A cylindrical tank with a large diameter is filled with water to a depth D =0.30 m. A hole of cross-sectional area A = 6.2 `cm^(2)` in the bottom of the tank allows water to drain out. (a) What is the drainage rate in cubic meters per second? (b) At what distance below the bottom of the tank is the cross-sectional area of the stream equal to one half the area of the hole?

Explanation

To solve the problem step by step, we will break it down into two parts: (a) calculating the drainage rate in cubic meters per second, and (b) finding the distance below the bottom of the tank where the cross-sectional area of the stream is half the area of the hole.

### Part (a): Calculate the drainage rate

1. **Identify the given values:**
- Depth of water, \( D = 0.30 \, \text{m} \)
- Cross-sectional area of the hole, \( A = 6.2 \, \text{cm}^2 = 6.2 \times 10^{-4} \, \text{m}^2 \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)
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