Final answer:
To find the radius of a pipe that fills a tank at a specified flow rate and speed, use the formula for volume flow rate and solve for the radius. The calculation involves dividing the volume of the tank by the filling time and comparing it to the product of the pipe's cross-sectional area and flow speed.
Step-by-step explanation:
To answer the question about the radius of a pipe that fills a tank at a certain rate, we first need to calculate the volume flow rate of water moving through the pipe. This is given by the volume of the tank divided by the time taken to fill it, which is 2200 m³ / 7 hr = 314.29 m³/hr. Since the water flows at 10 km/hr, and 1 km/hr is 1000 m/hr, the flow speed is 10,000 m/hr. To find the radius, we need to use the formula for the volume flow rate Q = A ⋅ v, where A is the cross-sectional area of the pipe and v is the flow speed.
The cross-sectional area can be found using A = πr², and rearranging the volume flow rate equation to solve for the radius r gives us r = √(Q / (πv)). Plugging in the given volume flow rate and velocity yields the radius of the pipe.
Through this process, we can determine that the radius of the pipe required to achieve this flow rate is 1.00 m.