In steady, incompressible flow, Bernoulli's equation relates pressure, velocity, and height along a streamline. What does it imply about a faster-moving region?

In steady, incompressible flow, Bernoulli's equation relates pressure, velocity, and height along a streamline. What does it imply about a faster-moving region?

• A. Higher velocity means higher pressure along a streamline
• B. Higher velocity corresponds to lower pressure along a streamline
• C. Velocity has no effect on pressure
• D. Pressure is constant along a streamline

Answer: (B)

Bernoulli's principle says that along a streamline, the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume stays constant for steady, incompressible, non-viscous flow. If you look at a region where the fluid moves faster and the height is the same, the kinetic energy term 1/2 ρv^2 increases. To keep the total constant, the static pressure P must decrease. So a faster-moving region along a streamline corresponds to lower pressure. This is why constrictions in pipes (Venturi effect) speed up the flow and lower the pressure there. Keep in mind real fluids have viscosity and losses, but in the idealized situation this inverse relationship between speed and pressure along a streamline holds.

Bernoulli's principle says that along a streamline, the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume stays constant for steady, incompressible, non-viscous flow. If you look at a region where the fluid moves faster and the height is the same, the kinetic energy term 1/2 ρv^2 increases. To keep the total constant, the static pressure P must decrease. So a faster-moving region along a streamline corresponds to lower pressure.

This is why constrictions in pipes (Venturi effect) speed up the flow and lower the pressure there. Keep in mind real fluids have viscosity and losses, but in the idealized situation this inverse relationship between speed and pressure along a streamline holds.