HYDRAULICS LET’S DO SOME MATH!
Fire Service Hydraulics During this presentation, we are going to explore the how and why of fire service hydraulics. We are going to start out fairly basic, and with each detail we cover, we will discover why it is important to know this material, and how it affects our performance on the fire ground.
Fire Service Hydraulics Some of this information may not be directly related to ‘hydraulics,’ but you will see how it ties together. Whatever happens, don’t be intimidated by the math. We’ll take it one step at time so that it is completely understandable. For some, this is fairly new territory, and for others, it will be a good refresher. Let’s get started.
Fire Service Hydraulics Why are hydraulics critical? We want the fire fighter to fight the fire, not the hose line. That is why knowing fire service hydraulics is so critical. Knowing hydraulics gives the fire engineer important safety information He needs to know: • what the apparatus discharge pressures need to be, • how much friction loss will he have to deal with, • how much water is left in a hydrant.
Fire Service Hydraulics It is critical to understand where the numbers come from when operating an apparatus pump. Odds are, your fire department has a “rule of thumb” regarding pump pressures for pre-connected hose lines or lines that are used more often. Therefore, you don’t have to remember or try to use these formulas at a fire. Unless the hose lay is different from what you are used to, a “rule of thumb” should work fine. BE AWARE … If you don’t know these formulas, you will one day need them because of a different hose lay, and it will happen at the worst possible time.
Fire Service Hydraulics Let’s go over some definitions Order of Operations Co-efficient Square & Square Root More to come …
Fire Service Hydraulics Order of Operations This is one of those math rules we have to live with. It basically states that certain math operations (add, subtract, multiply, divide) will be completed prior to others. Rule 1: First perform any calculations inside parentheses. Rule 2: Next perform all multiplications and divisions, working from left to right. Rule 3: Lastly, perform all additions and subtractions, working from left to right.
Please Excuse My Dear Aunt Sally #1 Parenthesis #2 Exponents ( sq and cubes) #3 Multiply #4 Divide #5 Add #6 Subtract
Please Excuse My Dear Aunt Sally Here’s an example 4 + 5 x 6 – 7 1st is to multiply 5 x 6 = 30 4 + 30 - 7 2nd is to add 4 + 30 = 34 34 - 7 Lastly, subtract 34 – 7 = 27 27 is the answer.
Fire Service Hydraulics Why is this important? When calculating friction loss formulas, the order of operation is critical otherwise you will not get the correct answer. Remember the 6 steps and you can’t go wrong.
Co-efficient Co-efficient is the resistance of one material passing next to another material. For example, water passing next to the material inside of a fire hose. For our purposes, we will define Co-efficient as the resistance to flow of water inside of a hose.
Fire Service Hydraulics Why is this important for me to know? With every different size, length and type of fire hose, the amount of resistance to water flow will change. When the resistance of flow changes, the pressure needed at the pump discharge will also change.
Co-efficient The Coefficient of a fire service hose is expressed with a numerical value. The higher the numerical value, the higher the coefficient. This means that more energy is required to push the water through the fire hose.
Square(²) and Square Root (√) To find the square of a number, simply multiply that number times itself. Example -- 4² = 16 is the same as 4 x 4 = 16 Or 7.07 ² which is 7.07 x 7.07 which equals 50. FYI- 50 happens to be the nozzle pressure for hand lines with smooth bore nozzles.
Square(²) and Square Root (√) For square root (√) operations, we must determine the two exact numbers, that when multiplied by each other, equal the number that we already have. (clear as mud?) The square root of 64 is 8. 8 x 8 = 64. Easy enough. It is written to look like this √64 = 8
Square(²) and Square Root (√) Fortunately for us in the fire service, there are only two main square roots we need to know. They are 50 and 80: • 50 is the amount of pressure for a hand line with a smooth bore nozzle • 80 is the amount of pressure for a master stream device with a smooth bore nozzle
Fire Service Hydraulics With this information, let’s find the square root ‘√’ of these two nozzle pressures. 1st – smooth bore pressure of a hand line is 50 psi √50 = 7.07 2nd – smooth bore pressure of a master stream device is 80 psi √80 = 8.94
Fire Service Hydraulics Let’s try a couple more square root problems with a calculator. √81 = ? √36 = ? √88 = ? *NOTE* Go to the next slide for some tips on using the Windows calculator.
Fire Service Hydraulics A couple of tips for using Windows® calculator: With Windows calculator using square roots, enter the number that you want to find the square root of and then click “sqrt”. To find a number’s “square” with this calculator: Select ‘View’ ‘Scientific’ Enter the number you would like to square, and then press the “x^2” key Note: You will need the decimal equivalent of the fraction part of the tip size to enter into the calculator. The next slide has a table with fraction and decimal equivalents.
Fire Service Hydraulics To find the decimal equivalent of any fraction, divide the top number by the bottom number.
Fire Service Hydraulics Did you get … √81 = 9 √36 = 6 √88 = 9.380831519646859109131260227 To shorten this a bit we’ll say 9.4
Please Excuse My Dear Aunt Sally O-K Now, let’s put a couple of the things we’ve learned together. 4 * √49 = ? Did you get… 4 * √49 = 28?
Please Excuse My Dear Aunt Sally Let us try another one … 5.5 * 2.5² Did you get … 5.5 * 2.5² = 34.375 Excellent!
Fire Service Hydraulics The following formula is the one that will be used the most. This little math formula will work with fog nozzles and smooth bore nozzles. We are going to find Friction Loss using only hoses, no appliances. (example: a gated wye)
Fire Service Hydraulics Finding Friction Loss FL = C*Q²*L FL = Friction Loss C = Friction Loss Coefficient Q² = Flow rate in hundreds of gallons (flow/100 and then squared) L = Hose length in hundreds of feet (length/100)
Fire Service Hydraulics We’ll start off with “C” which is the hose coefficient. “C” = the resistance to flow of water inside of a hose. The table on the next slide lists several sizes of fire hoses and their coefficients.
