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# 23.4 Hydraulic Calculation Procedures

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In systems having branch lines with an insufficient number of sprinklers to fulfill the 1.2 requirement, the design area shall be extended to include sprinklers on adjacent branch lines supplied by the same cross main.

A calculated system for a building, or a calculated addition to a system in an existing sprinklered building, shall supersede the rules in this standard governing pipe schedules, except that all systems shall continue to be limited by area.

The size of pipe, number of sprinklers per branch line, and number of branch lines per cross main shall otherwise be limited only by the available water supply.

Unless required by other NFPA standards, the velocity of water flow shall not be limited when hydraulic calculations are performed using the Hazen-Williams or Darcy Weisbach formulas.

However, sprinkler spacing and all other rules covered in this and other applicable standards shall be observed.

Hydraulic calculations shall extend to the effective point of the water supply where the characteristics of the water supply are known.

Pipe friction losses shall be determined on the basis of the Hazen-Williams formula, as follows:

where: | |

p | = frictional resistance (psi/ft of pipe) |

Q | = flow (gpm) |

C | = friction loss coefficient |

d | = actual internal diameter of pipe (in.) |

For SI units, the following equation shall be used:

where: | |

p_{m} |
= frictional resistance (bar/m of pipe) |

Q_{m} |
= flow (L/min) |

C |
= friction loss coefficient |

d_{m} |
= actual internal diameter (mm) |

For antifreeze systems greater than 40 gal (150 L) in size, the friction loss shall also be calculated using the Darcy-Weisbach formula:

where: | |

ΔP = | friction loss (psi) |

f | = friction loss factor from Moody diagram |

l | = length of pipe or tube (ft) |

p | = density of fluid (lb/ft^{3}) |

Q | = flow in pipe or tube (gpm) |

d | = inside diameter of tube (in.) |

Pressures at hydraulic junction points shall balance within 0.5 psi (0.03 bar).

The highest pressure at the junction point, and the total flows as adjusted, shall be carried into the calculations.

Pressure balancing shall be permitted through the use of a K-factor developed for branch lines or portions of systems using the formula in 23.4.2.5.

Table 23.4.3.1.1 shall be used to determine the equivalent length of pipe for fittings and devices unless manufacturer's test data indicate that other factors are appropriate.

**Table 23.4.3.1.1 Equivalent Schedule 40 Steel Pipe Length Chart**

Fittings and Valves | Fittings and Valves Expressed in Equivalent Feet (Meters) of Pipe | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

^{1}/_{2} in. | ^{3}/_{4} in. | 1 in. | 1^{1}/_{4} in. | 1^{1}/_{2} in. | 2 in. | 2^{1}/_{2} in. | 3 in. | 3^{1}/_{2} in. | 4 in. | 5 in. | 6 in. | 8 in. | 10 in. | 12 in. | |

(15 mm) | (20 mm) | (25 mm) | (32 mm) | (40 mm) | (50 mm) | (65 mm) | (80 mm) | (90 mm) | (100 mm) | (125 mm) | (150 mm) | (200 mm) | (250 mm) | (300 mm) | |

45°elbow | — | 1 (0.3) | 1 (0.3) | 1 (0.3) | 2 (0.6) | 2 (0.6) | 3 (0.9) | 3 (0.9) | 3 (0.9) | 4 (1.2) | 5 (1.5) | 7 (2.1) | 9 (2.7) | 11 (3.3) | 13 (4) |

90°standard elbow | 1 (0.3) | 2 (0.6) | 2 (0.6) | 3 (0.9) | 4 (1.2) | 5 (1.5) | 6 (1.8) | 7 (2.1) | 8 (2.4) | 10 (3) | 12 (3.7) | 14 (4.3) | 18 (5.5) | 22 (6.7) | 27 (8.2) |

