Equations for Engineers: Part I
FL= C * Q2/100 * L/100
Step one in producing a good engineer is the foundational knowledge and equations. If we can’t do simple math, then we are not going to be successful. Nobody expects you to be able to do this at 3 am, but we need to be able to gameplay and we should be predetermining our pressures prior to game day, then adapt if needed. I always recommend finding your friction loss per 100’ for each line and each flow so you can have those predetermined. If you add or extend lines, it’s a simple addition. The first equation is the friction loss equation. We all should know that hose has friction loss, which means as water is flowing through the hose, friction from the walls of the hose slows down the water. The smaller the hose, the more friction and vice versa, the larger the hose the less friction. When we pump, we are always fighting friction. No matter if its attack side or supply side, FRICTION IS THE ENEMY!
The first equation is friction loss as already stated. When looking at the equation, the first variable is coefficient. I get a lot of people asking what a coefficient is. It is constant value given to each size of the hose based its diameter and friction the hose causes. The definition states, “a numerical or constant quantity placed before and multiplying the variable in an algebraic expression or a multiplier or factor that measures some property” Oxford. Each size hose is given a coefficient. In todays fire service, it is important that you know your hose size. Most hose sizes are not true sizes, which changes the coefficient, therefore changing the friction loss. An example of this, 1.75” hose has a coefficient of 15.5. The hose we use, the coeffient is 6.5 because the hose is 1.91 internal diameter. This would drastically alter your pump calculations, to half. Knowing your equipment is critical. We run truID for our 2.5” so this coefficient is correct, but a lot of 2.5” is 2 11/16”. KNOW YOUR HOSE!
1.75”- 15.5
2.5”- 2
4”- 0.2
5”- 0.08
The second part of the equation is Q2. This is quantity squared or volume squared. So easiest way to determine this is to determine what your nozzle rated flow is. This is usually on the nozzle. most common are 150, 160, 175, 265, 300… Smoothbores are based on tip size at a flow of 50 psi at the tip, so 7/8 is 160 gpm, 15/16 is 185 gpm, 1 1/8 is 265, and 1 3/16 is 300 gpm. The quantity is then divide by 100. The next is L which is length of the hose divide by 100. To figure this, first we simplify by dividing by 100 for quantity and length. Next we square the quantity. Once we have that, then we multiple
6.5*150^2/100 * 200/100
6.5 * 1.5^2*2
6.5 * 2.25 * 2
FL= 29.25 or 30 psi
PDP= FL+NP+/- Elevation+ Appliance + Apparatus Loss
Next, we will discuss the second part of the basic equations, which is Pump Discharge Pressure. This is the number that the line gauge should be reading when set appropriately. To emphasize, Line gauge, NOT master discharge. We set pressure using the line gauge for several reason, which we will hit in another post.
To continue, first is our friction loss, which we just figured out using the above equation. Next is NP. This is nozzle pressure. For nozzles to properly flow, the required pressure is needed at the nozzle. If the nozzle is a 150gpm at 50 psi, the reading at the nozzle using an inline gauge has to be 50 psi. If it is not, then we are flowing too much or not enough. For smoothbore, we use a pitot gauge at the orifice opening. Common pressures are 50, 75, or 100.
Next is elevation. Elevation can be a positive or negative because we can either push water higher, which causes more resistance or we can pump down elevation which gravity helps. The value is 0.434psi/ foot or 5psi/ floor assuming the floors are 10’.
Next is appliance. This is another area where the books often get it wrong or it’s misinterpreted. Any time water is flowing through an object, it will have friction. When water flows through appliances or valves, an increase turbulence will be experienced because water is changing directions. Many teach this as a static number, 10 if flowing under 350gpm and 25 if flowing over 350 gpm. THIS COULDN’T BE FURTHER FROM THE TRUTH. The friction is determined by the design and the flow. Friction loss is exponential and is on a scale. Most manufacturers have a graph that will show you the friction loss at different flows (see below). You must know these otherwise you will under or over-pump the device. An example is the Elkhart R.A.M. portable master stream. This device is rated to flow 500 gpm at a max of 150 psi. At the max capacity, 427 gpm, the friction loss is only 9 psi. Most would count that towards 25 psi loss and it would be wrong. Know the loss in your master streams, portable master streams and what every devices you use, which I would recommend as little as possible.
The final variable is apparatus loss. How many have actually figured this into their calculations? I bet not many if none. The book again, fails to mention this critical aspect. From the impeller to the discharge, trucks have a massive amount of plumbing. Each turn, swivel or change in plumbing type will add friction loss. Again, this can be significant upwards of 5-15 or 20 psi depending on your setup. For our engines, we run 3” plumbing from the manifold to the rear of the engine (we have all rear hose bed). This equates to only 5 psi to our rear attack lines. On the other hand, our Rescue has 15 psi friction loss to the rear of the hose bed.