Motive of this “strange” question, which goes nearly against the basic concepts of Hydraulics (as I know): some researchers find Froude numbers significant in ram pumps.
For instance, Calvert (1957) and Young (1998) use different Froude numbers to select the drive pipe diameter for a given supply head or for a given static head. But I'm not convinced that these methods make much sense.
I have just taken a quick look at the paper, but if you see the equation for the Froude number it does not corresponds to the "usual" defintion of the Froude number. But this is in principle not a problem. Different forms of the Froude number exist (for example the open channel Froude number is not calculated with the same variables as the one used in Shipping engineering).
Since the Froud number is nothing else as the relationship between two forces (inertial and gravimetric) one of them being external. Thus it can be applied in any context when the two appear to be significant. Young relates the water velocity (internal and inertial) to the pressure needed to keep the valve closed. If the valves are free of springs, then this pressure acts against the gravity trying to open the valve, thus this pressure may be considered gravimetric and external. Thus I think Young correctly uses the Froude number.
It is though important that the Froud number has to be interpreted differently depending on the physicall system it is describing.
The genesis of this Froude number is as follows: The velocity uc is proportional to sqrt(g*Hs), but also to the wave propagation velocity c. By concentrating on installations with steel pipes (c=1000) on planet earth (g=9.81), the values of c and g are fixed and their dimension is made to disappear.
So, in a quantitative sense, values of Froude numbers make correct limits for the design of ram pumps with steel pipes, but this does indicate a Froude number influence in a physical sense. If the fluid and pipe material would produce a different value of wave speed c, then also the 'Froude numbers' would come out differently.
Thank you very much for your valuable answers and explanations.
I agree with you that the Froude number used by Young makes sense for the design of the drive pipe (length, diameter, supply head), although it differs widely from the typical Froude numbers we use in Hydraulics. - In fact, now I think that Young’s works about hydraulic ram pumps are excellent.
I’m uploading the old paper of Calvert (1957), which is difficult to get. So you can read it, because it is interesting as well. He uses another Froude number, but it has also a correct meaning, if I’m not wrong.
It is a bad PDF file but it is the only one I have.
Again thank you very much and my best regards from Spain.
Thank you for the Calvert and Young papers. It is interesting the possible influence of a Mach number was already studied by Calvert. I believe also the Mach number does not have its usual physical contex. I have never been working with rams, I looked into the papers for curiosity. Thank you for the information.
It is my first time to read such discussion since I know Peter, and also notice some old paper is shared among the discussion. Such discussion is more constructive or value than some e-Mails(private discussion). Thank you all.
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