A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross- sectional area is `10cm^2`, the water velocity is `1ms^-1` and the pressure is 2000 Pa. The pressure of water at another point where the cross-sectional area is `5cm^2`, is........Pa. (Density of water `=10^3kg.m^-3`)

Explanation

To solve the problem, we will use Bernoulli's equation and the continuity equation. Here are the steps:

### Step 1: Identify the given values
- Cross-sectional area at point 1, \( A_1 = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 = 0.001 \, \text{m}^2 \)
- Velocity at point 1, \( v_1 = 1 \, \text{m/s} \)
- Pressure at point 1, \( P_1 = 2000 \, \text{Pa} \)
- Cross-sectional area at point 2, \( A_2 = 5 \, \text{cm}^2 = 5 \times 10^{-4} \, \text{m}^2 = 0.0005 \, \text{m}^2 \)
- Density of water, \( \rho = 10^3 \, \text{kg/m}^3 \)
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