90°long-turn elbow | 0.5 (0.2) | 1 (0.3) | 2 (0.6) | 2 (0.6) | 2 (0.6) | 3 (0.9) | 4 (1.2) | 5 (1.5) | 5 (1.5) | 6 (1.8) | 8 (2.4) | 9 (2.7) | 13 (4) | 16 (4.9) | 18 (5.5) |

Tee or cross (flow turned 90°) | 3 (0.9) | 4(1.2) | 5 (1.5) | 6 (1.8) | 8 (2.4) | 10 (3) | 12 (3.7) | 15 (4.6) | 17 (5.2) | 20 (6.1) | 25 (7.6) | 30 (9.1) | 35 (10.7) | 50 (15.2) | 60 (18.3) |

Butterfly valve | — | — | — | — | — | 6 (1.8) | 7 (2.1) | 10 (3) | — | 12 (3.7) | 9 (2.7) | 10 (3) | 12 (3.7) | 19 (5.8) | 21 (6.4) |

Gate valve | — | — | — | — | — | 1 (0.3) | 1 (0.3) | 1 (0.3) | 1 (0.3) | 2 (0.6) | 2 (0.6) | 3 (0.9) | 4 (1.2) | 5 (1.5) | 6 (1.8) |

Swing check* | — | — | 5 (1.5) | 7 (2.1) | 9 (2.7) | 11 (3.3) | 14 (4.3) | 16 (4.9) | 19 (5.8) | 22 (6.7) | 27 (8.2) | 32 (9.7) | 45 (13.7) | 55 (16.8) | 65 (19.8) |

Note: Information on ^{1}/_{2} in. pipe is included in this table only because it is allowed under 8.15.19.4 and 8.15.19.5. | |||||||||||||||

*Due to the variation in design of swing check valves, the pipe equivalents indicated in this table are considered average. |

For saddle-type fittings having friction loss greater than that shown in Table 23.4.3.1.1, the increased friction loss shall be included in hydraulic calculations.

For internal pipe diameters different from Schedule 40 steel pipe [Schedule 30 for pipe diameters 8 in. (200 mm) and larger], the equivalent length shown in Table 23.4.3.1.1 shall be multiplied by a factor derived from the following formula:

The factor thus obtained shall be further modified as required by Table 23.4.3.1.1. This table shall apply to other types of pipe listed in Table 23.4.3.1.1 only where modified by factors from 23.4.3.1.1 and 23.4.3.2.

Table 23.4.3.1.1 shall be used with a Hazen-Williams C factor of 120 only.

For other values of C, the values in Table 23.4.3.1.1 shall be multiplied by the factors indicated in Table 23.4.3.2.1.

**Table 23.4.3.2.1 C Value Multiplier**

Value of C | 100 | 130 | 140 | 150 |

Multiplying factor | 0.713 | 1.16 | 1.33 | 1.51 |

Note: These factors are based upon the friction loss through the fitting being independent of the C factor available to the piping. |

Specific friction loss values or equivalent pipe lengths for alarm valves, dry pipe valves, deluge valves, strainers, and other devices shall be made available to the authority having jurisdiction.

Specific friction loss values or equivalent pipe lengths for listed fittings not in Table 6.4.1 shall be used in hydraulic calculations where these losses or equivalent pipe lengths are different from those shown in Table 23.4.3.1.1.

For all systems the design area shall be the hydraulically most demanding based on the criteria of Chapter 11, Chapter 12, or the special design approaches in accordance with the requirements of Chapter 22.

Where the design is based on the room design method, the calculation shall be based on the room and communicating space, if any, that is hydraulically the most demanding.

Where the design is based on the density/area method, the design area shall be a rectangular area having a dimension parallel to the branch lines at least 1.2 times the square root of the area of sprinkler operation

*(A)*used, which shall permit the inclusion of sprinklers on both sides of the cross main.Any fractional sprinkler shall be carried to the next higher whole sprinkler.

In systems having branch lines with an insufficient number of sprinklers to fulfill the 1.2 requirement, the design area shall be extended to include sprinklers on adjacent branch lines supplied by the same cross main.

