Water is flowing at a speed of 0.5 m/s through a horizontal pipe of internal diameter 3 cm. Determine the diameter of the nozzle if the water is to emerge at a speed of 3 m/s.

Explanation

To solve the problem of determining the diameter of the nozzle through which water flows, we can use the principle of continuity. This principle states that the mass flow rate must remain constant from one cross-section of a pipe to another.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of water in the pipe, \( v_1 = 0.5 \, \text{m/s} \)
- Diameter of the pipe, \( D_1 = 3 \, \text{cm} = 0.03 \, \text{m} \)
- Speed of water at the nozzle, \( v_2 = 3 \, \text{m/s} \)
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