Interaction between the rocket nozzle, plume, launch pad, flame trench and water deluge curtain. Plume color indicates heat flux level (blue = mild, red = extreme).
$$q = K\,\frac{F\,V_e}{r^{2}}\cos\theta, \qquad SPL = 10\log_{10}\!\frac{P_{\text{acoust}}}{4\pi r^{2}\,I_{0}}$$
Heat flux q (Bartz simplified) and pad SPL. F: total thrust, V_e: exit velocity, r: pad standoff distance, θ: tilt angle, K≈0.05 empirical constant, I_0 = 1×10⁻¹² W/m² reference intensity.
$$V_e = I_{\!sp}\cdot g_0, \qquad M_e = \frac{V_e}{\sqrt{\gamma R T_e}}$$
Specific impulse Isp times g_0 = 9.81 gives exit velocity V_e. With γ=1.2, R=287, T_e = 0.5·T_c the exit Mach number M_e is obtained.
$$Q_{\text{water}} = \dot{m}_{w}\,(c_{p}\Delta T + h_{fg})$$
Water deluge heat absorption capacity (c_p = 4186 J/kg·K, ΔT = 80 K, latent h_fg = 2.26 MJ/kg). Net load is pad heat flux minus this capacity.