Final answer:
To determine if a tank is filling or emptying, compare the inflow and outflow rates. For a pool with a capacity of 80,000 L and a hose at 60 L/min, it takes roughly 22 hours and 13 minutes to fill. Diverting a river at 5000 m³/s would fill it almost instantly.
Step-by-step explanation:
To determine whether a tank is filling or emptying, and at what rate the water level is changing, we must consider the capacity of the tank, the flow rate of the fluid going in or out, and whether the inflow is greater than the outflow. If the flow rate of the inflow is greater, the tank is filling, and if the outflow is greater, the tank is emptying.
For part (a), to estimate the time to fill a private swimming pool of 80,000 L using a garden hose delivering 60 L/min, we use the formula:
time = capacity / flow rate. Therefore, time = 80,000 L / 60 L/min = 1333.33 minutes, or approximately 22 hours and 13 minutes.
For part (b), filling the same pool by diverting a moderate size river with a flow rate of 5000 m³/s, we need to convert liters to cubic meters, since 1 m³ = 1000 L. Therefore, 80,000 L = 80 m³. The time taken would be time = 80 m³ / 5000 m³/s which results in a very small fraction of a second, technically an instantaneous fill.
Without additional information, for the questions involving flow rates and pressures, we would need to apply principles of fluid dynamics or hydrostatics considering variables such as the size of the hole, the depth of the water, the dimensions of the tank, and other factors to calculate the rate at which the water level is changing.