Depth of Flow in Pipe

[KANN]

For gravity flow in a pipe, I want to determine flow depth for a given gpm, pipe ID, slope, and Manning friction factor. The flow can be assumed steady and uniform. Flow is less than 1/2 ID.

Is this an iterative process with the Manning equation and hydraulic radius or is there another expression that will determine the flow depth outright?

 

[dicksewerrat]

I think it would be easier to calculate 'Q' from an assortment of slopes, Manning numbers , depths and pipe diameters. This could be set up in an 'Excel spreadsheet for hundreds of combinations very quickly and easily. Then put the results in table form and refered to without going through the calcs. every time. You could also do this with several depths and set 'Q' equal to a percentage of full flow. Doing it by starting with 'Q' is harder and will take a lot of time to set up. Starting with the But then if you want to go from 'Q' to depth have fun.

 

[KANN]

I would like to put an equation for the depth (h) in a spreadsheet. What you are suggesting, I think, would mean generating a table which the spreadsheet would have to lookup and interpolate for depth.

I think the crux of the matter is I need a relationship between depth and hydraulic radius (Rh) which I could substitute into the Manning equation for flow. Then I could solve the Manning equation for depth.

However, I have not been able to figured out this relationship through text references nor through geometry. It was my hope that the depth .vs. flow relationship would be a common enough need that the relationship has been presented, but (so far) overlooked or undiscovered in my search of the gravity flow references I've obtained.

 

[CarlB]

This relationship (depth/hydraulic radius) is not obscure, in a geometry reference look up the area of a sector, perimeter of a sector. From the depth you can get the sector angle, a few trigonmetric relations and ...boom (John Madden).... you've got the equation.

 

[gibfrog]

Here is a link for n/n(full), q/q(full), r/r(full), v/v(full) and a/a(full) for Manning for a circular pipe flowing partially full. You will need to free adobe acrobat reader available at

http://www.adobe.com

to view the chart.

http://ppi2pass.com/Errata/CERMApp19c.pdf

This link is from the ppi2pass site, the ERRATA for CERM 8 , 1st printing, appendix 17 (Civil Engineer's Reference Manual) Clifford H Laubstein
FL Certified PE #58662

 

[dicksewerrat]

CarlB got it all there. It is a little tough to remeber all those relationships but it can be put in a spreadsheet.

 

[PECPESC]

Here is a subroutine that does the job.


Sub getPartialPipeFlow()
'
'######################################
' Partial pipe flow subroutine
'Iterate with incremental TRIAL_D until pipe_flow_Partial = Given flow
'######################################
' Enter here with TRIAL_D = depth of flow
' SLOPE = Slope in ft/ft
' diaFt = Diameter of pipe in ft
' Routine returns:
' AREA = Area of pipe at flow
' PIPE_FLOW_PARTIAL = Discharge, CFS
' VELOCITY_PARTIAL = Velocity at flow
'
'circular
x_Val = (2 * trial_D - openDiaFt) / openDiaFt

If Abs(x_Val) < 1 Then
ArcCos = -Atn(x_Val / Sqr(-x_Val * x_Val + 1)) + 1.5708
PIPE_THETA = 2 * ArcCos
Else: PIPE_THETA = 0
End If

area = openDiaFt ^ 2 / 8 * (6.2832 - PIPE_THETA + Sin(PIPE_THETA))

AK = 1.486 * ((((6.2832 - PIPE_THETA + Sin(PIPE_THETA)) / 8) ^ 5) / (((6.2832 - PIPE_THETA) / 2) ^ 2 * (trial_D / openDiaFt) ^ 8)) ^ (1 / 3)

pipe_Flow_Partial = (AK * trial_D ^ (8 / 3)) / manN * slopeOut ^ 0.5


End Sub