## Info

and time t, [X] has the dimension of M/L . The factors <p has the dimensions of (M/M)(M/L3) = M/L3; thus, <p corresponds to [X]. In the theorem <p is a point value, while [X] is an average value inside the reactor. [X] then correspond to the value of <p that is averaged. Therefore, d\M<pdV = diM(<pp)aVedV = dJMftX-] dV = d[X] \MdV = d[X]V (90) dt dt dt dt dt

The volume of the reactor is constant, so V may be taken out of the differential:

dt dt dt

Now, let us determine the expression for fA<pv • n dA. This is the convective derivative and it only applies to the boundary. In the case of the reactor, there are two portions of this boundary: the inlet boundary and the outlet boundary. Let the inflow to the reactor be Q; this will also be the outflow. Note that Q comes from v • n dA and, because the velocity vector and the unit vector are in opposite directions at the inlet, Q will be negative at the inlet. At the outlet, because the two vectors are in the same directions, Q will be positive. The concentration at the outlet will be the same as the concentration inside the tank, which is [X]. Thus, letting the concentration at the inflow be [Xo]

<pv • n dA = (- Q)[Xo] (at the inlet) + (+ Q)[X] (at the outlet)

Was this article helpful?

Thousands Have Used Chemicals To Improve Their Medical Condition. This Book Is one Of The Most Valuable Resources In The World When It Comes To Chemicals. Not All Chemicals Are Harmful For Your Body – Find Out Those That Helps To Maintain Your Health.

Get My Free Ebook

## Post a comment