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Water flows steadily through a horizontal pipe of varying cross-section. At a section of area 0.02 m² the pressure is 4 x 10⁴ N/m² and the flow speed is 2 m/s. Find the pressure where the cross-sectional area narrows to 0.01 m². (Take density of water = 10³ kg/m³.)
- 1.4 x 10⁴ N/m²
- 3.4 x 10⁴ N/m²
- 2.4 x 10⁴ N/m²
- none of these
Correct answer: 3.4 x 10⁴ N/m²
Solution
Continuity: v2 = (A1/A2)*v1 = (0.02/0.01)*2 = 4 m/s. Bernoulli (horizontal): P2 = P1 + (1/2) rho (v1² - v2²) = 4e4 + 0.5*1000*(4 - 16) = 4e4 + 0.5*1000*(-12) = 4e4 - 6000 = 3.4 x 10⁴ N/m².
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