Test Academy | Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure. The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows: 𝑃 1 = 100 kPa, 𝜌 1 = 1.2 kg/m 3 , 𝑢1= 400 m/s The duct cross-sectional area at Location 2 is given by A 2 = 2A 1 , where A 1 denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity 𝑢 2 and pressure 𝑃 2 at Location 2 is TRUE? 𝑢2 < 𝑢1 , 𝑃2 < 𝑃1, 𝑢2 < 𝑢1 , 𝑃2 > 𝑃1, 𝑢2 > 𝑢1 , 𝑃2

Question

Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure.

The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:

𝑃₁ = 100 kPa, 𝜌₁ = 1.2 kg/m³ , 𝑢1= 400 m/s

The duct cross-sectional area at Location 2 is given by A₂ = 2A₁, where A₁ denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity 𝑢₂and pressure 𝑃₂ at Location 2 is TRUE?

Options :

𝑢₂ < 𝑢₁ , 𝑃₂ < 𝑃₁
𝑢₂ < 𝑢₁ , 𝑃₂ > 𝑃₁
𝑢₂ > 𝑢_{1 ,} 𝑃₂ < 𝑃₁
𝑢₂ > 𝑢₁, 𝑃₂ > P₁

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