At 20°C, the pressure gradient in a horizontal pipe is 60 kPa per 100 m and water flows at 3 L/min. Estimate the pipe radius. (Dynamic viscosity at 20°C = 10⁻³ Pa·s.)
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At 20°C, the pressure gradient in a horizontal pipe is 60 kPa per 100 m and water flows at 3 L/min. Estimate the pipe radius. (Dynamic viscosity at 20°C = 10⁻³ Pa·s.)

G1 Physics · Accepted Answer

Step 1: For laminar flow through a horizontal cylindrical pipe, Poiseuille's law is Q = πr⁴ ΔP/(8ηL). Step 2: Convert data: Q = 3 L/min = (3 × 10⁻³)/60 = 5.0 × 10⁻⁵ m³/s. Step 3: Pressure gradient is ΔP/L = (60 × 10³ Pa)/(100 m) = 600 Pa/m, and η = 1.0 × 10⁻³ Pa·s. Step 4: Rearrange: r⁴ = 8ηQ/[π(ΔP/L)]. Step 5: r⁴ = [8 × (1.0 × 10⁻³) × (5.0 × 10⁻⁵)]/(π × 600) = 2.122 × 10⁻¹⁰ m⁴. Step 6: r = (2.122 × 10⁻¹⁰)¹ᐟ⁴ m = 3.82 × 10⁻³ m = 0.382 cm. Final answer: 0.382 cm (CORRECTED Option C). The source…