Compressed Air System

[Pipeguy1509]

I've been reading a book about compressed air and i saw a equation for pressure drop that i can't find your origin:

Hf=(2/d).l.?.?.v²

Hf= Pressure Drop (kgf/m³)
d= Diameter (m)
l= Lenght (m)
?= Specific Weight (kgf/m³)
?= Coefficient given by (0,000507)+(0,00001294/d)
v= Velocity (m/s)

Can anybody help me?

 

[PersonalProfile]

D'Arcy-Weisbach euqation?

http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html

Regards,
Lyle

 

[Pipeguy1509]

No... almost this.

In this book Henry P.G. Darcy and other pioneers in hydraulics, (you can find in google books)page 29/30/31 Darcy propose an experimental equation:

R.I=a.v+b.v²

That que be expressed by:

R.I=b.v²

b=a+b/r

For Cast Irons

a=0,000507
b=0,00000647

so:

I=(2/d).(0,000507+2.0,00000647/d).v²

I=(2/d)(0,000507+2.0,00001294/d)v²

But the Darcy Manometer gives the result in m, thus:

I=(2/d)(0,000507+2.0,00001294/d)v²?

Hf=(2/d).l.?.?.v²

 

[BigInch]

Darcy = D'Arcy

http://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html

We will design everything from now on using only S.I. units ... except for the pipe diameter. Unk. British engineer

 

[Pipeguy1509]

Do not confuse the D'Arcy equation with the D'Arcy-Weisbach equation.

 

[vpl]

I've been reading a book about compressed air and i saw a equation for pressure drop that i can't find your origin

Ummm ... what book (title and author)? And what does the book say about the origin of the equation?

I was pretty much lost by your second post because you used "a" and "b" and seemed to define b in terms of itself. However, when I looked up "Henry P.G. Darcy and Other Pioneers in Hydraulics," (and please note the quotes and capitals which are visual clues that help a reader understand that it's a book title) I found that your second equation "R.I=b.v²" was supposed to be Ri=b₁v² where R is the pipe radius and i is the unit head loss



Patricia Lougheed

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[vpl]

OOPS! I hit submit when I meant to preview.

The listed book also defines b₁ as [α] + [β]/R

So then things started making a bit more sense ...

Additionally, I didn't understand how pipeguy1509 got from I=(2/d).(0,000507+2.0,00000647/d).v² to I=(2/d)(0,000507+2.0,00001294/d)v² until I realized that s/he were using "." as a symbol for multiplication (instead of the American use of "." as a decimal point.) Then it became clear that the second formula was in error as pipeguy1509 had already multiplied the 6,47E-6 value by 2 (it should simplify down to i= (2v²/d)(5,07E-4+(1,29E-5/d)) or even i = (v²/d)(1,01E-3+(2,59E-5/d)).

To thrown in an added wrinkle, I'm sure everyone recognizes that the above formula was proposed to fit experimental results done with water. Since the original post mentioned that the formula in question came out of a book on compressed air then it's possible to posit that someone, somewhere modified the Darcy "Ri=b₁v²" formula in an attempt to address compressibility. Perhaps if the OP identifies where he found the formula, it might be possible to identify who did it and if the assumptions make sense.

Finally, as a nit, the individual spelled his name "Darcy" -- without the apostrophe and with only one capital. The reason for it is explained in the book referenced in pipeguy1509's post (and which makes perfect sense if anyone has read anything about the French revolution).



Patricia Lougheed

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[Pipeguy1509]

Patricia, the decimal mark can be "." or ",". The fact that you are in America does not mean anything.

I really want to understand your conclusion. Maybe the different notation confused you, because is a really simple math.

I gonna use "." for multiplication and "," for decimal mark. ok??

R.i=b1.v²

The diameter is two times the radius. R=d/2 ok???

(d/2).i=b1.v²
i=(2/d).b1.v²

Analysing the term b1

b1=? + ?/R
b1=? + 2.?/d

if a=0,000507 and b=0,00000647

b1=0,000507 + 2.0,00000647/d
b1=0,000507 + 0,00001294/d

The Final Formula

i=(2/d).(0,000507 + 0,00001294/d).v² [m]

The formula is for water, but i already seen people using this for compressed air, and give great result if you compare with Atlas Copco and Worthington formulas.

The rest of answer, i will not comment

 

[vpl]

Pipeguy1509

You never did answer what book you found the original formula in -- which I understood to be the focus of your question, not whether either of us can do math. However, if you've answered your own question to your satisfaction, then more power to you.

The problem I originally had was that in your post on 26 August 2011 at 9:09, you defined b in terms of itself because you didn't distinguish between "b", "b₁, or [β] -- by the way check out the Process TGML link in the reply box to see how I'm doing the subscripts and greek letters.

Also, because I am used to seeing "." as a decimal point, when I read "2.0000647" I thought it was one number, not 2 times 0.00647. This was initially confusing, especially when you look at the two lines defining "I" in your 9:09 post(as shown below). It appears there is an error in the second one that should now be very obvious (as I have highlighted it).

I=(2/d).(0,000507+2.0,00000647/d).v²

I=(2/d)(0,000507+2.0,00001294/d)v²

(Note, I didn't delete the periods in the second post -- they weren't there to begin with.)

This error is then continued in the next equation (again from the 9:09 post by pipeguy1509):

I=(2/d)(0,000507+2.0,00001294/d)v²[δ]

However, let's get back to your original post. Have you answered your question?

Patricia Lougheed

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[Pipeguy1509]

yes, ty