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# 23.4.4* Calculation Procedure

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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.

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.

Sprinklers under the obstruction shall not be required to be included in the hydraulic calculation of the ceiling sprinklers.

Where the piping to sprinklers under obstructions follows the same sizing pattern as the branch lines, no additional hydraulic calculations shall be required for sprinklers under obstructions.

Water demand of sprinklers installed in concealed spaces shall not be required to be added to the ceiling demand.

Calculations shall begin at the hydraulically most remote sprinkler.

The calculated pressure at each sprinkler shall be used to determine the discharge flow rate for that particular sprinkler.

Where sprinklers are installed under a sloped ceiling, the area shall be calculated on a horizontal plane below the sprinklers.

Pipe friction loss shall be calculated in accordance with the Hazen-Williams formula with C values from Table 23.4.4.8.1, as follows:

- Pipe, fittings, and devices such as valves, meters, flow switches in pipes 2 in. (50 mm) or less in size, and strainers shall be included, and elevation changes that affect the sprinkler discharge shall be calculated.
- Tie-in drain piping shall not be included in the hydraulic calculations.
- The loss for a tee or a cross shall be calculated where flow direction change occurs based on the equivalent pipe length of the piping segment in which the fitting is included.
- The tee at the top of a riser nipple shall be included in the branch line, the tee at the base of a riser nipple shall be included in the riser nipple, and the tee or cross at a cross main-feed main junction shall be included in the cross main.
- Fitting loss for straight-through flow in a tee or cross shall not be included.
- The loss of reducing elbows based on the equivalent feet value of the smallest outlet shall be calculated.
- The equivalent feet value for the standard elbow on any abrupt 90-degree turn, such as the screw-type pattern shall be used.
- The equivalent feet value for the long-turn elbow on any sweeping 90-degree turn, such as a flanged, welded, or mechanical joint-elbow typeshall be used.
*(See Table 23.4.3.1.1.)* - Friction loss shall be excluded for the fitting directly connected to a sprinkler.
- Losses through a pressure-reducing valve shall be included based on the normal inlet pressure condition. Pressure loss data from the manufacturer's literature shall be used.

**Table 23.4.4.8.1 Hazen-Williams C Values**

Pipe or Tube | C Value* |
---|---|

Unlined cast or ductile iron | 100 |

Black steel (dry systems including preaction) | 100 |

Black steel (wet systems including deluge) | 120 |

Galvanized steel (dry systems including preaction) | 100 |

Galvanized steel (wet systems including deluge) | 120 |

Plastic (listed) all | 150 |

Cement-lined cast- or ductile iron | 140 |

Copper tube, brass or stainless steel | 150 |

Asbestos cement | 140 |

Concrete | 140 |

*The authority having jurisdiction is permitted to allow other C values. |

For antifreeze systems greater than 40 gal (150 L) in size, the pipe friction loss shall be calculated using the Darcy-Weisbach equation shown in 23.4.2.1.3 using a Moody diagram and e-factors that are representative of aged pipe otherwise following the methodology presented in 23.4.4.8.1.

Orifice plates shall not be used for balancing the system.

Unless the requirements of 23.4.4.9.3 or 23.4.4.9.4 are met, mixing of sprinklers of different K-factors by reducing the K-factor of adjacent sprinklers on the same branch line leading back to the main for the purpose of minimizing sprinkler over discharge shall not be permitted.

Sprinklers with different K-factors shall be acceptable for special use such as exposure protection, small rooms or enclosures, or directional discharge.

*(See 3.3.22 for definition of small rooms.)*Extended-coverage and residential sprinklers with a different K-factor shall be acceptable for part of the protection area where installed in accordance with their listing.

When calculating flow from an orifice, the total pressure

*(P*shall be used, unless the calculation method of 23.4.4.10.2 is utilized._{t})Use of the normal pressure

*(P*calculated by subtracting the velocity pressure from the total pressure shall be permitted. Where the normal pressure is used, it shall be used on all branch lines and cross mains where applicable._{n})Flow from a sprinkler shall be calculated using the nominal K-factor except that the manufacturer's adjusted K-factors shall be utilized for dry-type sprinklers.

Minimum operating pressure of any sprinkler shall be 7 psi (0.5 bar).

For extra hazard occupancies, palletized, solid-piled, bin box, back-to-back shelf storage, shelf storage, or rack storage, the maximum operating pressure of any sprinkler shall be 175 psi (12 bar).

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