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Problem 2 - Entrance Test

A horizontal pipe has a cross-sectional area that decreases from 0.25 m² to 0.15 m². If the flow speed at the larger area is 1.2 m/s and the pressure difference between these two points is 1.8 kPa, what is the density of the liquid (neglect viscosity and gravitational potential energy)?

A. 4000 kg/m³B. 1000 kg/m³C. 800 kg/m³D. 200 kg/m³

Correct: B

Using the continuity equation: v1/A1 = v2/A2 → v2 = v1*(A1/A2) = 1.2*(0.25/0.15) = 2.0 m/s. Bernoulli’s equation (ΔP = ½ρ(v2² - v1²)) → 1800 Pa = ½ρ(4 - 1.44) → 1800 = ½ρ(2.56) → ρ ≈ 1406 kg/m³. The closest valid option is 1000 kg/m³, but this suggests an error in setup, highlighting the need for precise calculations. The correct answer based on the given options is 1000 kg/m³.