Depth of Flow in Pipe
Depth of Flow in Pipe
(OP)
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?
Is this an iterative process with the Manning equation and hydraulic radius or is there another expression that will determine the flow depth outright?





RE: Depth of Flow in Pipe
RE: Depth of Flow in Pipe
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.
RE: Depth of Flow in Pipe
RE: Depth of Flow in Pipe
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
RE: Depth of Flow in Pipe
RE: Depth of Flow in Pipe
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