Chapter 4, Problem 4.29P

Interpretation Introduction

(a)

Interpretation:

The flow-chart for the given process is to be drawn and labelled. The degree of freedom analysis is to be done on the given system. Also, the volume of water fed to the tank is to be calculated.

Concept introduction:

A flowchart is the complete representation of a process through boxes or other shapes which represents process units and arrows that represents the input and output of the process. The flowchart must be fully labelled to infer important data about the process involved.

Degree of freedom analysis is the procedure to analyze any missing information needed for material balance calculations. The procedure involves complete labelling of the flowchart representing the process and then determining number of unknown variables $\left(n_{\text{unknowns}}\right)$ and independent equations $\left(n_{\text{indep eqns}\text{.}}\right)$ from that flowchart.

Mathematically, degree of freedom $\left(n_{\text{df}}\right)$ is formulated as:

$n_{\text{df}}=n_{\text{unknowns}}-n_{\text{indep eqns}\text{.}}$ ......... (1)

In a system, a conserved quantity (total mass, mass of a particular species, energy or momentum) is balanced and can be written as:

$\text{input+generation-output-consumpumtion=accumulation}$

Here, ‘input’ is the stream which enters the system. ‘Generation’ is the term used for the quantity that is produced within the system. ‘Output’ is the stream which leaves the system. ‘Consumption’ is the term used for the quantity that is consumed within the system. ‘Accumulation’ is used for the quantity which is builds up within the system.

All the equations which are formed are then solved simultaneously to calculate the values of the unknown variables.

Density $\left(\rho \right)$ of a substance is expressed as:

$\rho =\frac{m}{V}$ ......... (2)

Here, $m$ is the mass of the substance and $V$ is the volume of the substance. Density can be expressed in several units. For convenience, here it is expressed in $\text{kg}/{\text{m}}^3$.

Specific gravity $\left(\text{SG}\right)$ is a relative term used to express the ratio of density of a substance and density of the reference substance. Since it is the ratio of same quantity that is density, thus, specific gravity is dimensionless.

Interpretation Introduction

(b)

Interpretation:

The relative strengths of the specific gravity of coal and slate is to be determined.

Concept introduction:

Specific gravity $\left(\text{SG}\right)$ is a relative term used to express the ratio of density of a substance and density of the reference substance. Since it is the ratio of same quantity that is density, thus, specific gravity is dimensionless.

In a mixture containing two or more components, a substance with low density floats on the surface while the one with high density sinks. The layers of the individual components are formed according to the relative densities of the components.

Interpretation Introduction

(c)

Interpretation:

The reason for the alterations in the separation process along with the corrective measures is to be stated. Also, the relative strength of the specific gravity of coal, water and suspension is to be commented.

Concept introduction:

Specific gravity $\left(\text{SG}\right)$ is a relative term used to express the ratio of density of a substance and density of the reference substance. Since it is the ratio of same quantity that is density, thus specific gravity is dimensionless.

In a mixture containing two or more components, a substance with low density floats on the surface while the one with high density sinks. The layers of the individual components are formed according to the relative densities of the components.