Final answer:
The speed of water in a 2.0 cm-diameter pipe required to fill a 500L bathtub in 4.9 minutes is approximately 5.41 m/s.
Step-by-step explanation:
The student's question pertains to the speed of water flowing through a pipe. To calculate this, we use the volume flow rate which is the volume of water passing through the pipe per unit of time. Given that a 500-liter bathtub fills in 4.9 minutes using a pipe of 2.0 cm diameter, we can find the flow rate and subsequently determine the speed of the water.
First, we convert the bathtub volume to cubic meters (500 L = 0.5 m³) and time to seconds (4.9 min = 294 s). Using the relation Q = V/t, where Q is the volumetric flow rate, V is the volume (0.5 m³), and t is time (294 s), we find Q = 0.5 m³/294 s ≈ 0.0017 m³/s.
Now, we can calculate the speed (v) with the equation Q = v × A, where A is the cross-sectional area of the pipe. The area (A) of a pipe with a diameter (d) of 0.02 m is given by A = π(d/2)² = π(0.01 m)². The speed of the water (v) is then Q/A, which we calculate as follows:
A = π(0.01m)² = 3.14 × (0.01m)² ≈ 0.000314 m²
v = Q/A = 0.0017 m³/s / 0.000314 m² ≈ 5.41 m/s
Therefore, the speed of the water in the pipe is approximately 5.41 meters per second.