# 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 for which you would consider producing hydraulic calculations. The production of the calculations by hand took so long that we were content with using a pre-calculated pipe table for Light Hazard and Ordinary hazard sprinkler systems. No one had ever considered installing sprinklers in a house or care facility.

Even with a scientific calculator, you still have a lot of buttons that need to be pressed 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 calculation, 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 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 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 to 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, were produced by an insurance company for their own fire sprinkler inspection engineers.

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

The next invention to help with fire sprinkler hydraulic calculations was the programmable calculator, such as the Texas Instruments TI-58 and the TI-83, which was very expensive device at the time. With this calculator, you could program the Hayes William pressure loss formula and the sprinkler K-Factor formula, which was certainly a bonus and drastically reduced the number of keypresses. You could also enter a small program of around 200 lines that had to be manually entered (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 branch (tree) systems with dead-end lines. We could not calculate looped or gridded networks. You can 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; therefore, the flow 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, and times moved on, we all use hydraulic calculation software such as FHC to produce are calculations. We can optimise designs and try out numerous permutations of pipe sizes and head K-Factor.  I still believe that fire protection engineers need to understand the basic concepts of hydraulic calculations and the formulas underpinning them. Even if you use computer software, the saying "garbage in garbage out” is very true.

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

Computer software is excellent at doing repetitive tasks that are the fundamentals of hydraulic calculations repeating a series of steps.  I mentioned earlier that hand hydraulic calculations are only suitable for quite a simple branch line system, but of course, tremendous cost savings can be achieved in large installations by using a grid system.  In fact, I will say that some ESFR (early suppression fast response) with very high water densities are required and 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 gives the design engineer considerable time, which you can use to optimise the system for the best effect.  So I don’t think engineers spend any less time producing the calculations because their time is spent more efficiently fine-tuning their hydraulic model for the best effect and a more cost-effective solution.