Depth of Oil in Sloped Atmospheric Drain Line

[MarkMark220]

I have searched for hours now. This has to have been tackled before.
Knowing my flow rate, the size of my pipe, the specific gravity of my oil (.85) and the slope of the pipe (1/2" per foot) how can I calculate the depth of the oil in the pipe consistently?
API mandates that drain lines on oil systems shall run no more than half full. How can I calculate the actual depth based on the above criteria accurately?

Mark

 

[CarlB]

Fing a hydraulics textbook, open channel flow.

One approach, the manning's equation:

V=(1.486/n)(R^0.67)(S^0.5)

n for cast iron is 0.015
R is hydraulic radius =Ax-sect/wetted perimeter
Now this is for water, low viscosity, not sure if viscosity effects are significant for your case.

Say your pipe is 4" diam
S=1/2"/ft=1/24=.042
R=(pi*R^2/2)/(pi*R)=R/2=0.083
V=(1.486/.015)*0.166^.67*.042^.5=3.9 ft/sec
Q=VA=3.9*.09=0.34 cfs =150 gpm

Check my math, I was flyin'

Carl

 

[butelja]

I would NOT use information in the above post without checking the Reynold's number of the flow. As civil engineers typically work with water, they have a habit of neglecting viscosity. If your oil is very viscous, you will probably have laminar flow, and the friction factor will be different.

I would assume the pipe is half full. The hydraulic radius is the flow area divided by the wetted perimeter. For a half full pipe, this equates to (Pi*R^2/2) / (Pi*R) = R/2, or D/4. The hydraulic diameter is 4 times the hydraulic radius, or D. Assume a velocity, V, and calculate your Reynold's number using the hydraulic diameter as described earlier. The darcy friction factor is then obtained using the Moody chart or Colebrook equation with Reynold's number and absolute roughness as the inputs. You need to itterate and vary the velocity until the head loss per ft equals the pipe slope. If the resultant flow rate is adequate, you are done. If not, try a bigger pipe size.