Final answer:
To fill a pool with a garden hose delivering 60 L/min would take approximately 22.22 hours. Filling the same pool by diverting a river flowing at 5000 m³/s would take an implausibly brief 0.016 seconds. These calculations demonstrate the principles of flow rate and pressure in water systems.
Step-by-step explanation:
Calculating Time to Fill a Swimming Pool
The question involves mathematical calculations related to the rate of water flow. The scenarios given compare the differing times it would take to fill a swimming pool using two distinct methods: a garden hose and diverting a moderate-size river.
1. Firstly, to estimate the time it would take to fill a private swimming pool with a capacity of 80,000 liters (L) using a garden hose that delivers 60 L/min, we use the formula: Time = Volume / Rate. So the calculation is 80,000 L / 60 L/min = 1,333.33 min, which is approximately 22.22 hours.
2. Secondly, for filling the same pool by diverting a river with a flow rate of 5000 cubic meters per second (m³/s), we first convert the pool capacity to cubic meters since 1 L = 0.001 m³, resulting in 80 m³. Again using the formula Time = Volume / Rate, we calculate 80 m³ / 5000 m³/s = 0.016 s. This ridiculously short time illustrates the vast difference in scale between a garden hose and a river.
Understanding Water Flow Rates and Pressure
When discussing the flow of water through a garden hose and the associated pressure from a water main, the principles of fluid dynamics come into play. Pressure and flow rate are directly related through the equation of continuity and Bernoulli's principle for incompressible flow. In the context of the pressure changes experienced in a water main, we observe how this affects the flow rate through a garden hose and calculate the impact on household water supply.