Clarification on Moments and loads contributed by head in Zick Saddle Analysis. 1

[Some Curious Guy]

Hi All,

I am trying to understand the equation used in Zick Paper on Saddle Analysis of Horizontal vessel. The book Process equipment design by Brownell and Young has a chapter devoted to Saddle analysis. I will copy paste the portion where I am facing a problem.

The weight of the head is approximated equal to 2/3 length of a cylinder of the same radius. So the weight of the head is 2hw/3. The centroid of a hemisphere is 3h/8. So its easy to understand that a Vertical couple of force( 2hw/3)x lever arm(3h/8) will act. However I am clueless about the Horizontal couple of magnitude (Rw) X lever arm(R/4).

Can someone clarify things here.

 

[r6155]

Is the hydrostatic load on ends.
See PD 5500:2018 Specification for unfired fusion welded pressure vessels PAG 588/1026 in PDF, Figure G3.3-2

Regards

 

[Some Curious Guy]

Thanks @r6155. That saved me lot of hair splitting.
I just revised some Engineering fluid mechanics basics and found the center of Pressure of a Circle is about R/4 distance below the Center. The projected area of head is also a circle. So that explains the moment arm of R/4.

The total hydrostatic force acting on the circle is specific weight x vertical distance of Centroid x Area
this gives
= ( rho x g ) X (R) X (Pi R^2)
= ( rho x g x Pi x R^2 ) X R
= w x R ( The term ( rho x g x Pi x R^2 ) is Area x Sp weight which can approximated to udl w )

The above explains the couple of magnitude (wR) and lever arm ( R/4).