Water flows steadily through a horizontal pipe. At section 1, the cross-sectional area is four times the area at section 2 and the water speed is 2 m/s. Neglect viscosity and take the water density as 1000 kg/m³. What is the pressure difference P₁ - P₂?
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Question

Water flows steadily through a horizontal pipe. At section 1, the cross-sectional area is four times the area at section 2 and the water speed is 2 m/s. Neglect viscosity and take the water density as 1000 kg/m³. What is the pressure difference P₁ - P₂?

Options

G1 Physics · Accepted Answer

First use the equation of continuity. A₁v₁ = A₂v₂. Since A₁ = 4A₂ and v₁ = 2 m/s, we get 4A₂×2 = A₂v₂. Therefore, v₂ = 8 m/s. Because the pipe is horizontal, both sections have the same height. Bernoulli's equation gives P₁ + ½ρv₁² = P₂ + ½ρv₂². Hence, P₁−P₂ = ½ρ(v₂²−v₁²). Substitute: P₁−P₂ = ½×1000×(8²−2²) = 500×60 = 30000 Pa = 30 kPa. Correct option: C.

Water flows steadily through a horizontal pipe. At section 1, the cross-sectional area is four times the area at section 2 and the water speed is 2 m/s. Neglect viscosity and take the water density as 1000 kg/m³. What is the pressure difference P₁ − P₂?