## Hydraulic calculations and the slide rule

Before the scientific calculators and computers, we still produced hydraulic calculations for High Hazard sprinkler systems but this was a long-winded and time-consuming process and prone to error. I say High Hazard sprinkler systems as these were the only systems you would consider producing hydraulic calculations for as the production of the calculations by hand took so long that we were content in using pre-calculated pipe table for Light hazard and Ordinary hazard sprinkler systems and no one had ever thought of installing sprinklers into a house or care facility.

Even with a scientific calculator you still have a lot of buttons which need to be press to solve the Hayes William pressure loss formula, after all, each time we need to enter the pipe diameter, the flow rate and the C factor of the pipe. Of course, we can simplify the Hayes and William pressure loss formula for any pipe by producing a k-factor for each pipe size and pipe type, this certainly simplifies the input when using a calculate but we then need to look it up in a table so it is still quite laborious. If this was not enough we have not even considered the K-Factor formula for working out the flow through the sprinkler head or balancing the junction points at each tee or cross which needed yet another adjustment calculation. As an aside who thought it was a good idea to have “K” and “k” as two different formulas in fire sprinkler calculations, did someone not think that this may be confusing!

Fortunately, we had an answer the hydraulic calculator slide rule and no self-respecting sprinkler engineer would be without one. I seem to remember there were not that easy to get hold of. Some of the larger sprinkler companies produce their own such as Matter and Platt and others like the one shown was produced by an insurance company for their own fire sprinkler inspection engineers.

The use of a hydraulic slide rule was still a useful tool even after the invention of the scientific calculator, you may be wondering why! Well, it was just simpler especially for those quick estimates and I still know a few fire sprinkler engineers which still rely on their trusted slide rule to this day.

The next invention in helping with fire sprinkler hydraulic calculations was the programmable calculator such as the Texas Instruments TI-58 and the TI-83 which at the time was a very expensive device. With this calculator, you could programmer Hayes William pressure loss formula and the sprinkler K-Factor formula which was certainly a bonus and it reduced the number of keypresses drastically. You could also enter a small program of around 200 lines which had to be entered manually (no USB memory sticks or Bluetooth in those days) this was a laborious process and subject to error and if you let the battery go flat you lost the lot and had to re-enter it. In Harold S. Wass book ‘Sprinkler Hydraulics’ he devoted an entire Appendix to the subject ‘hydraulic program for the Texas instrument TI-58’ which included the program code which you needed to enter, I always wonder how many people successfully completed this task.

The downside to the hydraulic slide rule and the programmable calculator is that it was still only possible to calculate a branch (tree) systems with dead-end lines, we could not calculate looped or gridded networks. You can, in fact, calculate a simple loop system with little maths, paper and pen and a loop can provide additional efficiency with the advantage that it delivers water by more than one route and therefore the flow the decrease in each line and as the friction loss decrease is proportional to the flow to the power of 1.85, we will return to loops in a later blog.

I know some of you will be thinking why on earth are we talking about slide rules, times and moved on and we all use hydraulic calculation software such as FHC produce are calculation we can optimise designs and try out numerous permutations of pipe sizes and head K-Factor.  Well, I still believe that fire protection engineers need to understand the basic concepts of hydraulic calculations and formulas which underpinned them even if you are using computer software, the saying "garbage in garbage out” is very true.

You will find on this website a series of articles which explain the fundamental formulas which are used for hydraulic calculations for fire sprinkler and water mist systems.  We recently added an article which takes you through hand hydraulic calculation step-by-step for a simple branch (or raged pipe configuration).  Of course, you may not wish to use the slide rule or the scientific calculator as same can be achieved much more easily by using our Hcalc hydraulic calculator which can be freely downloaded from this website.

Something which computer software is excellent at is doing repetitive tasks that are the fundamentals of hydraulic calculations repeating a series of steps.  I mentioned earlier is that hand hydraulic calculations are only suitable quite simple branch line systems but of course, tremendous cost savings can be achieved in large installations by using a grid system.  In fact, I will go to say that some ESFR (early suppression fast response) with the very high water densities which are required could not be considered if it was not for the grid as the pipe sizes and water supply requirement would be just too high.  This is where our FHC hydraulic calculation software can pay for itself in one project by helping you optimise the design reducing the pipe sizes balancing supply.

It used to take us a day to calculate by hand a reasonably sized high hazard project with our slide rule.  This included the time to check and make one or two very minor alterations as the process was laborious.  But we certainly couldn’t consider trying different permutations as the process is so time-consuming whereas today enter the ray of pipework into a hydraulic model and press the calculate button your calculation be completed before you can blink.  This now says the design engineer considerable time which you can use optimising the system for best effect.  So I don’t think engineers spend any less time producing the calculations is just that their time is spent more efficiently fine-tuning their hydraulic model for best effect and a more cost-effective solution.