Dear Mahmoud,

Formulas such as Manning or Chezy are widely used. But the major problem is the evaluation of the Manning coefficient or that of Chezy. Usually, a constant value is assigned to Manning coefficient to solve the problem of computing the discharge or the assessment of normal depth. In recent years, studies have shown that these coefficients are not constant but depend primarily on the relative roughness (and therefore the absolute roughness characterizing the state of the inner wall of the channel), the aspect ratio of the water area and especially on the Reynolds number demonstrates the effect of kinematic viscosity. From these considerations, it was able to establish a general relationship of the discharge in a channel (or pipe) that takes into account all parameters influencing the flow. It is very well explained and demonstrates in the article that I join you (in particular relations 1.19 and 1.20)

 https://www.researchgate.net/publication/255872083_Discussion_Exact_solutions_for_normal_depth_problem_By_PRABHATA_K_SWAMEE_and_PUSHPA_N_RATHIE_Journal_of_Hydraulic_Research_Volume_42_2004_Issue_5_pp_541-548

With my best regards

Prof. Bachir ACHOUR

Article Discussion Exact solutions for normal depth problem By PRABH...

Dear Mahmoud,

Formulas such as Manning or Chezy are widely used. But the major problem is the evaluation of the Manning coefficient or that of Chezy. Usually, a constant value is assigned to Manning coefficient to solve the problem of computing the discharge or the assessment of normal depth. In recent years, studies have shown that these coefficients are not constant but depend primarily on the relative roughness (and therefore the absolute roughness characterizing the state of the inner wall of the channel), the aspect ratio of the water area and especially on the Reynolds number demonstrates the effect of kinematic viscosity. From these considerations, it was able to establish a general relationship of the discharge in a channel (or pipe) that takes into account all parameters influencing the flow. It is very well explained and demonstrates in the article that I join you (in particular relations 1.19 and 1.20)

 https://www.researchgate.net/publication/255872083_Discussion_Exact_solutions_for_normal_depth_problem_By_PRABHATA_K_SWAMEE_and_PUSHPA_N_RATHIE_Journal_of_Hydraulic_Research_Volume_42_2004_Issue_5_pp_541-548

With my best regards

Prof. Bachir ACHOUR

Article Discussion Exact solutions for normal depth problem By PRABH...

Manning equation can be useful as long as "n" is calculated perfectly. In addition, rating curves are often used as a traditional method.

Prof Dr Bachir Achour

Thank u very much for your kind reply

Dear S H Bari

so many thanks

Prof Dr Bachir Achour

can we add Reynolds number  to manning formula by bakingham theorem

V = φ/n R2/3S 1/2

Dear Mahmoud,

I do not think so because there is no kinematic viscosity in the Manning’s formula.

With my best regards

Prof. Bachir ACHOUR

Dear Mahmoud,

This is a great idea, but it's not easy to do. How to introduce the kinematic viscosity directly in the Manning’s formula? That is the question. In my article, it is primarily the general relationship of the discharge that is established first. This can be simply done by eliminating the friction factor between the Darcy-Weisbach formula and the Colebrook-White formula which is also valid in open channels (experimentally verified). Once the general relationship of the discharged settled, it will be compared to that of Manning. This comparison then leads to the identification of the Manning coefficient in which all the parameters influencing the flow are identified, in particular Reynolds number and therefore the kinematic viscosity.

With my best regards

Prof. Bachir ACHOUR

Prof. Bachir ACHOUR

so many thanks

Dear Mahmoud Ziad:

Manning coefficient is defined as the state of the pipe wall, and it is different to the roughness which is the height of roughness of the pipe inner wall. So for this case i think it is not very interesting to use manning coefficient for pipes transport pure water , compared to the wastewater where the state of the pipe wall can be changed due to the water nature .

For wastewater Manning is the best, but for pure water colebrook white is preferred, because the roughness can be estimated (See the paper of professor achour ).

dr Lotfi Zeghadnia

thank u very much

Each equation is good if the roughness coefficient is chosen in the right way. Manning equation has been widely applied and is probably one of the most used.

what about the viscosity of the flow 

It is OK for fully developed flows (near uniform flow , i.e., So=Sf) but selecting the right roughness poses a challenge.  Relying on a hydraulic control such as a weir, a gated structure, a contraction or a a free overall when available is often more reliable so long as you have estimates of the water levels, geometry and operational settings (e.g., gate opening, whether the flow free or submerged).

If uniform or critical conditions do not exist, you should consider relying on the gradually varied flow approximation. In this case you will require of channel x sections, estimates of the channel roughness and water stage at the station of interest and a reference station to account for water stage drop.  

If what you need is to establish a flow monitoring site, I suggest you review the various approaches in the literature for establishing rating stations in open channels.  In these case you will need direct concurrent measurements  of flow discharge and water levels required to established a rating (see fro example Rantz 1982).

Hope this helps.

Yes, I think manning coefficient would be good if you have wide manning data around the channels.  

yes

yes

thank u dr Mohamed Ashour

thank u dr Gugum Ahmad Gumbira

In open channel computation, Viscosity is neglected, Manning coefficient is more dominant. 

Dear Sigit,

In open channel, Manning's coefficient depends on both the relative roughness and the Reynolds number. Therefore, it depends on the viscosity.

With my best regards

Prof. Bachir ACHOUR

i agree with prof dr Bachir Achour 

I think a better answer and neglected by most of the discussion is no. Using a uniform flow equation, regardless of the one selected, will never be "the best method" to determine discharge simply because too many things are uncertain.  For example, the conventional application of Manning equation is to use bed slope in the analysis but it should be the energy slope that should be applied for gradually varied flows, which most open channel flows would better be approximated as.  So you need to use the right slope first of all.  Then there is the problem of roughness coefficient.  Manning equation effectively was developed under conditions that would best be approximated as high Reynolds number flows, so would need to conform to that.    Assuming that this condition is satisfied, there is some difficulty in estimating n value.  Even if we have some well-characterized channel lining such as concrete, for example, Sturm's Open Channel Hydraulics book has a detailed table providing Manning n values that range from 0.01 to 0.02 for concrete.  This implies that even for concrete lined channels, there could be tremendous uncertainty in the discharge and the problenm only gets worse in natural channels.   Having some sort of control such as gate or weir is a far better method to determine the discharge

dr Steven J. Wright

thank you

Dear Mahmoud,

Manning and Chezy equations are widely used for design of open channels nowadays. The most important problem is determining "n" for Manning and "C" for Chezy equations. Many researchers studied the variations of n in different materials and situations. But in fact, Manning equation has some fragiles. For example, according to Maghsoudi and Kouchakzadeh (1994), employing manning equations in flood analysis may result in incorrect answers because when the flood enters the plain, wetted perimeter increases rapidly, but area increases slowly. In this situation, hydraulic radius is increased as the depth of flow is increased and this result in deceasing of flow rate (Q). This answer is mathematically correct , but is physically incorrect. So, we need to modify the calculation to avoid incorrect answers that obtained by Manning equation.

For more information, see Henderson, F. M. (1966). Open channel flow. Macmillan.

A detailed table providing Manning n values ranged from 0.03 to 0.045 for natural, 0.022 to 0.035 for excavated earth, 0.01 to 0.025 for artificially lined channels and from 0.035 to 0.15 for floodplains is available in books of channel Hydraulics. This implies that there is tremendous uncertainty for determining the discharge in natural channels.