The Bernoulli equation applies to which type of flow along a streamline?

• A. Ideal, incompressible, non-viscous flow along a streamline
• B. Highly viscous flow with turbulence
• C. Compressible flow with shocks
• D. Laminar flow with energy losses

Answer: (A)

Bernoulli's equation expresses conservation of mechanical energy per unit weight along a streamline, which holds when viscous losses are negligible and density stays essentially constant. In that ideal, inviscid, incompressible flow, and with steady conditions along a single streamline, the sum of pressure head, velocity head, and elevation head remains the same. If there are significant viscous effects, turbulence, or density changes (as in compressible flow with shocks) or energy losses, the simple Bernoulli relation no longer applies. Therefore, the equation is best described by ideal, incompressible, non-viscous flow along a streamline.