Fluids - Head Loss complicated

In summary, the minimum diameter of the circular pipe that is to be heated using heated air at 1 atmosphere and 35 degrees Celsius is 150 meters. The head loss in the pipe is not to exceed 20 meters, so the diameter of the pipe needs to be greater than this.
  • #1
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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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  • #2
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...
 
  • #3
Do what you were doing in the first attempt, with V = Q/A. Keep in mind that A = (pi/4)*D^2
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 

1. What is head loss in fluids?

Head loss in fluids refers to the decrease in pressure that occurs as a fluid flows through a pipe or channel. It is caused by factors such as friction, turbulence, and changes in direction or velocity of the fluid.

2. How is head loss calculated?

Head loss can be calculated using various equations such as the Darcy-Weisbach equation, the Hazen-Williams equation, or the Manning equation. These equations take into account the properties of the fluid, the geometry of the pipe or channel, and other factors to determine the amount of head loss.

3. What causes complicated head loss in fluids?

Complicated head loss in fluids can be caused by a variety of factors such as changes in pipe diameter, sudden expansions or contractions, bends or elbows in the pipe, and roughness of the pipe surface. These factors can create complex flow patterns and increase the amount of head loss.

4. How can complicated head loss be minimized?

Complicated head loss can be minimized by using smoother pipes, avoiding sudden changes in pipe diameter, and reducing the number of bends or elbows in the pipe. Additionally, using laminar flow instead of turbulent flow can also help reduce head loss.

5. What are some practical applications of understanding head loss in fluids?

Understanding head loss in fluids is important in many engineering applications such as designing pipelines, irrigation systems, and water supply systems. It is also essential in calculating the efficiency of pumps and other fluid handling equipment. Understanding head loss can help ensure the safe and efficient transport of fluids in various industries.

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