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Consider a model of finite control volume (volume V and surface area S) fixed in space with elemental volume dV, vector elemental surface area dS⃗ , density ρ and flow velocity V⃗ . What is the net mass flow rate out of the surface area?

(a) ∬VρV⃗ .dV

(b) ρV⃗ .dS⃗

(c) ∭VρV⃗ .dS⃗

(d) ∬VρV⃗ .dS⃗

I got this question in examination.

This question is from Continuity Equation topic in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

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The correct answer is (d) ∬VρV⃗ .dS⃗

The explanation is: In general,

mass flow rate=density × velocity × area

For this case,

elemental mass flow rate = ρV⃗ .dS⃗

total mass flow rate=∬VρV⃗ .dS⃗

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