a) \(\vec{V}.\nabla T\) b) \(\frac{DT}{Dt}\) c) ∇T d) \(\frac{\partial T}{\partial t}\) Answer: a Explanation: \(\vec{V}.\nabla T\) (dot ...
View QuestionSubstantial derivative = _____ + _____
Substantial derivative = _____ + _____ a) Partial derivative, convective derivative b) Local derivative, convective derivative c) Local derivative, ...
View QuestionA flow property has substantial derivative. What does this imply?
a) The property is a function of both time and space b) The property is a ...
View QuestionWhich of these statements best defines local derivative?
a) Time rate of change b) Spatial rate of change c) Time rate of change of a moving point
View QuestionThe simplified form of substantial derivative can be given by __________
a) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\nabla T\) b) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\nabla .T\) c) \(\frac{DT}{Dt}=\frac{\partial T}{\partial t}+\vec{V}.\nabla T\) d) \(\frac{DT}{Dt}=\frac{\partial ...
View QuestionSubstantial derivative applies to ____________?
a) Both stationary and moving models b) Only moving models c) Only stationary models d) Neither stationary nor moving models
View QuestionExpand the substantial derivative Dρ/Dt.
a) \(\frac{D\rho}{Dt}=\frac{d\rho}{dt}+u \frac{d\rho}{dx}+v\frac{d\rho}{dy}+w\frac{d\rho}{dz}\) b) \(\frac{D\rho}{Dt}=\frac{\partial\rho}{\partial t}+u \frac{d\rho}{dy}+v\frac{d\rho}{dz}+w\frac{d\rho}{dx}\) c) \(\frac{D\rho}{Dt}=\frac{\partial\rho}{\partial t}+u \frac{d\rho}{dy}+v\frac{d\rho}{dz}+w\frac{d\rho}{dx}\) d) \(\frac{D\rho}{Dt}=\frac{\partial \rho}{\partial t}+u\frac{\partial \rho}{\partial x}+v\frac{\partial ...
View QuestionHow is the substantial derivative of velocity vector denoted?
a) \(\frac{D\vec{V}}{Dt}\) b) \(\frac{d\vec{V}}{dt}\) c) \(\frac{\partial \vec{V}}{\partial t}\) d) \(\frac{D\vec{V}}{Dx}\) Answer: a Explanation: ...
View QuestionLet, t → Instantaneous time v → Velocity in x-direction x → Instantaneous position x → Initial position
Let, t → Instantaneous time \( \vec{v} \) → Velocity in x-direction \( \vec{x} \) → Instantaneous position
View QuestionIn Lagrangian approach, the flow parcels follow __________
a) pressure field b) velocity field c) temperature field d) density field Answer: b Explanation: Velocity field ...
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