Final answer:
The fluid speed in the fire hose is approximately 2.26 m/s.
Step-by-step explanation:
To find the fluid speed in a fire hose, we can use the relationship between flow rate, area, and velocity. The flow rate is given as 80.0 L/s, which we can convert to cubic meters per second (m³/s) by dividing by 1000. The area of the hose can be calculated using the formula for the area of a circle. Once we have the flow rate and area, we can use the equation Q = Av to solve for the velocity.
Using the given diameter of 9.00 cm, the radius is 4.50 cm or 0.045 m. So the area of the hose is A = πr² = π(0.045 m)². The flow rate in m³/s is then 80.0 L/s divided by 1000, which is 0.08 m³/s. Plugging these values into the equation Q = Av, we can solve for the velocity (v).
So, the fluid speed in the fire hose is approximately 2.26 m/s.