Hi Everyone,

I know this is an old thread, but I've been trying to do partially filled heads for ASME 100-6 F&D heads and stumbled across this thread and signed up. After learning about xcalcs, I decided to use it to estimate surface areas at different liquid levels. However, I have deep concerns about the xcalc results. In the chart the SL89 posted, you can see that there is a "bump" in the curve for the xcalc result. But there's no dramatic change in the shape of the head that would warrant such a "bump". Like ankur, I tried googling an analytical solution to the problem and had no luck. But I was able to get results of my own using Google's SketchUp software.

In google SketchUp, I made both a 10 ft diameter 2:1 Semi-elliptical head and a 100-6% ASME F&D head. Each head was then segmented into twenty 6" levels as shown in the screenshot above. You can also see that the 2:1 SE head total calculated surface area is 108.34 ft2 which corresponds well to the analytical solution of the total head surface area (1.084*D^2 = 1.084*10^2 = 108.4 ft2). SketchUp calculates the area of a given selection numerically and so I was able to get the surface area of each of the twenty segments. Using the chart the SL89 posted, I've added my results, which are different than xcalcs, Doane, and Wong.

Obviously, I'm quite biased, but I think my results are the best (mostly because I know how I got the results whereas the others I don't)!

Using a polynomial fit, I get the following equation for a 2:1 semi-elliptical head:

Ah/At = -0.4884*(h/D)^3 + 0.7341*(h/D)^2 + 0.7549*(h/D)

Also, for those interested, I get the following equation for an ASME 100-6% F&D head:

Ah/At = -0.8010*(h/D)^3 + 1.2051*(h/D)^2 + 0.5974*(h/d)

Where Ah is the partially filled surface area, At is the total head surface area, h is the liquid level, and D is the head diameter.

**Edited by justboud, 12 October 2012 - 03:32 PM.**