Geometry factor for determining flow area given fraction full and ID

[Bernoulli31]

Hello,
first post, even though I have been member of this forum for ten+ years (oh my!), but under different name. I had to change it after I lost my password and recovery mail was sent to old work email.

I'm trying to perform calculations for gravity flow in partially filled pipes using Colebrook (Waste water drains in plastic piping). I have tables that would give me the values I'm looking for, or I could use an online calculator, but I'm actually trying to derive the formulas myself, the old fashioned way.

What I am missing at this point, is a geometry factor to determine the flow area given diameter and percent full of the pipe, e.g. 50%. I have a reference to Brater and King: a = C.d², with C tabulated as function of x in a table in Brater and King's. I assume it's a reference to their Handbook of Hydraulics.

Now, before I cash out money for this book when all I need is a table, I wanted to ask if there are other sources, or other means to calculate the stream cross section of a partially filled pipe using % full?

Thanks,
B.

 

[robyengIT]

in Europe we use formulas from Thormann-Franke here attached (in spanish : I hope You can manage)