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The fluctuation speed $q$ and the integral scale of turbulence $L_u$ give a turnover time $L_u/q$. Dividing the velocity-variance scale $q^2$ by that time gives a turbulent kinetic energy dissipation rate proportional to $q^3/L_u$. Likewise mass density variance $\overline{{\rho }^{\prime 2}}$ removed over scalar mixing time $L_{\rho }/q$ gives the density-variance dissipation rate proportional to $\overline{{\rho }^{\prime 2}}q/L_{\rho }$. Absorbing dimensionless proportionality coefficients into the specified length scales givesThese are integral-scale closure estimates, not exact consequences of dimensional analysis alone. In particular $q^2=2k$ for the turbulent-energy convention in Question 3. The normalization of $\chi$ is the one fixed by the printed scalar balance; if the budget is written for the full variance rather than one half of it, both production and dissipation terms acquire a factor two.