# Hydraulic Calculations for Designing Sprinkler System (With Formulas)

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Hydraulic calculations are very important when designing fire protection systems since they ensure that the piping delivers enough water to extinguish any fire. In particular, automatic sprinkler systems are subject to the NFPA 13 Standard in the US, and the equivalent international standard is EN 12845.

The hydraulic calculation procedure deals with three very important aspects of a fire suppression system:

• If a fire occurs, how much water is required to extinguish it?
• Is the available water supply enough?
• What is the optimal layout of the piping system, and what friction losses are produced?

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An adequate fire protection design safeguards your building and its occupants. If you are developing commercial spaces for rent, reliable fire protection is also a valuable feature for potential tenants.

## How Much Water Is Required for Fire Protection?

A water flow test is required before starting a hydraulic calculation. This can be accomplished by measuring pressure and flow at a water hydrant, but this information may also be available publicly from the municipal water department.

There may be cases in which the municipal water supply is insufficient for fire protection, or not available. When this happens, the piping can be designed to draw water from other sources, which can be classified as open or closed:

• Lakes, ponds, and rivers are examples of open sources.
• Underground, above-ground, and elevated water tanks are examples of closed sources.

When water is obtained from a static source like a lake or buried tank, additional pressure is required for effective fire protection. This must be considered in the hydraulic calculation procedure, and the pressure boost can be achieved with a fire pump or pressurized tank.

## Piping System Configurations

The piping layouts of most fire protection systems can be classified into three main types, based on how individual pipes are arranged: tree, loop, and grid.

 Piping Configuration Description Tree This configuration uses a main pipe that branches out into smaller pipes, similar to how a tree has branches that grow from its trunk. The branching pipes provide water for individual sprinklers and other fire protection elements. Loop This configuration also has a main pipe, from which all other pipes branch out. However, the main pipe returns to the starting point, completing a loop at the source. Grid This configuration uses two main lines that run parallel to each other, connected by smaller piping segments. There is more than one route leading to each sprinkler, which reduces friction.

Fire protection standards normally require the Hazen-Williams method to determine friction losses in a piping system, regardless of the layout used:

• Tree and loop piping layouts have a simpler procedure, and manual calculations are feasible.
• On the other hand, grid piping layouts require software to analyze and balance the water flow through all the possible paths.

Modern fire protection systems are normally designed with computerized calculations, regardless of the layout used. Software calculations allow changes and recalculations in just a fraction of the time required with manual procedures.

There are many factors that influence the intensity and extent of a fire, which include the materials stored in a building and their arrangement. Fire protection codes provide tables and typical design values, which come from decades of testing and detailed simulation of fire incidents. The NFPA 13 Handbook has a supplement that covers the theory and procedures behind hydraulic calculations.

## Calculating Sprinkler Density Based on Demand

The occupancy hazard classification is a critical factor when designing an automatic sprinkler system. If the fire hazard is underestimated, the resulting sprinkler system will be undersized for the fires that may occur. The system will be unable to extinguish the flames, causing extensive property damage and potential casualties.

The hazard classification should be determined by experienced fire protection engineers. There is no calculation procedure, and the analysis is qualitative - it depends on experience and being familiar with NFPA standards.

• Based on the hazard classification, fire protection engineers can determine the optimal layout of pipes and fire sprinklers.
• The next step is to determine the maximum number of sprinklers that could activate at once and calculate the required pressure to guarantee enough water flow.
• In any scenario with less active sprinklers than the maximum assumed, the piping and water supply will be more than enough.

The number of sprinklers considered for design calculations is mainly determined by the hazard classification. However, there is freedom for adjustments that are considered suitable by the designer.

The NFPA provides graphs that establish a relationship between covered area and flow density. Fire protection designers select an adequate combination of area and density, depending on the application.

• The fire sprinkler design can range from high flow density over a small area, to low density over a large area.
• In both cases, the goal is to control the fire before it spreads outside of the design area.

## How to Calculate Sprinkler Flow Requirements?

The flow calculation is relatively simple since design engineers only have to multiply the covered area and the flow density that was previously determined:

• Q (flow) = Coverage Area x Flow Density

Listed sprinklers normally have minimum flow requirements in their technical specifications, which depend on spacing. The manufacturer's flow requirements must prevail if they exceed the calculated values.

## How to Calculate Sprinkler Pressure Requirements?

The pressure calculation is more complex since fire sprinklers involve an energy conversion from pressure to kinetic energy.  The calculation uses the formula for water flow through an orifice, based on the pressure inside the pipe:

• Q (flow) = 29.83 x CD x d2 x √P
• CD is the discharge coefficient, which is based on the orifice characteristics and determined experimentally.
• On the other hand, the letters d and P simply represent diameter and pressure.

Since fire sprinklers already have a design diameter, all factors other than the pressure can be combined into a "K-factor" for simpler calculations. This results in a more compact formula:

• Q = K x √P

When the required flow (Q) is known, the formula can be rearranged as follows to calculate the required pressure (P):

• P = (Q / K) 2

NFPA 13 establishes a minimum pressure of 7 psi, even when the calculation procedure yields a smaller value. This ensures that sprinklers produce the correct spray pattern. However, NFPA 13 also provides exceptions to the method, which are covered in Chapter 7.  The following are some examples:

• Applications in which dry pipe sprinkler systems are used.
• Quick response sprinklers under flat smooth ceilings with limited height.
• Non-sprinklered and combustible concealed spaces in a building.
• Spaces that are broken down into multiple compartments, where alternative methods allow a smaller number of sprinklers.
• Dwelling units and adjacent corridors, which use a simplified procedure with a four-sprinkler design area.

## Conclusion

Automatic sprinkler systems have stringent design requirements, which makes sense due to their importance in fire protection. Designing a sprinkler system that meets code at optimal cost is an engineering challenge, which requires fire protection experience and familiarity with standards.

In New York City, all commercial properties covered by Local Law 26 were required to have fire sprinklers by July 1, 2019. If you have a property that missed the deadline, the best recommendation is to get in touch with a qualified MEP engineering firm ASAP.

Fire protection systems are critical for building safety and are subject to stringent codes. NY Engineers offers 80% first-time approval, and you can write at info@ny-engineers.com or call.