Answer:
Therefore, the speed of the water in the 2.5-cm-diameter pipe is 163 m/min.
Explanation:
To solve this problem, we need to find the volume flow rate of the water and then use it to calculate the speed of the water in the pipe.
Given information:
- Pipe diameter: 2.5 cm
- Bathtub volume: 400 L
- Time to fill the bathtub: 5.0 min
Step 1: Convert the bathtub volume from liters to cubic meters.
1 L = 0.001 m³
400 L = 0.4 m³
Step 2: Calculate the volume flow rate of the water.
Volume flow rate = Bathtub volume / Time to fill the bathtub
Volume flow rate = 0.4 m³ / 5.0 min = 0.08 m³/min
Step 3: Calculate the cross-sectional area of the pipe.
Pipe diameter = 2.5 cm = 0.025 m
Cross-sectional area = π × (pipe diameter/2)² = π × (0.025 m/2)² = 0.000491 m²
Step 4: Calculate the speed of the water in the pipe.
Speed = Volume flow rate / Cross-sectional area
Speed = 0.08 m³/min / 0.000491 m² = 163 m/min