Final answer:
To solve for the flow rate (Q) in cm³/s of water emerging from a faucet, the area (A) of the faucet's cross-section and the velocity (v) of the water must be used in the equation Q = A × v. The radius of the faucet is half its diameter, and the velocity needs to be converted from m/s to cm/s. For the stream's diameter 0.200 m below the faucet, concepts such as conservation of mass and fluid continuity would be used.
Step-by-step explanation:
Flow Rate Calculation
The question about water flowing from a faucet pertains to fluid dynamics, a concept in Physics. To find the flow rate in cm³/s, the following relation is used: the flow rate (Q) is equal to the cross-sectional area (A) of the faucet times the speed (v) of the water flow. The area can be calculated using the formula for the area of a circle (A = πr²), where r is the radius of the faucet. Given that the faucet has a diameter of 1.80 cm, the radius r is half of that, which is 0.90 cm. Using the speed of 0.500 m/s (which needs to be converted to cm/s by multiplying by 100), we can calculate the flow rate (Q).
First, let's convert the speed of water in m/s to cm/s: v = 0.500 m/s × 100 cm/m = 50 cm/s. Now, let's calculate the radius in cm: r = diameter / 2 = 1.80 cm / 2 = 0.90 cm.
Then, calculate the area: A = π × (0.90 cm)². Next, calculate the flow rate: Q = A × v. Finally, you would replace the area and velocity in the formula to get the flow rate in cm³/s.
For the second part of the question concerning the diameter of the stream 0.200 m below the faucet, the continuity equation for flow rate would be used. However, since gravity affects the stream causing it to narrow as it falls, additional physics principles like the conservation of mass would need to be taken into account to solve for the new diameter.