Water is forced out of a fire extinguisher by air pressure,...

Water is forced out of a fire extinguisher by air pressure, as shown in Figure P9.70. What gauge air pressure in the tank (above atmospheric pressure) is required for the water to have a jet speed of $30.0 \mathrm{~m} / \mathrm{s}$ when the water level in the tank is $0.500 \mathrm{~m}$ below the nozzle?

Key Concepts

Hydrostatic Pressure

This concept refers to the pressure in a fluid at rest due to the gravitational force acting on it. The pressure increases with depth and is calculated by the product of the fluid density, gravitational acceleration, and vertical height difference. In problems involving fluid ejection, the hydrostatic head must be considered when determining the total effective pressure at a particular elevation.

Dynamic Pressure

Dynamic pressure is the kinetic energy per unit volume of a fluid and is given by one-half the product of the fluid density and the square of its velocity. It represents the portion of the fluid's energy that is being converted into kinetic energy as it exits a nozzle, and it is essential for relating the fluid speed to the applied pressure in the system.

Bernoulli's Principle

This principle states that along a streamline, the sum of the pressure energy, kinetic energy per unit volume, and potential energy per unit volume is constant for an incompressible, non-viscous fluid. It is used to relate the pressure differences in the fluid to changes in velocity and elevation, which is key in determining the necessary pressure to achieve a specified jet speed.

Gauge Pressure

Gauge pressure is the pressure measured relative to ambient atmospheric pressure. In many practical applications, like in the fire extinguisher example, the required pressure is provided as the excess pressure above the atmospheric value, which is then used to overcome energy losses and accelerate fluid to a desired speed.

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