A non-viscous liquid of density 1000 kg m⁻³ flows steadily through an inclined tube. At P: height 2 m, area 4 × 10⁻³ m², speed 1 m s⁻¹. At Q: height 5 m, area 8 × 10⁻³ m². Find the work done per unit volume by pressure force and by gravity as the fluid moves from P to Q. Image
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Question

A non-viscous liquid of density 1000 kg m⁻³ flows steadily through an inclined tube. At P: height 2 m, area 4 × 10⁻³ m², speed 1 m s⁻¹. At Q: height 5 m, area 8 × 10⁻³ m². Find the work done per unit volume by pressure force and by gravity as the fluid moves from P to Q. Image

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G1 Physics · Accepted Answer

Step 1: Use continuity A₁v₁ = A₂v₂ and Bernoulli's equation P + ½ρv² + ρgh = constant; for jets use momentum flux ṁΔv. Step 2: Substitute the stated areas, levels and pressures, including Torricelli v = √(2gh) where applicable. Applying these relations to the given data gives A: +29625 J m⁻³, −30000 J m⁻³. Final answer: A.