/2] - (friction factor times length over diameter times velocity squared over 2)

V=Q/A

Re= ro*v*d / meu



The Attempt at a Solution



Okay so first I tried to calculate diameter using a combination of the major head loss equation and the Q=VA eq. I got a huge mess involving large calculations to the 1/5th power. I don't that that was the right approach.

I also got the density and dynamic viscosity of air at 35 deg-

ro(air@35deg.C)=1.15kg/m^3
meu(air@35deg.C)=1.88E-5

Okay so then I thought I could get the Reynolds # but I am missing velocity and diameter.

NEXT- I figured- there is no head loss because (being that the pipe is smooth) there are no losses to friction and there are no components (valves, elbows etc) so there are no major or minor head losses. Where would they come from if not from friction? So now I am a little lost with this one. Am I applying the wrong formula? Not having the velocity OR diameter is really messing me up. Any help is appreciated. Thanks
 
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I have also tried the Swamee-Jain formula... but that does not apply to smooth pipes. I can't think of any other way to get diameter when you only have Q, hl, L, and the properties of the fluid...
 
Do what you were doing in the first attempt, with V = Q/A. Keep in mind that A = (pi/4)*D^2
 
Well like I said earlier, I ended up using the Swamee-Jain equation form 3, and calculated the diameter. But, since the Swamee Jain eq is only accurate for pipes with a relative roughness greater than smooth, I needed to check this. I set up a spreadsheet with hundreds of diameters. Then calculated the Reynolds number and friction factor for each (friction factor using the Head Loss eq.). I then plotted these on the Moody Chart. Where this curve intersected with the curve for smooth pipes, I had my diameter. It matched the diameter I calculated courtesy of Swamee and Jain.
 
Seeing how you don't have velocity or friction factor leads me to believe that this might be an iterative solution.

Assume a value of velocity, use that to find your Reynolds, find your friction using the Colebrook equation. Find the diameter. Rinse and repeat until you get some sort of convergence.
 
My piping systems design textbook says that for a smooth pipe, you can take your roughness e = 0.0015mm.

Try that and see what kind of answer you come up with.
 

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