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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 d\(\vec{S}\), density ρ and flow velocity \(\vec{V}\). What is the net mass flow rate out of the surface area?(a) \(\iint_V\rho \vec{V}.dV\)(b) \(\rho \vec{V}.d \vec{S}\)(c) \(\iiint_V\rho \vec{V}.d\vec{S}\)(d) \(\iint_V\rho \vec{V}.d\vec{S}\)I got this question in examination.This question is from Continuity Equation topic in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer»

The correct ANSWER is (d) \(\iint_V\rho \vec{V}.d\vec{S}\)

The explanation is: In general,

MASS FLOW rate=density × VELOCITY × area

For this CASE,

elemental mass flow rate = \(\rho \vec{V}.d \vec{S}\)

total mass flow rate=\(\iint_V\rho \vec{V}.d\vec{S}\)



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