What is the dynamic pressure equation?

• A. P = F/A
• B. q = pV^2
• C. q = 1/2pV^2
• D. q = pV

Answer: (C)

Dynamic pressure is the pressure that comes from the motion of a fluid, effectively the kinetic energy per unit volume. It is given by q = 1/2 ρ V^2, where ρ is the fluid density; if your course uses p for density, this can be written as q = 1/2 p V^2. The 1/2 factor arises from the kinetic energy formula (1/2 m v^2) when you express energy per unit volume. Because it uses density and velocity squared, this expression has the units of pressure (Pa). This is different from static pressure, which is simply force per area (F/A). The other forms either omit the essential 1/2 or multiply density by velocity (without squaring), which do not yield pressure units. Dynamic pressure also features in Bernoulli’s principle as the portion of total pressure due to fluid motion.