Depth of Flow in a Conduit

[rzerr]

I am trying to locate the equations needed to figure out the depth of flow of storm water in a closed conduit flowing partially full.

I have read other post(s), but still have not found the equation(s) needed to determine the depth of flow.

I know the rate of flow (Q), the pipe diameter (D), Manning's roughness coefficient , pipe slope (S), and mean velocity (V).

I need additional equations to figure out theta (in radians), dpeth of flow (d), and possibly some constant that takes in account Q, D, n, S, and V, then substitutes this constant value into some other equation to find theta. Once theta is known, than I can substitute it into the d=0.5*[1-cos(theta/2)]*D equation to find the depth of flow.

Please advise. Thanks in advance.

 

[BRIS]

Mannings equation

Q = (A . R ^2/3 . S ^1/2)/n (SI Units)

A = Area of flow segment of circle

R = A/P

P = Wetted Perimiter = wetted arc of circle

D = depth of flow

I assume you can calcluate the area of the segment of a circle and its arc length from simple school geometry ??

If not check the link below:

http://mathworld.wolfram.com/CircularSegment.htm

Enter the equatiion on an Excel spread sheet, fill in the known variables (D,Q,n,S) and use goal seek to find the unknown variable - Depth.

There are two solutions if depth is greater than 80%.But in this case you take the solution at 100% full.

 

[Bbird]

Let me advocate the greatest engineering technique

"Trial and error"

Just tabulate the Manning equation on a spreadsheet

List a depth and compute the flow

When the flow first exceeds your known target flow refine the depth to any accuracy you fancy.

If you know a bit of Visual Basic you can have it done in no time at all.

Even if you know and go for other methods I would still recommend the "trail and error" as your sanity check or the second line of defence.

 

[BRIS]

Bbird - The advantage of Excel is it will do the trial and error for you - go to tools - go to goal seek - give it the flow and it will find the depth.

 

[waterguy]

I agree with the others....use Excel to your advantage. You might also consider looking through some hyraulics textbooks to find a partial flow graph that will relate your knowns to your unknowns.

 

[TD2K]

If you have access to a copy of Crane, it also discusses flow in partially filled pipes. Again, I'd recommend setting it up in Excel and using trial and error to get the depth.

 

[blackwed]

At first glance this looks very similar to a problem I had about level in a horizontal cylindrical tank. I was trying to get an equation for the rate of change in depth based on a known inflow rate. There's not "an equation" that will do it. You basically have to solve V=Const*(alpha-sin(alpha)) for alpha and it can't be done. The iterative approach using Excel is your best bet.

DB