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# A nitric acid solution flows at a constant rate of 6 L/min

ISBN: 9780321747730 43

## Solution for problem 3E Chapter 3.2

Fundamentals of Differential Equations | 8th Edition

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Problem 3E

Problem

A nitric acid solution flows at a constant rate of 6 L/min into a large tank that initially held 200 L of a 0.5% nitric acid solution. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 8 L/min. If the solution entering the tank is 20% nitric acid, determine the volume of nitric acid in the tank after t min. When will the percentage of nitric acid in the tank reach 10%?

Step-by-Step Solution:

Step 1:

In this problem, we have to determine the volume of the nitric acid in the tank after t second when percentage of the nitric acid in the tank reach 10%.

Step 2:

This problem related to the compartmental analysis.Therefore, the mathematical concept for the process can be use

=input rate- output rate

The given value for this problem  we will consider

V(t) be the volume of the solution(water and nitric acid)

t- time in minutes

x(t) be the volume of the nitric acid in the solution after t minutes

As we know V=200L

The volume V at any time t can be given as

v(t)=200-8t-6t

Then the concentration of the nitric acid c(t) is

c(t)==

We can write

=I(t)-O(t)

Where I(t) is the input rate of the nitric acid

And O(t) is the output rate of the nitric acid

Now calculate the input rate

In the given problem the input flow rate is 6L/min and 20% nitric acid

So we can write the input rate =rate of the solution x concentration

I(t)=.= Ltr/min

Similarly we will calculate for the output rate

O(t)=.= Ltr/min=0.08 x(t)Ltr/min

The equation

=I(t)-O(t)

=-

+=

Step 4 of 5

Step 5 of 5

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