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A liquid of density 750 kg/m³ flows steadily through a horizontal pipe whose cross-section narrows from A1 = 1.2 x 10⁻² m² to A2 = A1/2. The pressure difference between the wide and narrow sections is 4500 Pa. Find the volume flow rate of the liquid (in units of 10⁻³ m³/s).
- 24
- 12
- 36
- 18
Correct answer: 24
Solution
Continuity gives v2 = 2*v1 (since A2 = A1/2). Bernoulli for a horizontal pipe: delta_P = (1/2)*rho*(v2² - v1²) = (1/2)*rho*(4v1² - v1²) = (3/2)*rho*v1². So 4500 = 1.5*750*v1² = 1125*v1² => v1² = 4 => v1 = 2 m/s. Flow rate Q = A1*v1 = 1.2x10⁻² * 2 = 2.4x10⁻² m³/s = 24 x 10⁻³ m³/s.
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