Gradual contractions in pipe

[dbecker]

Hello,

I am looking at page A-26 in Crane's manual. It shows that for pipe with a gradual contraction with an angle of convergence of between 45 and 180, we are to use Formula 4.

Formula 4 is dependant on the sine of half the angle.

If I use an angle of 180 (abrupt change in diameter) then should this correlation not be equal to Equation 2-10 on page 2-11???

This does not make sense, since Formula 4 is divided by Beta ^ 4, there can't be legitimacy here?? They must equal if the wall angle = 180!!

Please explain this to me.

Thank you.

 

[katmar]

In my (1988) edition of Crane it seems you are referring to Formula 2 on Page A-26, and not Formula 4.

[√](sin(180/2)) = [√](sin(90)) = [√]1 = 1

Equation 2-10 gives the value for K₁, which is based on the smaller pipe diameter. Formula 2 gives the value for K₂, which is based on the larger diameter. K₁ and K₂ are related by equations 2-5 and 2-11.

Katmar Software
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http://katmarsoftware.com

 

[dbecker]

But it is divided by B^4?

Or is 1/B^4 just a factor that need not be considered when comparing the two equations?

Thanks katmar

 

[vpl]

dbecker

Yes. Formula 2 is Equation 2-10 ([Κ]1) divided by [Β]⁴; that's what the second "=" is telling you.
Yes. You need to consider the [Β]⁴ when comparing the two equations. [Κ]1 [≠] [Κ]2.

As katmar stated, it's because Equation 2-10 is in terms of [Κ]1, while Formula 2 is in terms of [Κ]2. (Actually this applies to all the formulas on page A-26)

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[dbecker]

Thanks for the clarification.

Makes sense now.