Let's break it down step by step:
### Part (a): Finding the Water's Speed on the Second Floor
**Given:**
- Initial diameter of the pipe, \( d_1 = 5 \, \text{cm} = 0.05 \, \text{m} \)
- Initial speed of water, \( v_1 = 2 \, \text{m/s} \)
- Initial pressure, \(
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