A uniform-cross-section siphon carries water from a large open reservoir to an outlet 5 m below the reservoir surface. Its highest point is 2 m above the reservoir surface. Take atmospheric pressure as 100 kPa, ρ = 1000 kg/m³ and g = 10 m/s². Neglect losses. If the absolute pressure at the highest point is N kPa, find N.
Physics · Fluid Mechanics · equation of continuity and bornullie theorem
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Question

A uniform-cross-section siphon carries water from a large open reservoir to an outlet 5 m below the reservoir surface. Its highest point is 2 m above the reservoir surface. Take atmospheric pressure as 100 kPa, ρ = 1000 kg/m³ and g = 10 m/s². Neglect losses. If the absolute pressure at the highest point is N kPa, find N.

Physics · Fluid Mechanics · equation of continuity and bornullie theorem

G1 Physics · Accepted Answer

Between the reservoir surface and outlet, ½ρv² = ρg(5). Hence, v = 10 m/s. Apply Bernoulli's equation between the reservoir surface and the highest point. At the reservoir surface, P = 100000 Pa, v ≈ 0, z = 0. At the highest point, z = 2 m, v = 10 m/s. Therefore, 100000 = P(top) +1000×10×2 +½×1000×10². Thus, P(top) = 100000−20000−50000 = 30000 Pa = 30 kPa. Hence, N = 30.