Air of density 1.2 kg/m³ flows steadily through a horizontal Venturimeter. The inlet cross-sectional area is twice the throat area. The pressure at the inlet exceeds the throat pressure by 180 Pa. Treat the air density as approximately constant over the meter. What is the air speed at the throat?
Options

Question

Air of density 1.2 kg/m³ flows steadily through a horizontal Venturimeter. The inlet cross-sectional area is twice the throat area. The pressure at the inlet exceeds the throat pressure by 180 Pa. Treat the air density as approximately constant over the meter. What is the air speed at the throat?

Options

G1 Physics · Accepted Answer

Let the inlet speed be v₁ and the throat speed be v₂. Continuity gives A₁v₁ = A₂v₂. Since A₁ = 2A₂, we get v₂ = 2v₁. For a horizontal Venturimeter, P₁−P₂ = ½ρ(v₂²−v₁²). Substitute P₁−P₂ = 180 Pa, ρ = 1.2 kg/m³, v₂ = 2v₁. Then, 180 = ½×1.2×(4v₁²−v₁²) = 1.8v₁². Therefore, v₁² = 100, so v₁ = 10 m/s. Hence, v₂ = 20 m/s. Correct option: C.