A uniform-cross-section siphon carries water from a large open reservoir to an outlet 5 m below the reservoir surface. The highest point of the siphon is 2 m above the reservoir surface. Neglect viscosity and take atmospheric pressure as 100 kPa, ρ = 1000 kg/m³ and g = 10 m/s². What is the absolute pressure at the highest point of the siphon?
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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. The highest point of the siphon is 2 m above the reservoir surface. Neglect viscosity and take atmospheric pressure as 100 kPa, ρ = 1000 kg/m³ and g = 10 m/s². What is the absolute pressure at the highest point of the siphon?

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G1 Physics · Accepted Answer

First find the flow speed from Bernoulli's equation between the reservoir free surface and the outlet. Both are exposed to atmospheric pressure. Take the reservoir surface as z = 0 and the outlet as z = −5 m. Then, ½ρv² = ρg(5). Thus, v = √(2×10×5) = 10 m/s. Now apply Bernoulli's equation between the reservoir surface and the highest point of the siphon. At the free surface, P = 100 kPa, v ≈ 0, z = 0. At the highest point, z = +2 m, v = 10 m/s. Therefore, 100000 = P(top) + 1000×10×2 + ½×1000×10…