Chapter 10, Problem 10.14P

Interpretation Introduction

(a)

Interpretation:

The total mass balance on the tank needs to be determined and it is to be proved that the total mass of the liquid in the tank remains the same.

Concept introduction:

Assume tank is perfectly mixed

Mass balance over tank =ṁ ${}_{in}$ − ṁ ${}_{out}$

= (volumetric inlet feed rate x Density of solution) -

(volumetric outlet feed rate x Density of solution)

Interpretation Introduction

(b)

INTERPRETATION:

The balance on sodium nitrate needs to be determined and converted into equation for $dx/dt$ by providing initial condition.

Concept introduction:

Sodium Nitrate is denoted by NaNO_3.

By using derivation equation we will calculate the mass of fraction of NaNO_3.

So, Considered, x(t,ṁ) equal to mass of fraction of NaNO_3.

Interpretation Introduction

(c)

Interpretation:

The shapes of the plots gives mass rates needs to be sketched on a single graph of x versus t.

Concept introduction:

The graph will be first drawn for x vs t.

For x vs t graph

$\begin{array}{l}dx/x=m/V\rho dt\hfill \\ -lnx=m/V\rho \times \rho \times t+C\hfill \end{array}$

Interpretation Introduction

(d)

Interpretation:

The expression for $x\left(t,\stackrel{.}{m}\right)$ needs to be obtained and the plots of x versus t for given mass rates needs to be generated on a single graph.

Concept introduction:

The graph will be first drawn for x vs t.

For x vs t graph

$\begin{array}{l}dx/x=m/V\rho dt\hfill \\ -lnx=m/V\rho \times \rho \times t+C\hfill \end{array}$

Interpretation Introduction

(e)

Interpretation:

The time taken to flush out 90%, 99% and 99.9% of the sodium nitrate needs to be calculated.

Concept introduction:

The following equation will be taken to find the equation for time calculation:

$\ln \frac{x}{0.45}=-\frac{m}{200}t$

The derivation will produce:

$t=-2\ln (x_f/0.45)$

Interpretation Introduction

(f)

Interpretation:

The shapes of the plots of x versus t expected with the impeller on and off that shows the difference between the two curves at small and large t values needs to be sketched on the same chart.

CONCEPT INTRODUCTION:

The graph will be first drawn for x vs t.

For x vs t graph

$\begin{array}{l}dx/x=m/V\rho dt\hfill \\ -lnx=m/V\rho \times \rho \times t+C\hfill \end{array}$