Which statement best describes the behavior of air in a divergent duct at subsonic speeds?

• A. Constant density, pressure rises, velocity falls
• B. Density increases with velocity increases
• C. Density decreases with pressure increase
• D. Pressure falls with velocity increase

Answer: (A)

In a subsonic flow through a divergent duct, the cross-sectional area increases along the path, so the velocity must decrease to conserve mass (continuity: A·v = constant). With the velocity dropping, the kinetic energy term in Bernoulli’s principle reduces, and for air at subsonic speeds the density changes are minimal, so the density can be treated as essentially constant. This means the static pressure must rise as velocity falls to keep the energy balance along the streamline. So the description of constant density with pressure rising and velocity falling aligns with how subsonic flow behaves in a divergent duct.

Why this fits better than the others: if velocity were to increase in such a duct, Bernoulli would indicate a pressure drop, which isn’t the case here. Density would not meaningfully rise with velocity in this subsonic, nearly incompressible scenario, and it wouldn’t decrease in response to an increasing pressure in the same context.