$$\text { For a fixed control volume, the reason why } \frac { d } { d t } \int _ { \text {c.. } } \rho \eta d V = \int _ { \text {c. } . } \frac { \partial } { \partial t } ( \rho \eta ) d V \text { is: }$$
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 ρη is independent of position

Question

Quizplus · Accepted Answer

$\text { The limits of integration are independent of time}$
$\text {Apply the Leibniz rule of differentiating an integral. If the two limits depend on time}$ $\text {(this would require the control volume $V$ to bechanging with time and not be}$$\text { fixed), there would be two additional terms, involving the time derivative of the}$ $\text {limits, added to the equation in the problem statement.}$

A) the Integrand Is Independent of Time B) the Limits

A) the Integrand Is Independent of Time
B) the Limits