A fire sprinkler head has a k-factor of 7.6. What is the flow rate in gallons per minute at a pressure of 15 psi?

To determine the flow rate through a fire sprinkler head based on its k-factor and the pressure at which it operates, you can use the formula:

[

\text{Flow Rate (gpm)} = k \times \sqrt{\text{Pressure (psi)}}

]

In this case, the k-factor is given as 7.6, and the pressure is 15 psi. Plugging these values into the formula:

1. Calculate the square root of the pressure:

(\sqrt{15}) is approximately 3.872.

2. Multiply the k-factor by this value:

[

7.6 \times 3.872 \approx 29.4

]

Thus, at a pressure of 15 psi, the flow rate through the sprinkler head with a k-factor of 7.6 is approximately 29.4 gallons per minute (gpm). This matching of calculated flow rate to one of the choices confirms that the answer is indeed correct. Understanding how to apply this equation is essential for fire protection professionals to determine adequate water supply flow rates for various applications.