The blue bar shows the current DO (mg/L). A paddle-wheel aerator on the surface drives bubbles; fish colour shifts green→orange→red as the O₂ deficit grows.
$$V_{\text{pond}} = A\cdot d, \qquad M_{\text{fish}} = V_{\text{pond}}\cdot \rho_{\text{stock}}$$
Pond volume V and total fish biomass M. A: pond area (m²), d: depth (m), ρ_stock: stocking density (kg/m³).
$$\text{DO}_{\text{sat}} = 14.652 - 0.41\,T + 0.008\,T^{2}$$
Saturation DO of fresh water versus temperature T (°C) in mg/L. Solubility drops as temperature rises.
$$\dot m_{\text{O}_2}^{\,\text{supply}} = \text{SOTR}\cdot P_{\text{kW}}\cdot 24\cdot \frac{\text{DO}_{\text{sat}}-\text{DO}_{\text{design}}}{\text{DO}_{\text{sat}}}$$
Actual aerator supply (kgO₂/day). SOTR: standard oxygen transfer rate (kgO₂/kWh), P: power (kW). The closer DO is to saturation, the smaller the driving force.
$$P_{\text{req}} = \frac{\dot m_{\text{O}_2}^{\,\text{demand}}}{\text{SOTR}\cdot 24\cdot (\text{DO}_{\text{sat}}-\text{DO}_{\text{design}})/\text{DO}_{\text{sat}}}$$
Aerator kW required to hold the target DO. If demand exceeds supply, the fish go hypoxic.