Consider a small control volume V with the surface dS with a normal vector \(\vec{n}\). This moves in a fluid flow in time Δt into another position at a velocity \(\vec{V}\) (V in the diagram). What is the change in volume of this small control volume ΔV?(a) \([(\vec{V}\Delta t).\vec{n}]\)(b) \([(\vec{V}\Delta t).\vec{n}]dS\)(c) \([(\vec{V}\Delta t)]dS\)(d) \([(\vec{V}).\vec{n}]dS\)I had been asked this question in a job interview.The query is from Governing Equations in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Consider a small control volume V with the surface dS with a normal ve

1.	Consider a small control volume V with the surface dS with a normal vector \(\vec{n}\). This moves in a fluid flow in time Δt into another position at a velocity \(\vec{V}\) (V in the diagram). What is the change in volume of this small control volume ΔV?(a) \([(\vec{V}\Delta t).\vec{n}]\)(b) \([(\vec{V}\Delta t).\vec{n}]dS\)(c) \([(\vec{V}\Delta t)]dS\)(d) \([(\vec{V}).\vec{n}]dS\)I had been asked this question in a job interview.The query is from Governing Equations in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics
Answer» The correct OPTION is (b) \([(\vec{V}\Delta t).\vec{n}]dS\) The explanation is: The CHANGE in CONTROL VOLUME can be calculated as the volume of a cylinder with altitude \((\vec{V}\Delta t).\vec{n}\) (product of velocity and time) and BASE area dS.

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