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UPRVUNL JE ME 2016 Official Paper Shift 1

Option 4 : Efflux rate of mass through the control surfaces is zero

RRB JE ME 2019 CBT 2 Full Mock Test

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__Explanation:__

The law of conservation of mass states that mass may neither created nor destroyed. With respect to a control volume, the law of conservation of mass may be simply stated as:

\(\left\{ {\begin{array}{*{20}{c}} {Rate\;of\;mass}\\ {efflux\;from}\\ {control\;volume} \end{array}} \right\} - \left\{ {\begin{array}{*{20}{c}} {Rate\;of\;mass}\\ {flow\;into}\\ {control\;volume} \end{array}} \right\} + \left\{ {\begin{array}{*{20}{c}} {Rate\;of\;accumulation}\\ {of\;mass\;within}\\ {control\;volume} \end{array}} \right\} = 0\)

The net outward flow of mass across the control surface or the net mass efflux from the control volume:

\(\mathop \smallint \limits_{CS}^{} \rho \vec V.d\vec A\)

The rate of accumulation of mass within the control volume:

\(\frac{\partial }{{\partial t}}\mathop \smallint \limits_{CV}^{} \rho dV\)

The integral expression for the mass balance over a general control volume:

\(\mathop \smallint \limits_{CS}^{} \rho \vec V.d\vec A + \frac{\partial }{{\partial t}}\mathop \smallint \limits_{CV}^{} \rho dV = 0\)

For Steady-state flow:

\(\mathop \smallint \limits_{CS}^{} \rho \vec V.d\vec A = 0\)

∴ The continuity for a steady flow that efflux rate of mass through the control surfaces is zero.