9 replies to this topic

[ankur2061]

Dear All,

The Manning equation is extensively used for cold water hydraulic calculations and the equation expressed in terms of average velocity is:

v = (1/n)*R_H^2/3*S^1/2

where:

n = Manning coefficient, dimensionless
R_H = Hydraulic Radius, m
S = slope of the conduit, m/m

R_H is further defined as:

R_H = A/P

where:
A = cross-sectional area of the conduit, m²
P = Wetted perimeter of the conduit, m

For a fully filled circular conduit the hydraulic radius R_H becomes as follow:

R_H = (Pi*D²/4) / Pi*D

which when simplified becomes

R_H = D/4

where

D = Internal Diameter of the circular conduit.

This is the background of Manning equation with respect to fully filled circular conduit (pipe). However, the answer I am seeking is how to calculate the hydraulic radius of a partially filled pipe, say for example, 1/4-filled, 1/2-filled and 3/4-filled.

In some reference I found that the hydraulic radius of a partially filled pipe can be calculated by multiplying the diameter D of the pipe with a factor 'F'. The unanswered question is how to find this factor 'F' and is there a calculation method for this factor 'F'.

Any help regarding this query would be appreciated.

Regards,
Ankur.

[breizh]

Hi Ankur ,

Should support your query.
http://www.ajdesigne...uation_pipe.php

regards
Breizh

[SPOOK]

R_H = A/P

where:
A = cross-sectional area of the conduit, m²
P = Wetted perimeter of the conduit, m

For a fully filled circular conduit the hydraulic radius R_H becomes as follow:

R_H = (Pi*D²/4) / Pi*D

Ankur,

Find the attached excel sheet which shows how to find the perimeter of the partially filled circular pipe.

Now using this perimeter in the above equation of yours for hydraulic radius you will be able to find the appropriate hydraulic radius.

Hope this info is helpful

Regards
SPOOK

Attached Files

•  Perimeter_of_sector.xls   892.5KB   220 downloads

[ankur2061]

Should support your query.
http://www.ajdesigne...uation_pipe.php

regards
Breizh

Breizh,

Thanks. This is what I was looking for. I converted it into a spreadsheet with inputs as % filling of pipe and internal diameter of the pipe.

Regards,
Ankur.

[TechExpert]

not able to open the file.

R_H = A/P

where:
A = cross-sectional area of the conduit, m²
P = Wetted perimeter of the conduit, m

For a fully filled circular conduit the hydraulic radius R_H becomes as follow:

R_H = (Pi*D²/4) / Pi*D

Ankur,

Find the attached excel sheet which shows how to find the perimeter of the partially filled circular pipe.

Now using this perimeter in the above equation of yours for hydraulic radius you will be able to find the appropriate hydraulic radius.

Hope this info is helpful

Regards
SPOOK

[breizh]

Hello Ankur ,
additional information on this site :
http://en.wikipedia....Manning_formula

Go to external link where you can find other shapes :Manning formula calculator for several channel shapes .

Regards
Breizh

[ankur2061]

Dear All,

Please find attached the spreadsheet for calculating the hydraulic radius for partially filled pipes, which can be used in the 'Manning Equation' for hydraulic calculations of water.

Comments from our members are most welcome.


Regards,
Ankur.

Attached Files

•  Hydraulic_Radius_Partially_Filled_Pipes.xls   41.5KB   217 downloads

[narendrasony]

Basically the first set of equations (on left hand side in your first sheet) is valid for both the scenarios if you take "h" as the liquid level from bottom for both the cases i.e for h<r as well as for h>r.

Regards

[ankur2061]

Basically the first set of equations (on left hand side in your first sheet) is valid for both the scenarios if you take "h" as the liquid level from bottom for both the cases i.e for h<r as well as for h>r.

Regards

Narendra,

The left hand side equation is only valid for filling <50%. For 50% and above the equations on the right hand side are valid. Initially I had done as you have suggested but the results were not correct when I checked with another source.

Hope this clarifies why I have used two sets of equations.

Regards,
Ankur.

[narendrasony]

Ankur,
Please find attached the file with both approaches. Method-1 is with two set of equations, Method-2 is with single set of equations.

Regards
Narendra

Attached Files

•  Hydraulic_Rad_Partially_filled_pipe_2.xls   21.5KB   192 downloads