A fire hose has a circular cross-section which has a diameter of 20 cm. The hose is full of water and the water in the hose is flowing at a speed of 5m/s.
How many liters of water can flow from the hose in 1 minute? (1m^3 = 1000 L)
Area of a cross-section is
π(10)^2 = 100π cm^2
5 m = 500 cm
So a volume of 100π(500) or 50000π cm^3 flows every second
or 50000π/1000 L will flow every second
flow is 50π L/sec
so in 1 minute 60(50π) or 3000π L will flow
To find the volume of water that can flow from the hose in 1 minute, we need to calculate the volume of water that flows out of the hose in 1 second and then multiply that by 60 to get the volume in 1 minute.
The volume of water flowing out of the hose in 1 second can be calculated using the formula:
Volume = Cross-sectional area * Velocity
To find the cross-sectional area of the circular hose, we need to use the formula:
Area = π * (radius)^2
Given that the diameter of the hose is 20 cm, we can calculate the radius by dividing the diameter by 2:
Radius = 20 cm / 2 = 10 cm
Converting the radius to meters:
Radius = 10 cm * 0.01 m/cm = 0.1 m
Now we can calculate the cross-sectional area:
Area = π * (0.1 m)^2 = 0.0314 m^2
Next, we'll calculate the volume of water flowing out of the hose in 1 second:
Volume = 0.0314 m^2 * 5 m/s = 0.157 m^3/s
Finally, to find the volume of water flowing in 1 minute, we'll multiply this volume by 60:
Volume in 1 minute = 0.157 m^3/s * 60 s/min = 9.42 m^3/min
Since 1 m^3 is equal to 1000 liters, we can convert the volume to liters:
Volume in 1 minute = 9.42 m^3/min * 1000 L/m^3 = 9420 L
Therefore, approximately 9420 liters of water can flow from the hose in 1 minute.