Where the available floor area for a specific area/density design criteria, including any extension of area as required by 11.1.2 and Section 12.3, is less than the required minimum design area, the design area shall be permitted to only include those sprinklers within the available design area.

Where the total design discharge from these operating sprinklers is less than the minimum required discharge determined by multiplying the required design density times the required minimum design area, an additional flow shall be added at the point of connection of the branch line to the cross main furthest from the source to increase the overall demand, not including hose stream allowance, to the minimum required discharge.

For CMSA sprinklers, the design area shall be a rectangular area having a dimension parallel to the branch lines at least 1.2 times the square root of the area protected by the number of sprinklers to be included in the design area. The design area protected by the number of sprinklers to be used by the 1.2 rule shall be based on the maximum allowable area per sprinkler.

Any fractional sprinkler shall be carried to the next higher whole sprinkler.

For ESFR sprinklers, the design area shall consist of the most hydraulically demanding area of 12 sprinklers, consisting of four sprinklers on each of three branch lines, unless other specific numbers of design sprinklers are required in other sections of this standard.

For gridded systems, the designer shall verify that the hydraulically most demanding area is being used.

A minimum of two additional sets of calculations shall be submitted to demonstrate peaking of demand area friction loss when compared to areas immediately adjacent on either side along the same branch lines, unless the requirements of 23.4.4.5.3 are met.

Computer programs that show the peaking of the demand area friction loss shall be acceptable based on a single set of calculations.

System piping shall be hydraulically designed using design densities and areas of operation in accordance with 11.2.3.2 or Chapter 12 as required for the occupancies or hazards involved.

The density shall be calculated on the basis of floor area of sprinkler operation. Where sprinklers are installed under a sloped ceiling, the area used for this calculation shall be the horizontal plane below the sprinklers.

The area covered by any sprinkler used in hydraulic design and calculations shall be the horizontal distances measured between the sprinklers on the branch line and between the branch lines in accordance with 8.5.2.

Where sprinklers are installed above and below a ceiling or in a case where more than two areas are supplied from a common set of branch lines, the branch lines and supplies shall be calculated to supply the largest water demand.

For sloped ceiling applications, the area of sprinkler application for density calculations shall be based upon the projected horizontal area.

Each sprinkler in the design area and the remainder of the hydraulically designed system shall discharge at a flow rate at least equal to the stipulated minimum water application rate (density) multiplied by the area of sprinkler operation.

Where the design area is equal to or greater than the area in Table 23.4.4.7.2 for the hazard being protected by the sprinkler system, the discharge for sprinklers protecting small compartments 55 ft

^{2}(5.1 m^{2}) or less, such as closets, washrooms, and similar compartments that are in the design area, shall be permitted to be omitted from the hydraulic calculations.**Table 23.4.4.7.2 Minimum Design Area**

Occupancy Hazard Classification | Minimum Design Area to Omit Discharge from Sprinklers in Small Compartments in Design Area [ft ^{2} (m^{2})] |
---|---|

Light hazard-wet pipe system | 1500 (139) |

Light hazard-dry pipe system | 1950 (181) |

Ordinary hazard-wet pipe system | 1500 (139) |

Ordinary hazard-dry pipe system | 1950 (181) |

Extra hazard-wet pipe system | 2500 (232) |

Extra hazard-dry pipe system | 3250 (300) |

The sprinklers in these small compartments shall be capable of discharging the minimum density appropriate for the hazard they protect in accordance with Figure 11.2.3.1.1.

The requirements of 23.4.4.7.2 shall only apply where the area of application is equal to or greater than the area shown in Table 23.4.4.7.2 for the appropriate hazard classification (including a 30 percent increase for dry pipe systems).

The requirements of 23.4.4.7.1.1 to include every sprinkler in the design area shall not apply where sprinklers are provided above and below obstructions such as wide ducts or tables.

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