Water flows through a horizontal pipe. At section 1 the cross-sectional area is four times that at section 2 and the speed at section 1 is 2 m/s. Taking ρ = 1000 kg/m³ and neglecting viscosity, the pressure difference P₁ − P₂ is N kPa. Find N.
Physics · Fluid Mechanics · equation of continuity and bornullie theorem
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Question

Water flows through a horizontal pipe. At section 1 the cross-sectional area is four times that at section 2 and the speed at section 1 is 2 m/s. Taking ρ = 1000 kg/m³ and neglecting viscosity, the pressure difference P₁ − P₂ is N kPa. Find N.

Physics · Fluid Mechanics · equation of continuity and bornullie theorem

G1 Physics · Accepted Answer

From continuity, A₁v₁ = A₂v₂. Since A₁ = 4A₂, v₁ = 2 m/s, we obtain v₂ = 8 m/s. For a horizontal pipe, P₁ + ½ρv₁² = P₂ + ½ρv₂². Thus, P₁−P₂ = ½ρ(v₂²−v₁²) = ½×1000×(64−4) = 30000 Pa = 30 kPa. Hence, N = 30.