Fluid Dynamics and the Francis Formula

In summary, Preet is looking for information on calculating the rate of flow of water through a weir for his technical report. He has come across the Francis formula, but is unsure if it is applicable to his specific situation where the water will cling to the surface. He is also looking for other formulas and information on calculating flow rate for his application. Preet recommends a book called "Hydraulics and its Applications" by A.H. Gibson for more in-depth information on his situation.
  • #1
preet
98
0
Hey all...

I'm trying to write a technical report and one part involves calculating the rate of flow of water through a straight horizontal weir. Searching on the web has led me to the Francis formula, which seems to be pretty straightforward. The problem I have is that my specific application has a much lower head (height of water) then used in any of the sample problems and on the net with the Francis formula. In addition, the Francis formula seems to apply to water flowing over a weir, in almost waterfall like fashion. For my purposes, the water will cascade down a surface... I don't know if this will affect the flow rate, or if I can use the formula in my situation.

So basically, I want to know if there is a threshold that is "safe", in which I would be okay using the formula (getting reasonable values). I would really appreciate all the information I could get on the Francis formula (and any other ones that apply).

Thanks,
Preet
 
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  • #2
I'm sorry for bumping my post up so quickly, but I don't think I really explained what I was looking for properly...

Normal applications of weirs tend to require that the water that escapes from the weir does not cling to the surface (as seen in 1. [attached]):

My application requires they DO cling to the surface (as seen in 2.). Unfortunately I cannot find any information on how to calculate flow rate with a clinging nape since in general that is a situation that would be avoided.

In addition, I see a few different versions of the "Francis formula" which is the most common method I see being used to calculate flow rate from weirs, and I've read specifically that a clinging nape distorts the accuracy of the results heavily.

The formula I'm looking for is a relation between the Width of the weir, Head (height) of water on top of weir plate, and Flow Rate of water.

I'm having a lot of trouble finding good relevant information, so I'd appreciate any advice or links.

Thanks,
Preet
 

Attachments

  • weir.gif
    weir.gif
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  • #3
I found a really helpful book, which in one part, covers my situation in detail. I posted to recommend you check the book out (it's free due to copyright expiry).

The book is called "Hydraulics and its Applications" by A.H. Gibson

http://www.archive.org/details/hydraulicsapps00gibsrich
 

1. What is fluid dynamics?

Fluid dynamics is a branch of physics that studies the motion of fluids (liquids and gases) and the forces that act on them. It involves the study of how fluids flow, how they interact with their surroundings, and how they can be controlled or manipulated.

2. What is the Francis Formula?

The Francis Formula is an empirical equation used to calculate the power output of a hydraulic turbine, based on the flow rate and head (difference in water level) of the fluid. It was developed by British engineer James B. Francis in the mid-19th century and is still widely used in the design and analysis of hydropower systems.

3. How is the Francis Formula derived?

The Francis Formula is derived from the conservation of energy principle, which states that energy cannot be created or destroyed, only transformed. By applying this principle to the flow of water through a turbine, Francis was able to develop an equation that relates the power output to the properties of the fluid and the turbine.

4. What are the limitations of the Francis Formula?

While the Francis Formula is a useful tool for estimating the power output of a hydraulic turbine, it has some limitations. It assumes ideal conditions, such as a perfectly shaped turbine and uniform flow of fluid, which may not always be the case in real-world situations. Additionally, it does not take into account factors such as friction and turbulence, which can affect the accuracy of the calculations.

5. How is fluid dynamics and the Francis Formula relevant to real-world applications?

Fluid dynamics and the Francis Formula have many practical applications, particularly in the design and operation of hydraulic turbines for hydropower generation. They are also used in other industries such as aerospace, automotive, and environmental engineering to study and improve the performance of fluid systems. Additionally, understanding fluid dynamics can help us better understand and predict natural phenomena such as weather patterns and ocean currents.

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