Air of density 1.2 kg/m³ flows steadily through a horizontal Venturimeter whose inlet area is twice the throat area. The inlet pressure exceeds the throat pressure by 180 Pa. Treat the density as constant. If the throat speed is N m/s, find N.
Physics · Fluid Mechanics · equation of continuity and bornullie theorem
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Question

Air of density 1.2 kg/m³ flows steadily through a horizontal Venturimeter whose inlet area is twice the throat area. The inlet pressure exceeds the throat pressure by 180 Pa. Treat the density as constant. If the throat speed is N m/s, find N.

Physics · Fluid Mechanics · equation of continuity and bornullie theorem

G1 Physics · Accepted Answer

Let inlet speed be v₁. Continuity gives v₂ = 2v₁. Bernoulli gives 180 = ½×1.2×(v₂²−v₁²). Substitute v₂ = 2v₁: 180 = 0.6×3v₁² = 1.8v₁². Hence, v₁² = 100, so v₁ = 10 m/s. Therefore, v₂ = 20 m/s. Thus, N = 20.