Design Example: Flow Through a Fire Extinguisher

A fire extinguisher that uses pressurized water relies on fluid dynamics principles to generate a high-velocity stream capable of suppressing flames. The water is stored at a much higher pressure inside the extinguisher than the surrounding atmosphere. This pressure difference forces the water to flow rapidly when the extinguisher is activated, and the behavior of the water as it exits the nozzle can be understood using fundamental equations of fluid dynamics.

The key to understanding how the water accelerates lies in the pressure difference between the inside of the extinguisher and the outside environment. Bernoulli's equation, which relates pressure and velocity, calculates how fast the water will exit the nozzle.

According to this principle, as pressure decreases, velocity increases. This means that the high internal pressure within the extinguisher is converted into the velocity of the water as it flows out. As the water approaches the nozzle, the decrease in nozzle diameter further accelerates the flow, transforming pressure energy into kinetic energy.

After determining the exit velocity of the water, the flow rate, or the volume of water expelled over time, is calculated. The calculation uses the continuity equation, ensuring that the water flowing through the system remains constant. The flow rate is the product of the water's velocity and the cross-sectional area of the nozzle.

Since the nozzle has a small diameter, the water is expelled at high velocity, providing a consistent and powerful stream necessary for fire suppression. By applying these principles, the performance of the extinguisher can be optimized to ensure effective operation.