Final answer:
The fluid speed in the fire hose is approximately 12.58 m/s.
Step-by-step explanation:
To find the fluid speed in a fire hose, we can use the equation:
Q = Av
where Q is the flow rate, A is the cross-sectional area of the hose, and v is the fluid speed. We are given that the diameter of the hose is 9.00 cm and it carries 80.0 L of water per second. First, we need to convert the diameter to meters and the flow rate to cubic meters per second:
9.00 cm = 0.09 m and 80.0 L/s = 0.08 m³/s
Next, we can find the cross-sectional area of the hose:
A = πr²
where r is the radius of the hose. Since the diameter is 9.00 cm, the radius is half of that: 0.045 m. Plugging in the values:
A = π(0.045)² = 0.00636 m²
Finally, we can solve the equation for v:
0.00636 m² * v = 0.08 m³/s
v = 0.08 m³/s / 0.00636 m² = 12.58 m/s
Therefore, the fluid speed in the fire hose is approximately 12.58 m/s.