Which statement correctly defines dynamic pressure and its appearance in head loss expressions?

• A. Dynamic pressure q = ρ v^2/2; it appears as the velocity head term v^2/(2g) in energy equations and head loss expressions.
• B. Dynamic pressure q = ρ g h; it appears as a potential energy term.
• C. Dynamic pressure q = (P/β)^2; it appears in friction factor calculations.
• D. Dynamic pressure q = μ v / D; it appears in Reynolds number expressions.

Answer: (A)

Dynamic pressure represents the kinetic energy per unit volume of a moving fluid. It is defined as q = ρ v^2 / 2, which can be read as the energy per unit volume due to the fluid’s motion. In fluid-energy equations, this energy is expressed as the velocity head, v^2/(2g). That velocity head is exactly what appears in head loss expressions such as the Darcy–Weisbach form, where the frictional head loss Δh_f is written as f (L/D) times the velocity head, i.e., Δh_f = f (L/D) (v^2/(2g)). So dynamic pressure shows up as this velocity head term in the energy balance and in head loss calculations, linking the fluid’s motion to the energy losses along a pipe. The other options mix up different physical quantities: ρ g h represents potential energy per unit volume (static or hydrostatic pressure related to height), μ v / D is related to viscous effects, not dynamic pressure, and q = (P/β)^2 is not a standard dynamic-pressure expression.