A fluid stream emerges from a chemical plant with a constant mass flow rate w and discharges
Question:
A fluid stream emerges from a chemical plant with a constant mass flow rate w and discharges into a river (see Figure a). It contains a waste material A at mass fraction wA0, which is unstable and decomposes at a rate proportional to its concentration according to the expression RA = k1?A (a first- order reaction).
To reduce pollution it is decided to allow the effluent stream to pass through a holding tank of volumeV, before discharging into the river (see Figure b). The tank is equipped with an efficient stirrer that keeps the fluid in the tank at very nearly uniform composition. At time t = 0 the fluid begins to flow into the empty tank. No liquid flows out until the tank has been filled up to the volume V.
Develop an expression for the concentration of the fluid in the tank as a function of time, both during the tank-filling process and after the tank has been completely filled. What is the mass fraction of A when the tank is full? What is the steady-state mass fraction of the pollutant for the second case (b) when time goes to infinity?
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell