Question

One method to determine the flow rate of a turbulently flowing stream is to inject a small, metered amount of some easily dispersed fluid and then to measure the concentration of this fluid in a sample of the mixed stream withdrawn a suitable distance downstream. In pharmaceutical plants, there are often many inert gas streams (i.e., streams that contain mostly nonreacting gases). In a particular plant, there is a process stream that is composed of 95mol% N2(inert) and 5 mol% O2. To determine the flow rate of this process stream, O2 is injected at a flow rate of 16.3 mol/hr. A downstream sample analyzes the O2 content at 10 mol%. You can assume that no reactions occur in the pipe and that the flows are operating at a steady-state.

a) How many balanced equations can you write? How many of these are linearly independent?

b) Calculate the flow rate of the process stream containing 95 mol% N2 and 5 mol% O2.

Answer 1

a)Since there are 2 components, we can write two indpenednet equatinos. We can also wirte overall balance equation.

So there are two equations andonly two are independent

b) Let F = flow rate of stream containing 95% nitrogen and 5% oxygen

Let F1= down stream flow rate

writing nitrogen balane gives

Nitrogen in nitrogen rich stream + nitrogen in oxygen stream= nitrogen in down stream

F*0.95= F1*0.9 ( since downstream contains 10 Mole% O2 and rest N2)

F= F1*0.9/0.95=F1*0.9473 (1)

Oxygen balnce gives

F*5/100+16.3= F1*0.1

F*0.05+16.3 =F1*0.1 (2)

F1*0.9473*0.05+16.4= F1*0.1

F1*(0.1-0.0474)= 16.4

F1= 16.4/0.0526=311.7 moles/hr

from (1), Eq.2 becomes