Final answer:
To find the speed of water flowing through the pipe, calculate the cross-sectional area of the hose using its internal diameter, convert the given flow rate from liters per minute to cubic meters per second, and use the flow rate formula to solve for the speed, yielding a speed of 1.06 m/s.
Step-by-step explanation:
To calculate the speed of water flowing through the pipe, we can use the formula of flow rate, which is the volume of water passing through a section of the pipe per unit time. Given that the internal diameter of the hose pipe is 1 cm, we can first find the cross-sectional area of the pipe, and then use the flow rate of 5 liters per minute to find the speed.
We start by converting the internal diameter to meters to ensure that all units are consistent:
- Diameter (d) = 1 cm = 0.01 m
- Radius (r) = d/2 = 0.005 m
- Cross-sectional area (A) = π * r2 = 3.14159265 x (0.005 m)2
Now, we convert the flow rate from liters to cubic meters:
- Flow rate = 5 liters/min = 0.005 m3/min
Since we want the speed in meters per second, we convert the flow rate to cubic meters per second:
- Flow rate = 0.005 m3/min * (1 min/60 s) = 0.0000833 m3/s
Finally, we use the formula of flow rate (Q = A * v) to find the speed (v):
- Speed (v) = Q / A = 0.0000833 m3/s / 0.00007854 m2 = 1.06 m/s
Therefore, the water is flowing through the pipe at a speed of 1.06 m/s.