Differences between the Francis Formula & Torrecelli Formula

[14andyhigg]

Hi,

My name is Andy I am a new user here. I am having a bit of trouble deriving the difference between the Francis Formula and the Torricelli Formula. I have the following question to work on as part of many which could be covered in an exam shortly:

Provide an expression for the Francis Formula used for calculating flow over a weir, explaining any improvement over the simple Torricelli derived formula and a reliance on the concept of contractions to a weir.

I am comfortable using each of the formulas and solving problems based on them but I am not too sure on how they relate to each other and the benefits of using one or the other.

Any advice would be much appreciated!

 

[Almsco]

Hi Andy, welcome to the forum!

The difference between the Francis Formula and the Torricelli Formula is that the Francis Formula takes into account the effects of contraction of the water when passing over a weir. The Torricelli Formula does not account for this contraction, while the Francis Formula does, which makes it more accurate. The expression for the Francis Formula is Q = 2.49Cd√2gh, where Cd is the coefficient of contraction, g is the acceleration due to gravity, h is the height of the weir, and Q is the volumetric flow rate of water.

I hope this helps and good luck on your upcoming exam!