In a divergent flow, what happens to velocity and pressure?

In a divergent flow, what happens to velocity and pressure?

• A. Velocity decreases and pressure increases
• B. Velocity increases and pressure decreases
• C. Velocity increases and pressure increases
• D. Velocity constant and pressure decreases

Answer: (A)

In a divergent flow, the cross-sectional area increases downstream, so the flow slows down as it expands. For steady, incompressible flow, mass flow rate is constant, so velocity must decrease as the area grows. Then, by Bernoulli’s principle, along a streamline the sum p + ½ρv² remains constant (ignoring losses). If velocity decreases, the dynamic pressure term ½ρv² decreases, so the static pressure p must rise to keep the total the same. Therefore, velocity decreases and pressure increases in a divergent flow. This deceleration and pressure recovery is exactly what a diffuser or engine intake uses to prepare air for the compressor.

In a divergent flow, the cross-sectional area increases downstream, so the flow slows down as it expands. For steady, incompressible flow, mass flow rate is constant, so velocity must decrease as the area grows. Then, by Bernoulli’s principle, along a streamline the sum p + ½ρv² remains constant (ignoring losses). If velocity decreases, the dynamic pressure term ½ρv² decreases, so the static pressure p must rise to keep the total the same. Therefore, velocity decreases and pressure increases in a divergent flow. This deceleration and pressure recovery is exactly what a diffuser or engine intake uses to prepare air for the compressor.