Let,V → Control VolumeB → Flow propertyb → Intensive value of B in any small element of the fluidρ → Density of the flowt → Instantaneous timeWhich of these terms represent the ‘instantaneous total change of the flow property within the control volume’ after Leibniz rule is applied?

\(\rho \int_v \frac{\partial b}{\partial T} dV \)

\( \frac{d}{dt}(\int_vb \rho dV)\)

\( \int_v \frac{\partial}{\partial T}(b \rho)dV\)

\(\rho \int_v \frac{\partial b}{\partial T} dV \)

\(\rho \int_v \frac{\partial \rho}{\partial b} dV\)

Let,V → Control VolumeB → Flow propertyb → Intensive value of

1.	Let,V → Control VolumeB → Flow propertyb → Intensive value of B in any small element of the fluidρ → Density of the flowt → Instantaneous timeWhich of these terms represent the ‘instantaneous total change of the flow property within the control volume’ after Leibniz rule is applied?
A.	\( \frac{d}{dt}(\int_vb \rho dV)\)
B.	\( \int_v \frac{\partial}{\partial T}(b \rho)dV\)
C.	\(\rho \int_v \frac{\partial b}{\partial T} dV \)
D.	\(\rho \int_v \frac{\partial \rho}{\partial b} dV\)
Answer» C. \(\rho \int_v \frac{\partial b}{\partial T} dV \)

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Let,V → Control VolumeB → Flow propertyb → Intensive value of B in any small element of the fluidρ → Density of the flowt → Instantaneous timeWhich of these terms represent the ‘instantaneous total change of the flow property within the control volume’ after Leibniz rule is applied?

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