An unknown liquid flows steadily through a horizontal pipe that tapers from a wider cross-section to a narrower one. The cross-sectional areas of the wide and narrow sections are 6 cm ^2 and 2 cm ^2 respectively. If the volume flow rate of the liquid is 0.6 L s ⁻¹ and the pressure difference between the two sections is 3200 Pa , the density of the liquid is _____ kg m ⁻³ .

Step-by-step solution

By the equation of continuity, the volume flow rate is Q = A₁ v₁ = A₂ v₂ . Given Q = 0.6 L s ⁻¹ = 0.6 10⁻³ m ^3 s ⁻¹ = 6 10⁻⁴ m ^3 s ⁻¹ . The velocities at the wide and narrow sections are: v₁ = Q A₁ = 6 10⁻⁴ 6 10⁻⁴ = 1 m s ⁻¹ v₂ = Q A₂ = 6 10⁻⁴ 2 10⁻⁴ = 3 m s ⁻¹ Applying Bernoulli's equation for a horizontal pipe: P₁ + 1 2 v₁^2 = P₂ + 1 2 v₂^2 P = P₁ - P₂ = 1 2 (v₂^2 - v₁^2) Substituting the given values: 3200 = 1 2 (3^2 - 1^2) 3200 = 1 2 (9 - 1) 3200 = 4 = 800 kg m ⁻³ Answer: 800