In the mechanical energy balance equation shown, what does the symbol rho represent?

• A. Temperature
• B. Pressure
• C. Fluid density
• D. Velocity

Answer: (C)

rho is the density of the fluid—the mass per unit volume. This property matters in a mechanical energy balance because energy terms often come as energy per unit mass, so you convert volumes moving through a boundary into mass flow using density. For example, a fluid with density rho flowing through a cross-section with area A at speed v has a volumetric flow rate Q = A v, and a mass flow rate of rho times Q. If water (rho ≈ 1000 kg/m^3) flows with A = 0.01 m^2 and v = 2 m/s, the volumetric flow is 0.02 m^3/s and the mass flow is 20 kg/s. Temperature and pressure are described by T and p, while velocity is v; rho specifically denotes density.