Limitations to Maximum Fluid Flow Velocity in a Sprinkler System Hydraulic Calculation

The NFPA 13 does not prescribe the maximum limit for velocity allowed in a pipe while performing hydraulic calculations for a sprinkler system design to the requirements of NFPA 13. The reason for this is that velocity is a self-correcting parameter that adjusts to accommodate changes in other parameters of fluid flow in a pipe. To fully understand why there need not be any limitation on velocity, we need to first cover some basic fluid dynamics concepts related to fluid flow in a pipe. Figure 1. A diagram of water flow through a pipe; where A is the cross-sectional area of the pipe, d is the length of the pipe under discussion and v is the velocity.

In fluid dynamics, Flow rate (Q) is defined to be the volume of fluid passing through an area during a period of time, as shown in Figure 1 above. The figure displays two parameters that influence the flow rate (Q) in a pipe; the cross-sectional area of the pipe (A) and velocity (v). The following formula displays the relationship between the cross-sectional area of a pipe and velocity.

Q = A x v

Or, v = Q / A.

This equation shows that velocity is proportional to flow rate, and inversely proportional to the cross-sectional area of the pipe. In a hydraulic calculation for a sprinkler system, the fluid is water, which is essentially incompressible. Therefore, the equation of continuity is applied in such a way that the flow rate must be constant to ensure continuity of flow. When the cross-sectional area of the pipe is reduced, the velocity will increase and vice versa, in order to maintain a constant flow rate, as depicted in Figure 2 below. Figure 2 Based on the equation of continuity for incompressible fluids, the Flow Rate (Q) will be a constant, and therefore Q = A1 x v1 = A2 x v2

The friction loss formulas used in hydraulic calculations such as the Hazen-Williams Formula, depict that pressure loss across a section of pipe is directly proportional to the flow rate and inversely proportional to the diameter of the pipe.

Frictional Resistance (Frictional Pressure Loss) P = 4.52 x Q1.85 / (C1.85 x d4.87)

Where, Q is the flow, C is friction loss co-efficient, and d is the internal diameter of pipe.

Since we established previously that the flow rate will be a constant, the pressure loss will now directly be proportional to the velocity and inversely proportional to the cross-sectional area of the pipe. Therefore, if the velocity through a section of pipe is high, the pressure loss across that section will also be high. In order to reduce the pressure loss, the pipe size will need to be increased which in turn will reduce the velocity in the pipe.

Any concerns to limit the maximum velocity due to noise or pipe erosion are also irrelevant to the design of a sprinkler system. Sprinkler systems operate only during a fire or during testing, thus eliminating concern for noise and erosion that consistent use would present in other types of mechanical systems.

While NFPA 13 also cautions that the exclusion of a specific velocity limitation is not a confirmation that the Hazen-Williams formula can be used for any velocity of water flow and when the velocity in the pipe exceeds the limits used to determine the formula, it might no longer be valid, it also reports that there has been some research performed in which results using the Hazen-Williams formula and the Darcy-Weisbach formula were compared, and the conclusion was that a specific velocity limit applied to all pipe sizes is not appropriate.

So, there is no magic number that needs to be put forward as the maximum allowed velocity for fluid flow through a pipe, when the standard of reference for the design is NFPA 13.