Water flows steadily through a horizontal pipe: cross-sectional areas at P and Q are 40 cm² and 20 cm². The pressure at P exceeds that at Q by 15 N m⁻². Water density is 1000 kg m⁻³. Find the volume flow rate in cm³ s⁻¹. Image
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Question

Water flows steadily through a horizontal pipe: cross-sectional areas at P and Q are 40 cm² and 20 cm². The pressure at P exceeds that at Q by 15 N m⁻². Water density is 1000 kg m⁻³. Find the volume flow rate in cm³ s⁻¹. Image

Options

G1 Physics · Accepted Answer

Step 1: Continuity gives Aₚvₚ = A_qv_q. As Aₚ/A_q = 40/20 = 2, v_q = 2vₚ. Step 2: Bernoulli's equation for a horizontal pipe gives Pₚ − P_q = (ρ/2)(v_q² − vₚ²). Step 3: Substitute ΔP = 15 Pa and v_q = 2vₚ: 15 = (1000/2)(4vₚ² − vₚ²) = 1500vₚ². Step 4: vₚ² = 0.01, so vₚ = 0.1 m s⁻¹. Step 5: Flow rate = Aₚvₚ = (40 × 10⁻⁴ m²)(0.1 m s⁻¹) = 4 × 10⁻⁴ m³ s⁻¹. Final answer: 400 cm³ s⁻¹ (Option D).