Sec. 4.3 / System-to-Control-Volume Transformation 133 dot product nV accounts f

Question

Sec. 4.3 / System-to-Control-Volume Transformation 133 dot product nV accounts for the appropriate component of V that produces a flux through the area. The net property flux out of the control surface is then obtained by integrat- ing over the entire control surface: net flux of property-l n.V dA (4.3.2) If the net flux is positive, the flux out is larger than the flux in Let us return now to the derivative DNsyD. The definition of a derivative from calculus allows us to write DN sys -= lim (4.3.3) The system is shown in Fig. 4.4 at times 1 and t + . Assume that the system occu- pies the full control volume at time t; if we were considering a device, such as a pump, the particles of the system would just fill the device at time t. Since the device, the control volume shown in Fig. 4.4, is assumed to be fixed in space, the system will move through the device. Equation 4.3.3 can then be written KEY CONCEPT The system occupies the full control volume at timet DN sys lim (4.3.4a) = lim +lim (4.3.4b)

Explanation / Answer

Basically when we Derive reynold's transport theorem we have to calculate the change in property(N) of system with respect to time,We have to use Total derivative because if we assume partial derivative we are fixing all other properties as constants which is not true in Actual scenario.

Suppose for example if we take velocity as property N , We know partial derivative of velocity with repect to time gives only Local accelration but if we use total derivative we end up with both Local and Convective accelration. Hence the difference.

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