1. Mathematics for the Driver/ Operator

2. Knowledge Objectives
List the elements needed to calculate pump discharge pressure.
Describe the concepts underlying theoretical hydraulic calculations.
Describe the concepts underlying fire-ground hydraulic calculations.
Describe how to utilize fire-ground hydraulic calculations during an incident.

3. Skills Objectives (1 of 5)
Calculate the smooth-bore nozzle flow.
Calculate the friction loss in single hose lines.
Calculate the friction loss in multiple hose lines.
Calculate the elevation pressure loss and gain.
Calculate the friction loss in an appliance.
Use a Pitot gauge to test the friction loss in a portable master stream appliance through 3” (76-mm) hose.

4. Skills Objectives (2 of 5)
Use in-line gauges to test the friction loss in a specific hose.
Determine the pump discharge pressure in a wye scenario with equal lines.
Determine the pump discharge pressure in a wye scenario with unequal lines.
Determine the pump pressure for a Siamese connection line by the split flow method.

5. Skills Objectives (3 of 5)
Calculate the friction loss in Siamese connection lines by coefficient.
Calculate the friction loss in Siamese connection lines by percentage.
Calculate the pump discharge pressure for a pre-piped elevated master stream device.
Calculate the pump discharge pressure for an elevated master stream.

6. Skills Objectives (4 of 5)
Calculate the pump discharge pressure for a standpipe during preplanning.
Calculate the pump discharge pressure for a standpipe.
Calculate the flow rate (GPM) for a given hose size and nozzle pressure using a slide rule calculator.
Calculate the friction loss for a given hose size and nozzle pressure using a slide rule calculator.

7. Skills Objectives (5 of 5)
Perform calculations by hand.
Perform the hand method of calculation for 2½” (51-mm) hose.
Perform the hand method of calculation for 1¾” (44-mm) hose.
Perform the subtract 10 method of calculation.
Perform the condensed Q method of calculation.

8. Introduction (1 of 5)
Fire service hydraulic calculations determine the required pump discharge pressure (PDP) for fire-ground operations.
Driver/operator has responsibilities at each incident.

9. Introduction (2 of 5)
Driver/operator is critical to the success of the firefighting attack.
Actions ensure the safety of the attack team, occupants within the fire-involved structure, personnel on scene, and any exposures.
Decisions are often a matter of life and death

10. Introduction (3 of 5) Fire service hydraulics
Study of the characteristics and movement of water pertaining to calculations for fire streams and fire-ground operations
Two categories
Theoretical hydraulics: scientific or more exact calculations
Fire-ground hydraulics: less exact but more user-friendly calculation methods

11. Introduction (4 of 5) Hydraulics is part scientific and part inexact.
Requires balance
Many numerical values influence the calculations.
Manufacturers offer nozzles, appliances, and hose with individual specs that vary from those on traditional charts.
Flow tests with department equipment confirm pressures to use.

12. Introduction (5 of 5)
Driver/operator applies his or her knowledge of specific equipment on the apparatus to the methodology underlying hydraulic theory.
Driver/operator must adjust for variables in scenarios.
Practice and experience with hydraulics calculations are imperative.

13. Pump Discharge Pressure (1 of 4)
Fighting fire with water: water flow (GPM or L/min) versus heat generation (Btu or kcal)
Critical rate of flow is the flow required to overcome heat generated by the fire.
Proper hose and nozzle selection is one of the most important attack decisions after securing a water supply.

14. Pump Discharge Pressure (2 of 4)
Driver/operator supplies hose lines with optimal PDP.
Pressure too great: stream breaks up, lessening its effectiveness
Inadequate pressure: insufficient flow to overcome the fire, could endanger the safety of the team

15. Pump Discharge Pressure (3 of 4)
PDP is the total pressure needed to overcome all friction, appliance, and elevation loss while maintaining adequate nozzle pressure to deliver effective fire streams.
Several factors
Nozzle pressure
Friction loss in hose lines
Elevation gain or loss
Friction loss in appliances

16. Pump Discharge Pressure (4 of 4)
Calculations become more complex based on the fire attack operation.
Start with a basic PDP formula: PDP = NP + FL
PDP = pump discharge pressure
NP = nozzle pressure
FL = friction loss

