A gas flows steadily through a pipe. At section 1, the cross-sectional area is twice that at section 2. The speed at section 2 is three times the speed at section 1. If the gas density at section 1 is ρ, what is the gas density at section 2?
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Question

A gas flows steadily through a pipe. At section 1, the cross-sectional area is twice that at section 2. The speed at section 2 is three times the speed at section 1. If the gas density at section 1 is ρ, what is the gas density at section 2?

Options

G1 Physics · Accepted Answer

For a compressible fluid, continuity must be applied to mass flow rate: ρ₁A₁v₁ = ρ₂A₂v₂. Given, A₁ = 2A₂, v₂ = 3v₁, ρ₁ = ρ. Therefore, ρ(2A₂)v₁ = ρ₂A₂(3v₁). Cancel A₂ and v₁: 2ρ = 3ρ₂. Hence, ρ₂ = 2ρ/3. Correct option: B.