For a fixed control volume, the reason why the equation below is:
(A) The integrand is independent of time
(B) The limits of integration are independent of time
(C) The flow is a steady flow
(D) The quantity ?? is independent of position
(B) The limits of integration are independent of time
Apply the Leibniz rule of differentiating an integral. If the two limits depend on time (this would require the control volume V to be changing with time and not be fixed), there would be two additional terms, involving the time derivative of the limits, added to the equation in the problem statement.
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