17. Nozzle Pressures (1 of 3)
Establish the nozzle pressure from the scenario to use in the formula.
Pressure required at the nozzle to deliver a fire stream and flow rate for the nozzle’s design
Defined by the nozzle manufacturer
Determined through testing

18. Nozzle Pressures (2 of 3)

19. Nozzle Pressures (3 of 3)
Manufacturer’s specs for max water flow from an aerial device is listed with the nozzle specs.
Broken-stream nozzles are available in fog and smooth-bore varieties.
Three standard nozzle pressures (SNPs) sufficient for fire-ground operations:
100 psi (700 kPa) for all fog nozzles
50 psi (350 kPa) for smooth-bore handline
80 psi (560 kPa) for smooth-bore master stream

20. Determining Nozzle Flow
Flow rate is the volume of water moving through a nozzle, measured in GPM or L/min.
Fog nozzles are designed with predetermined flow rates based on a set nozzle pressure.
Flow and pressure differ by design and the purchaser’s selection.

21. Friction Loss (1 of 2)
After determining the nozzle pressure, determine the friction loss.
Pressure lost from turbulence as water passes through pipes, hoses, fittings, adapters, and appliances
Measured in psi or kPa

22. Friction Loss (2 of 2) Modern FL equation: FL = C Q2 L
Widely accepted as fire service standard
Success of equation is due to its ability to adapt to changes in hose diameter, water flow, and hose length

23. Calculating Friction Loss (1 of 3)
FL = C Q2 L
FL = friction loss
C = coefficient, numerical measure constant for each specific hose diameter
Q = quantity of water flowing (GPM or L/min) divided by 100
L = length of hose in feet or meters, divided by 100

24. Calculating Friction Loss (2 of 3)
May express FL formula as FL = C × (Q/100)2 × L/100
Since driver/operators use the formula frequently, Q and L are divided by 100 mentally to simplify and shorten the written form to FL = C Q2 L.

25. Calculating Friction Loss (3 of 3)
Multiple hose lines of different sizes and lengths
On the fire ground, you may need multiple water pressures from one pumper.
Under normal conditions, fully open the valve to prevent excess turbulence and friction loss through the valve.
Situations may occur where partially closing a valve is necessary.

26. Elevation Pressure (EP) (1 of 4)
Adjust calculations for EP: distance the nozzle is above or below the pump
Elevation loss: pressure lost when the nozzle is above the pump
Elevation gain: pressure gained when the nozzle is below the pump
After calculating the EP, it must be added to or subtracted from the PDP.

27. Elevation Pressure (EP) (2 of 4)
Elevation is relative to grade; altitude is relative to sea level.
Water exerts pressure of psi per 1’ (9.817 kPa/m) of water column.
For water discharging below the center line of the pump, subtract.
For water discharging above the pump, add.

28. Elevation Pressure (EP) (3 of 4)
To speed the calculation process further, determine the elevation change in 10’ (3 m) increments and multiply by 5 psi (5 psi per 10’) [(10 kPa per 3 m)].
5 psi per 30 kPa of grain or loss for each floor of elevation change in a residential structure where floor spacing is commonly 10’ (3 m)
Not all buildings have floors spaced every 10’ (3 m)

29. Elevation Pressure (EP) (4 of 4)
© haveseen/ShutterStock, Inc.

30. Appliance Loss (AL) (1 of 4)
Appliances are devices that connect and adapt hoses and direct and control water flow in hose layouts.
Adapters and reducers
Gated wyes
Siamese connections
Water thieves
Monitors and manifolds
Elevated master stream devices

31. Appliance Loss (AL) (2 of 4)
Courtesy of Akron Brass Company
Courtesy of Akron Brass Company

32. Appliance Loss (AL) (3 of 4)
Determining friction loss in appliances
Need two in-line pressure gauges for testing hose
Friction loss is minimal until the pump is flowing 350 GPM (1300 L/min) or greater.
Conduct tests on level ground and complete the process at various flows to see how the friction loss changes.

33. Appliance Loss (AL) (4 of 4)

34. Total Pressure Loss (TPL)
Insert AL and EP into the friction loss formula.
Start with PDP = NP + FL and determine NP.
Determine the TPL.
Expanded FL formula becomes: TPL = C  Q2  L + AL + EP
After calculating the TPL, apply it to the PDP formula, now expressed as PDP = NP + TPL.

