If we have a perfect gas of mass density m kg/m 3 , and we assign a

If we have a perfect gas of mass density ρm kg/m³, and we assign a velocity U m/s to each differential element, then the mass flow rate is ρmU kg/(m² − s). Physical reasoning then leads to the continuity equation, ∇ · (ρmU) = −∂ρ_m/∂t.

(a) Explain in words the physical interpretation of this equation.

(b) Show that ∮_s ρ_m U· dS = −dM/dt, where M is the total mass of the gas within the constant closed surface S, and explain the physical significance of the equation.