some empirical relations are given in books including a book by Dr Chitale ( ex Joint Director CWPRS Pune)

Hi Dr.Khurjekar,

based on the entropy theory, there is a linear relationship between mean flow velocity, um, and maximum flow velocity, umax, (Chiu, 1987). This is of great interest for the monitoring of high flow considering that umax occurs in the upper portion of flow area and can be easily sampled by simple equipments, e.g. propellers. To be correct, the real value of umax is unknown, but the maximum value of velocity points sampled in the upper portion of flow area can be assumed for it.

The linear relationship depends on parameter, M, which can be easily determined if a dataset of (um, umax) pairs is available at gauged site (Moramarco and Singh, 2010). In addition, between umax and the maximum surface flow velocity, umax_s, a formulation based on entropy velocity profile is identified as well by Chiu (1989), so allowing to estimate umax just sampling umax_s.

These findings are very useful for the practical hydrology addressed to the monitoring of discharge. Recently, several works showed that the sampling of umax_s by no-contact radar sensors provides a satisfactory estimate of um (Fulton and Ostrowsky, 2008; Corato et al. 2011; Moramarco et al., 2013). Finally, the new satellite missions (e.g. SWOT) are also exploring the possibility to retrieve umax_s, considering the considerable benefit that may ensue for the discharge monitoring at ungauged sites.

Best Regards,

Tommaso Moramarco

References

Chiu, C.L., 1987. Entropy and probability concepts in hydraulics. J. Hydraul. Eng.,

ASCE 113 (5), 583–600.

Chiu, C.L., 1989. Velocity distribution in open channel flow. J. Hydraul. Eng., ASCE

115 (5), 576–594.

Corato, G., Moramarco, T., Tucciarelli, T., 2011. Discharge estimation combining flow

routing and occasional measurements of velocity. Hydrol. Earth Syst. Sci. 15,

2979–2994.

Fulton, J., Ostrowski, J., 2008. Measuring real-time streamflow using emerging

technologies: radar hydroacoustics and the probability concepts. J. Hydrol. 357,

1–10.

Moramarco, T., Singh, V.P., 2010. Formulation of the entropy parameter based on

hydraulic and geometric characteristics of river cross sections. J. Hydrol. Eng.

15, 852

Moramarco, T., Corato, G., Melone, F. and Singh, V.P. 2013. An entropy-based method for determining the flow depth distribution in natural channels. Journal of Hydrology, 497,176-188

The surface velocity at any point depends upon factors such as channel shape, roughness (natural or built) of the surface(s) over which the water flows, net slope between any two points and between multiple points, volume of flow, and other factors such as channel or path obstructions, and sediment or debris load.

Since you may not have enough information on surfaces, you might stary with actual flow/sec measurements at various points along the path, flow depth, flow channels shapes basis at those points, and mean velocity (across the x-y sections - the y-cross section variation is typical and linked to shear stress variation).

The flow characteristics such as the FroudeNumber-roughness relationships, and energy and momentum relationships as mentioned in the texts above and elsewhere, might then be formulated (a- or post-priori) to come up with a mass-energy balance approach.

I'd guess that Parcival is right and the topic is less simple than a linear relation between um and umax. Let me mention winds, which generate counterflows at the surface. They are efffective especially in backwaters. To estimate the discharge I always recommend multipoint methods, preferably across the river. The vertical distribution may be with certain accuracy be derived theoretically (if wind may be neglected). But the cross section is relevant because the distribution of local depth is often very irregular. I know of an operational dischange measurement system in Berlin, based on ultrasound crossing river Spree near Köpenick. Good luck, Helmut

Actually, the multipoint methods cannot applied for monitoring discharge during high flows. One doesn't have any possibility to sample velocity points in the lower portion of flow area, e.g. by currentmeters. Moreover, dangers for operators are very high during this flow conditions.One should have a look at the numerous works published in refereed journals showing: i) the reliability of linear relation between um and umax in rivers worldwide; iii) the capability of entropy models to estimate discharge by considering only the maximum surface velocity; iii) how the radar technology is of great support to estimate discharge by monitoring only the maximum surface velocity; iv) the considerable interest for the new satellite missions (SWOT, Sentinel-3) for monitoring discharge exploiting water surface level and surface velocity. Finally, I fully agree about the relevance of cross-section. Indeed, if a whatever discharge monitoring system (ultrasonic, radar, ..) was also able to provide the most accurate measurement in terms of velocity, never one would achieve an accurate discharge observation if the river cross-section changes during the flood. This is the point for the discharge monitoring. Best. Tommaso

You can follow Saint Venant equations (Continuity and Equation of motion) for unsteady flow. These are very popular equations for Gradually Varied Unsteady Flow (GVUF). Equations are available in the "Unsteady Flow" Chapter of any standard Open Channel Flow/Hydraulics books.

VERY GOOD REPLIES BY Subhasish Das, T. Moramarco, Helmut Baumert , Percival Miller. I put it as follows

Optical current Developed by me and My Guru GV RAO( no more on earth) has advantage of scanning in many sections of a flow and collecting data of surface velocity by looking at flow using this equipment from an accessible bank of a river or stream. This also has correction facility. I have yet to work on this to modernize the equipment. I believe this non contact flow measurement method may help arrive at better solutions to flow related problems.

Dear Mandar, very interesting. Thank you! Can you send me more details about the optical equipment. As I wrote, we use a non-contact method based on radar sensors able to measure the maximum surface velocity. It would be great to compare performances of equipments in rivers with different geometric and hydraulic characteristics. Best.

Hi

My present interests are in Flow Measurement in Open Canal (Alluvial and Non-Alluvial). I have 2 questions:

Question 1:

What will be the accuracy of a Surface Velocity Measurement Technique in Flow and hence Discharge measurements.

Question 2

How does the Surface Velocity Measurements based techniques compare with the others, such as, ADCP in accuracy.

Many thanks in advance.

Harish Chouhan

I WILL TRY RETRIEVE MY PAPER PUBLISHED IN IAHR CONFERENCE HELD IN NEW DELHI IN 1981. WE HAD, THAT TIME,  USED THIS IDEA LEARN FROM OUR UN ADVISER. HE HOWEVER WAS USING THIS GADGET FROM TOP OF A BRIDGE ON THE RIVER. WE FOUND IT USEFUL TO CALIBRATE THE INSTRUMENT . BUT OUR MODIFICATION WAS TO INSTALL IT FROM A BANK OF A RIVER AND SCAN THE RIVER WIDTH FROM A BANK . THIS WAS OUR MAKE IN INDIA INSTRUMENT .  THE MODIFICATION WAS PROVED  USEFUL TO LARGE RIVER WIDTHS. HOWEVER THIS HAD AN APPLICATIONS ALSO FOR RIVERS IN SPATE. WE OF COURSE COULD NOT REACH RIVERS IN SPATE BUT THOUGHT THAT VELOCITY MEASUREMENTS BE POSSIBLE EVEN IN THESE CASES. I WILL TRY GET THAT PAPER AND WILL THEN LOAD HERE AS SOON AS POSSIBLE.

It would be great, if you uploaded your paper. Best Regards, Tommaso