In a divergent duct, what happens to the velocity and pressure?

In a divergent duct, as the cross-sectional area increases, the flow characteristics are affected significantly. Specifically, the behavior of gases or fluids in such a duct is well understood from the principles of fluid dynamics.

In a divergent duct, the velocity of the flowing fluid decreases as it expands into a larger area. This might seem counterintuitive at first, as one might expect that an increase in cross-sectional area would allow for more room for the fluid to travel. However, due to the conservation of mass (continuity equation), as the area increases, the velocity must decrease to maintain the same mass flow rate, assuming the density remains fairly constant.

When the velocity decreases, the kinetic energy of the fluid also decreases, which leads to a rise in static pressure. This corresponds to Bernoulli's principle, which states that an increase in the static pressure occurs as the velocity of the fluid decreases in a flowing system.

This understanding aligns with the correct choice, where the pressure increases as the velocity decreases. Temperature is typically related to the changes occurring in pressure and velocity, but the primary focus here is on the relationship between velocity and pressure in a divergent duct, which critically demonstrates that as you expand the duct, the velocity decreases and pressure increases.