35. Wyed Hose Lines A wye splits a single line into two.
Requires calculations to find the final FL

36. Siamese Hose Lines (1 of 2)
A Siamese connection is a device allowing multiple hose lines to converge into one.
Often used on the intake side of a pump, allowing multiple lines to supply the pumper
Used by departments that do not have a large-diameter hose
May be used to bring two or three lines into one attack line

37. Siamese Hose Lines (2 of 2)
Methods to calculate FL in lines to a Siamese connection when lines are of equal size and length
Split flow method
Coefficient method
Percentage method

38. Calculating Elevated Master Streams (1 of 3)
Prepiped elevated master stream
Aerial fire apparatus (ladder truck) with fixed waterway attached to the underside of the ladder with a water inlet at the base supplying a master stream device at the end
No single FL amount can adequately encompass all prepiped elevated master stream devices.

39. Calculating Elevated Master Streams (2 of 3)
© Kurt Hegre, The Fresno Bee/AP Photos

40. Calculating Elevated Master Streams (3 of 3)
Water comes into the intake, splits in a “T”, turns with an “L”, goes toward the front of the truck, turns again with an “L”, and again with another “L” into the pump.
All of these turns increase the FL.
Use at least 25 psi (175 kPa) FL for all master stream appliances.

41. Standpipe Systems (1 of 4)
Standpipe operations pose a challenge.
Fire fighters must know buildings, occupancy, fire load, special hazards, and hydrant locations.
For these buildings, water supply is critical.
Standpipe systems require the greatest number of calculations and very demanding pump pressures.

42. Standpipe Systems (2 of 4)
Driver/operator controls only one pressure to the standpipe: the highest pressure needed at any one discharge (regardless of the floor it is on)
Operator must pump to the highest pressure required.
In commercial buildings and multistory structures, attack hose should be 2½” lines (64 mm) with smooth-bore nozzles.

43. Standpipe Systems (3 of 4)
Fire fighter needs to know the required operating pressure of attack hose lines to control the pressure from the outlet.
Attack hose line must be flowing water if the crew member is to obtain an accurate gauge reading.
Using an in-line gauge is preferred for standpipe operations.

44. Standpipe Systems (4 of 4)
PDP for standpipe operations requires that calculations be made for supply lines to the standpipe, FL within the standpipe system, FL for the attack handlines, and pressure loss due to an increase in elevation.
If there is no preincident plan and the riser size is unknown, add 25 psi (175 kPa) to account for the standpipe riser.

45. Pressure-Regulating Valves (PRV) (1 of 3)
Installed on standpipe risers where static pressures exceed 175 psi (1225 kPa) per NFPA 13
If pressures while flowing exceed 100 psi (700 kPa), NFPA 14 requires the installation of a device at the outlet to restrict or reduce flow pressure to a maximum of 100 psi (700 kPa).

46. Pressure-Regulating Valves (PRV) (2 of 3)
To determine the pressure
Head: height of the column of water above the discharge
Head pressure: pressure in the column of water
Divide the number of feet (height) by
For metric, divide the number of meters by
The water column is in a standpipe riser.
As the riser height increases, the head pressure could exceed the burst pressure of the fire hose.

47. Pressure-Regulating Valves (PRV) (3 of 3)
Standpipe test documentation should be on file in the building’s maintenance office.
Design pressure of the building’s standpipe system should meet the minimum PRV pressure.

48. Net Pump Discharge Pressure (NPDP)
Static water sources require pulling a draft.
Dynamic sources are positive-pressure sources.
Incoming pressure: pump does not have to work as hard to achieve proper PDPs
NPDPpps: pressure created by the pump after receiving pressure from a hydrant or another pump

49. Fire Service Hydraulic Calculations (1 of 3)
Theoretical hydraulic calculations present more exact calculations, require more mathematical skills, and take more time to compute.
Away from the fire ground, they may be computed on paper, calculator, or computer.
Used on the fire ground by more experienced driver/operators

50. Fire Service Hydraulic Calculations (2 of 3)
Fire-ground hydraulic calculations estimate calculations more quickly due to incident urgency.
Used as a backup, to check results, or to ensure reasonable accuracy
Reinforce learning as the driver/operator computes theoretical hydraulics calculations in the field
Methods yield working approximations but are not as accurate as theoretical computation.

