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Open Channel, Partially full pipe flow in excel. Please help!

Open Channel, Partially full pipe flow in excel. Please help!

I am looking for a way to use excel to calculate the velocity in partially full pipes. I noticed that it had been a previous topic and I am hoping that darth051 will respond to this message and help me with this problem. I am stuck on the hydraulic radius.  I would greatly appreciate your response.  Thank you so much.

You may email me at: "kga" followed by
Thank you again!

RE: Open Channel, Partially full pipe flow in excel. Please help!

You have to write out the equation for the area of a section of the circle and the area of the triangle formed by the circle section and the water surface. I'm trying to remember the name of the line that starts and stops on the circle, perpendicular to the center of the circle section. I did this at work but don't have the formulae here. It is not that tough to do. you just have to go back to basic geometry.

RE: Open Channel, Partially full pipe flow in excel. Please help!

Sorry its taken so long to respond but I've been in the field/on holiday.

Unfortunately I don't have access to the spreadsheets at the moment but here is the basic method:

1) Set up a table for %full depth based on a pipe diameter of 1. Depth increments of 0.01 are what I traditionaly use.

2) For the depth calculate the water area and wetted perimeter. You'll need to dig out your geometry formulas to find the equations. (Don't forget that the formulas will change once you are over half full.)

3) Calculate hydrualic radii for each depth.

4) Calculate the % Velocity based on the full flow velocity. Since its a ratio, the slope factor drops out.

5) Calculate the % Capacity based on the full flow capacity. Make this column the column immediately to the left of the %Velocity column. (% Capacity = % Velocity * Area which you already calculated.)

6) Use Excel's VLookUp function to search the table for the closest % Capacity and return the corresponding % Velocity.

7) Use your full flow velocity and the the % velocity to determine your partial flow velocity.

You end up with a Workbook that has 1 Spreadsheet containing the "Partial Flow Table" and 1 Spreadsheet where you do your calculations.

You can always refine your spreadsheet further by setting up another Table containing the standard pipe characteristics you use. Let the first column of that table be the size & material of pipe with the other columns the diameter(s), area, etc. Then name your list of pipes (Insert Name Define). Use Data Validation to use your named list of pipes as a selection list in your spreadsheet. This forces you to pick from a list of known pipes. You can then use VLookUp to pull the pipe properties from your pipe table automatically.


David Dietrich
KMK Consultants Ltd
Windsor, Ontario, Canada

RE: Open Channel, Partially full pipe flow in excel. Please help!

Search the web for SMADA. Its free and can calculate partial full pipes flow.


RE: Open Channel, Partially full pipe flow in excel. Please help!

All above are correct.  However, the whole matter of v/vf is, in my opinion largely academic.  Good to know how to do it for the PE exam, but I've never applied it in the real world.  I always just design to vf.  Here's why:

I would never design a pipe to use Q less than 0.3Qf, for economics.  By the time Q/Qf = 0.3, d/D already is approx. 0.45 and v/vf is around 0.75.

In fact, I try to design for much better than Q/Qf = 0.3, so basically I am almost always dealing with v/vf > 0.85 or 0.9.  Very rarely does this small differtial benefit the client.

Remember: The Chinese ideogram for “crisis” is comprised of the characters for “danger” and “opportunity.”

RE: Open Channel, Partially full pipe flow in excel. Please help!

It all depends on the situation as to whether flows less than 30% of pipe capacity are "acedemic". In my area everything is flat enough that pipes are often minimum allowable diameter and grade and flows are in the 0-30% range often enough to be an issue. The whole reason for the "actual velocity" check was to try and ensure that flow velocities came at least close to those needed to keep the pipes self-cleaning.

Sure it would be cheaper for the private sector developers to install the pipes at a shallower slope and therefore less depth but the public sector which looks after maintenance isn't willing to pick up the cost to keep flushing the system every couple years to keep it operating correctly.

David Dietrich
KMK Consultants Ltd
Windsor, Ontario, Canada

RE: Open Channel, Partially full pipe flow in excel. Please help!

Regarding the geometry, here are the equations. The charts can be obtained from the Concrete Pipe Design Manual (American Concrete Pipe Association)
for a circular pipe:
Area = (D**2)* (O-sinO)/8  Where O is theta- the angle in radians form by the top width (T) (line across the water surface) from the center of the pipe.
The top width (T)= D*Sin(O/2)
Wetted perimeter P = DO/2
Hydraulic radius = D/4*(1 - SinO/O)
Hdraulic depth = (D/2)* ((O-SinO)/Sin(O/2))

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