Question

Substantial derivative is the same as ________ of differential calculus.

(a) Partial derivative

(b) Instantaneous derivative

(c) Total derivative

(d) Local derivative

The question was posed to me in final exam.

My question is taken from Governing Equations in portion Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Right option is (c) Total derivative

For explanation: Substantial derivative is the same as total derivative. However, total derivative is completely mathematical.

\(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y}+w \frac{\partial T}{\partial z}\)

\(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+u \frac{\partial T}{\partial x}+v \frac{\partial T}{\partial y}+w \frac{\partial T}{\partial z}\).