A pressure meter when attached with a closed horizontal pipe shows a reading of `5 xx 10^(5)" N/m"^(2).` When the valve of the pipe is opened, the reading of the pressure meter falls to `3.5 xx 10^(5) N//m^2.` Determine the speed of the water flowing in the pipe.

Explanation

To determine the speed of the water flowing in the pipe, we can use Bernoulli's equation. Here are the steps to solve the problem:

### Step 1: Identify the pressures
We have two conditions for the pressure in the pipe:
- Condition 1 (when the pipe is closed): \( P_1 = 5 \times 10^5 \, \text{N/m}^2 \)
- Condition 2 (when the valve is opened): \( P_2 = 3.5 \times 10^5 \, \text{N/m}^2 \)

### Step 2: Apply Bernoulli's equation
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