Home> Notes> Equations> Substantial Derivativeof scalar field θ- also known as Total derivative @WolframDDtt∂=+⋅∇∂VIn rectangular coordinates DuvwDttxyzθθθ∂∂∂∂++∂where Vis the fluid velocity field, uis the component of Vin the xdirection, vis the velocity component in the ydirection, and wis the velocity component in the zdirection. We encounter the substantial derivatives of the scalar fields of density in the Continuity Equation, and of enthalpy and temperature in the Energy Equation. Substantial Derivativeof velocity vector field appears in the Equation of Motion. DDtt∂⋅∇
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