Fire Service HydraulicsYou can print this for future referencethis is slide #27
Fire Service Hydraulics Next is “Q²” which is the flow rate of the water. Note: Unless you know the flow rate of the nozzle that you are using, you will have to use another formula(which we will discuss later) to find your gallons per minute. Once this value is known, we have to divide it by 100 and then square the result Q= (nozzle flow/100) ²
Fire Service Hydraulics Now, let’s try one. Using an adjustable gallonage fog nozzle with the flow rate set at 125 gallons per minute. Divide 125 by 100= 1.25 Then square it, 1.25² = 1.56
Fire Service Hydraulics “L” = Total feet of hose divided by 100. Example: 150 feet of any size hose is 150 / 100 = 1.5 Note: Hose diameter is not important for this part of the equation. Also note: Some fire service hydraulic calculations use hose length as 100’ minimums, even if it requires two sections to make a 100’. We will look at these in more detail later on.
Fire Service Hydraulics Now let’s put this together. 150 feet of 1-1/2” hose flowing 125 gallons per minute. We know that we need 100 pounds of pressure at the fog nozzle.
Fire Service Hydraulics FL = C*Q²*L C=24 (from the hose coefficient table) Q²=1.56 (125 gallons per minute divided by 100 and then squared) L=1.5 (150 feet of hose divided by 100) Our formula is: FL=24*1.56*1.5
Fire Service Hydraulics FL=24*1.56*1.5 Did you get … FL = 56 ? Let’s try another one.
Fire Service Hydraulics FL = C*Q²*L You are flowing 250 gallons per minute through 2-1/2” line that is 200 feet long.
Fire Service Hydraulics Did you get FL = 25 ? Very Good. We know now that we have 25 psi of friction loss in our hose lay. Remember, we have to have 100 psi at the nozzle for adequate water flow. With that said, what does our pump discharge pressure have to be?
Fire Service Hydraulics Let’s have another formula for that. EP = NP + FL EP = Engine Pressure (pump discharge pressure) NP = Nozzle Pressure (which is 100 psi) FL = Friction Loss (which we now know is 10 psi) EP = 100 + 25 Engine Pressure (pump discharge pressure) = 125 psi
Fire Service Hydraulics Remember, we want the fire fighter to fight the fire, not the hose line. That is why knowing fire service hydraulics is so critical.
Fire Service Hydraulics We mentioned about finding flow rates or gallons per minute (GPM). Before we go any further, the following formula is used for smooth bore nozzles. Depending on the region and department you are on, you might not use smooth bore nozzles often, but it is important to know how this formula works.
GPM for smoothbore nozzles The formula used to determine GPM for smoothbore nozzles. GPM = 29.7 * d² * √NP
Fire Service Hydraulics GPM = 29.7 d² √NP • 29.7 is a constant • d² = the diameter of the nozzle squared • √NP = square root of the nozzle pressure • Master stream devices operate at 80 psi therefore the square root will be 8.9 • Handline devices operate at 50 psi therefore the square root will be 7.07
Fire Service Hydraulics What is d² when using a 1-1/4 inch smooth bore tip? 1-1/4² Or 1.25 * 1.25 (Refer to slides 20 & 21 if you need assistance) Did you get 1.56? Great!
Fire Service Hydraulics Finally, the square root (√) of the Nozzle Pressure (NP) We discussed earlier that the nozzle pressure for a smooth bore master stream device is 80 psi. So, the square root of 80 is 8.9 √80 = 8.9
Fire Service Hydraulics O-K, let’s put it together. GPM = 29.7 * d² * √NP Our example: We are flowing a hand line with a 7/8” smooth bore nozzle.
Fire Service Hydraulics O-K, Did you get 160 GPM? GPM = 29.7 * d² * √NP gpm = 29.7 * .765 * 7.07 gpm 22.7 * 7.07 160 gpm The next slide is very important.
Fire Service Hydraulics CHEAT! Every Chance You Get! Not on a test, but at a fire. Use EVERYTHING to your advantage at a fire. The fire does not care! With that being said, Remember two things:*
Fire Service Hydraulics *The square root of a smooth bore nozzle on a hand line is 7.07 *The square root of a smooth bore on a master stream device is 8.9 Use the chart with decimal conversions on slide #20. Develop your own conversion charts that you have easy access to at a fire. If you do this, you will not be known as a ‘cheater’ but as being clever. Your chief will say, “That engineer knows his stuff”. Use everything to your advantage.
Fire Service Hydraulics Let’s try one more GPM formula. You are flowing water through a master stream device with a 1-3/8” tip. GPM=29.7 *d² * √NP
Fire Service Hydraulics O-K, Did you get 499 GPM? EXCELLENT ! If you have any questions about this stuff don’t hesitate to let me know. I can be reached via e-mail at email@example.com Please include your phone number on the e-mail thanks
Fire Service Hydraulics Next Step: We have discussed finding friction loss, engine pressure, and gallons per minute. Let’s put it together. You are pumping at a commercial structure fire. You have a hand line on the ground with 200 feet of 1-3/4” hose with a 3/4” smooth bore tip. What is your: 1: GPM 2: Friction Loss 3: Engine Pressure
Fire Service Hydraulics Let’s start with GPM. We have a hand line (7.07) with a 3/4” (.75) tip. GPM = 29.7 * d² * √NP GPM = 29.7 * .56 * 7.07