51. Fire Service Hydraulic Calculations (3 of 3)
Formulas for determining PDP
PDP = NP + FL
FL = C Q2 L + AL + EP
Most fire-ground hydraulic methods account for FL only.
Acquired FL added to formula to determine PDP.
Consider all essential components of hydraulics when using fire-ground hydraulic methods.
Each reduces the math required

52. Charts (1 of 3)
Created by fire fighters for handline and master stream calculations for hoses, nozzles, and devices specific to the apparatus within the department
List common pressures for attack hose and nozzle combinations at different lengths
Calculations must be accurate for the chart to be reliable.

53. Charts (2 of 3)

54. Charts (3 of 3) May be prepared for complex problems
Charts for high-rise buildings suggest a pressure for a range of floors.
Attack team should know in advance what pressure is needed from a riser for the particular attack line and nozzle combination in their high-rise/standpipe bag.

55. Hydraulic Calculators
May be manual (mechanical) or electronic
Manual hydraulic calculator may consist of a sliding card or slide rule.
Can handle calculations involving a variety of nozzle pressures, flow rates, and hose diameters
Electronic calculators may be mounted or hand-held devices.
Allows the calculation of engine pressure, FL, application rate, flow rate, and reaction force

56. Hand Method (1 of 2)
Purpose of the hand method (counting fingers method) is to quickly determine the FL per 100’ (30 m) of hose
Add AL, EP, and NP to provide the PDP.
Hand calculation methods for almost every hose size
Methods for 1¾” and 2½” hose are most common.

57. Hand Method (2 of 2)
Hand method for 2½” hose works nicely because the coefficient for 2½” hose is 2 when using imperial units.

58. Subtract 10 Method (GPM Flowing Method)
Determines FL in 2½” hose only
For flows of 160 GPM or greater
Useful for either fog or smooth-bore nozzles
Simplicity of method is its strength
Can determine FL in 2½” hose very quickly

59. Condensed Q Method (1 of 9)
Quick method for calculating FL per 100’ in 3” to 5” hose line only
Useful when the apparatus is part of a relay and supplying another pumper
There is no simple metric equivalent to this method.

60. Condensed Q Method (2 of 9)
Condensed Q formulas
3” hose FL = Q2
3½” hose FL = Q2/3
4” hose FL = Q2/5
5” hose FL = Q2/15

61. Condensed Q Method (3 of 9)
Condensed Q method in a relay operation
When two pumpers arrive at the scene at the same time, the first pumper positions for attack while the other lays a line from the attack pumper to a hydrant to establish a water supply.
The operator of the supply pumper must quickly calculate the PDP for the supply line to the attack pumper.
If pressure is too high or too low, the operator of the attack pumper will radio the supply operator.

62. Condensed Q Method (4 of 9)
Flow meters and electronic pump controllers
Flow meter: straight section of pipe, threaded on each end, and placed between two sections of hose
Sensing device on top of the meter is designed to measure the flow (GPM) through the hose.
Indicate the actual volume of water discharged through each line

63. Condensed Q Method (5 of 9)
Using a flow meter lessens the calculations to determine the PDP.
Many flow meters are available from a variety of manufacturers.
Flow meters are generally accurate within 1 to 3 percent but require periodic calibration to maintain accuracy.

64. Condensed Q Method (6 of 9)
Flow meter can deliver a desired flow without the operator knowing the length of the hose lines, FL, or EP.
Useful in multistory buildings
Eliminate math needed for relay operation

65. Condensed Q Method (7 of 9)
Electronic pump controllers and pressure governors
Technology has reduced the calculations that the driver/operator must perform.
Multiplexing: combining information from several different sources
Trend in modern apparatus is to use electronic control and monitoring equipment.

66. Condensed Q Method (8 of 9)
Electronic components are designed by independent contractors and integrated into a manufacturer’s apparatus.
Technological innovation assists the driver/operator but causes a possibility of electrical failure disabling the apparatus.
The threat of electrical malfunction increases.

67. Condensed Q Method (9 of 9)
Preincident plan
Conducted with the owner’s permission at a convenient time
The survey yields valuable information.
Gather building blueprints or diagrams and relevant data.

68. Summary
Fire service hydraulic calculations are used to determine the required PDP for fire-ground operations.
PDP = NP (nozzle pressure) + FL (friction loss).
Fire service hydraulic calculations may generally be categorized as either theoretical hydraulics or fire-ground hydraulics.
Fire-ground hydraulic calculations reinforce the learning process.