Question

A fire hose for use in urban areas must be able to shoot a stream of water to a maximum height of 32 m. The water leaves the hose at ground level in a circular stream 2.5 cm in diameter.

a) 6 m/s
b) 12 m/s
c) 24 m/s
d) 48 m/s

Answer 1

The fluid speed in a fire hose is approximately 162,972 m/s.

Step-by-step explanation:

The fluid speed in a fire hose can be determined using the equation:

v = Q / A

where v is the fluid speed, Q is the flow rate, and A is the cross-sectional area of the stream.

To find the flow rate, we can use the equation:

Q = π * r2 * v

where r is the radius of the stream.

First, we need to convert the diameter of the stream to radius:

r = 2.5 cm / 2 = 1.25 cm = 0.0125 m

Next, we can calculate the cross-sectional area of the stream:

A = π * r2

= π * (0.0125 m)2

= 0.0004909 m2

Finally, we can calculate the fluid speed:

v = Q / A

= 80.0 L/s / 0.0004909 m2

≈ 162,971.9 m/s

Therefore, the fluid speed is approximately 162,972 m/s.