The Hardy Cross method for analysis of fluid systems assumes that in inlet flows and outlet flows for the system are known. However, when one constructs such a system in real life, how do we ensure that the flow entering and exiting the system will be exactly equal to the parameters set initially? e.g. if the system is connected to a water tank for input, and has a loop with 3 outlets, and we assume that the input water flow is 300 l/s and the outlet flows are 100 l/s each. We decide all lengths and diameters as part of stating the initial condition to apply the Hardy Cross equation, and the method tells us what the flow rates will be based on the analysis. How do I know that the system will obey these parameters, and that the flow rates will match the initial assumptions I made.
2 Answers
In addition to the points made by @mart: the Hardy Cross method is a fixed algorithm. Therefore, it can be implemented in a parametric spreadsheet with the inlet and outlet flow rates as parameters set in the top couple of rows, or in an Octave or MATLAB script with the inlet and outlet flow rates as global variables with values set in the first few lines. That way, if you're not sure what the inlet and outlet flow rates will be, you can try out lots of different values for them quickly and easily.
However, looking at it this way raises a tricky foundational issue... An iteration of the Hardy Cross method is an approximation to an iteration of the full multivariate Newton-Raphson method. Hardy Cross introduced the approximation in the 1930s, when electronic computers were not available, because implementing the full multivariate Newton-Raphson method with pen and paper is a huge hassle. If you've got access to modern electronic computers (especially ones on which the full multivariate Newton-Raphson method comes ready-implemented in widely available, open-source and therefore amenable to inspection and review, library functions), why (other than in purely pedagogic contexts) would you be using the Hardy Cross method at all, rather than the full multivariate Newton-Raphson method?
You design the system for a demand that it should meet, 3x 100l/s in your example. If the demand is higher, the sytem will likely fail to deliver the actual demand. If the demand is lower, no problem.
On the network side, you know the pressure you want to deliver the water at. You could supply valves at the tap that deliver only (say) 100l/s at 4 bar, but in most cases actual water flow has to be managed on the consumer side and there are countless ways to do that:
- manually turning down the tap (if the consumer is a shower or something like that)
- If the consumer needs a constand water flow, they can use a combination of pressure regulator, simple flow meter and manual valve.
