Let \(\hat{u}\) be the specific internal energy of a system moving along with the flow with a velocity \(\vec{V}\). What is the time rate of change of the total energy of the system per unit mass?(a) \(\hat{u}+\frac{1}{2}\vec{V}.\vec{V}\)(b) \(\frac{D}{Dt}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)(c) \(\frac{\partial}{\partial t}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)(d) \(\frac{D}{Dt}(\hat{u}+\vec{V}.\vec{V})\)The question was asked during an internship interview.My query is from Energy Equation topic in portion Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Let \(\hat{u}\) be the specific internal energy of a system moving alo

1.	Let \(\hat{u}\) be the specific internal energy of a system moving along with the flow with a velocity \(\vec{V}\). What is the time rate of change of the total energy of the system per unit mass?(a) \(\hat{u}+\frac{1}{2}\vec{V}.\vec{V}\)(b) \(\frac{D}{Dt}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)(c) \(\frac{\partial}{\partial t}(\hat{u}+\frac{1}{2}\vec{V}.\vec{V})\)(d) \(\frac{D}{Dt}(\hat{u}+\vec{V}.\vec{V})\)The question was asked during an internship interview.My query is from Energy Equation topic in portion Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» RIGHT answer is (B) \(\frac{D}{Dt}(\HAT{u}+\frac{1}{2}\vec{V}.\vec{V})\) The best explanation: The total ENERGY of the system is \(E=\hat{u}+\frac{1}{2}\vec{V}.\vec{V}\) Take its substantial derivative as the model is not stationary. rate of change of total energy=\(\frac{DE}{Dt}=\frac{D}{Dt}(\hat{u}+\frac{1}{2} \vec{V}.\vec{V})\).

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