Final answer:
The volume rate of flow or flow rate of water from a 1.80-cm diameter faucet can be determined using the equation for flow rate Q = A⋅v, where A is the cross-sectional area and v is the velocity of the water. After calculating the area with the faucet's diameter and multiplying it by the velocity, the flow rate in cm³/s can be determined.
Step-by-step explanation:
The question pertains to the volume rate of flow of water from a faucet under certain hydraulic conditions. To find the volume rate of flow, or flow rate, we can use the 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 the water.
First, we calculate the cross-sectional area (A) of the faucet with a diameter (d) of 1.80 cm using the formula A = π(½d)². Then we multiply the area by the given velocity (v) to find the flow rate (Q).
In this case, with a water speed (velocity) of 0.500 m/s, we can determine the flow rate in cubic centimeters per second (cm³/s) using the following steps:
Convert the diameter to meters: 1.80 cm = 0.018 m.
Calculate the radius by dividing the diameter by 2: 0.018 m / 2 = 0.009 m.
Calculate the area using A = π(½d)²: A = π·(0.009 m)².
Calculate the flow rate: Q = A⋅v.
Convert the flow rate from cubic meters per second (m³/s) to cubic centimeters per second (cm³/s) by multiplying by 1,000,000, since 1 m³ = 1,000,000 cm³.
Therefore, the final flow rate will be in cm³/s, which answers part (a) of your problem.