Final answer:
Using the cross-sectional area of the faucet and water velocity, we calculate the flow rate for part (a). Part (b) is theoretical as the question neglects real-world factors like surface tension and gravity, implying the stream's diameter remains constant.
Step-by-step explanation:
The problem at hand involves calculating the flow rate of water from a faucet and understanding the behavior of water flow under the influence of gravity. To solve part (a), we'll use the flow rate equation Q = A × v, where Q is the flow rate, A is the cross-sectional area of the faucet, and v is the velocity of water. The diameter of the faucet is given as 1.80 cm, which we'll need to convert to meters for consistency in units when applying the formula. The cross-sectional area A can be calculated using the formula for the area of a circle, A = πr².
For part (b), we neglect the effects of surface tension and assume the velocity of the water does not change as it falls 0.200 m below the faucet, due to the construction of the faucet that ensures no speed variation across the stream. However, in reality, the diameter of the water stream would likely decrease slightly as it falls due to the conservation of mass and acceleration due to gravity, but this is a more complex fluid dynamics problem that is beyond the scope of this question.