Chapter 10, Problem 10.6P

Interpretation Introduction

(a)

Interpretation:

The time taken for benzene to reach the desired point should be calculated.

Concept introduction:

The relation between mass, volume and density is as follows:

$m=V\rho$

In terms of mass rate, it is written as follows:

$\dot{m}=\frac{V}{t}\rho$

Rearranging,

$t=\frac{V}{\dot{m}}\rho$

The volume can be calculated using the following formula:

$V=\frac{\pi r^{2}L}{2}$

Interpretation Introduction

(b)

Interpretation:

Suppose the flowrate into the tank is unknown. A sight gauge on the tank allows determination of the liquid level, and instructions are to stop the flow when the tank contains $3000kg$. The value of $h$ at which this needs to be done should be calculated.

Concept introduction:

The relation between mass, volume and density is as follows:

$m=V\rho$

In terms of mass rate, it is written as follows:

$\dot{m}=\frac{V}{t}\rho$

Rearranging,

$t=\frac{V}{\dot{m}}\rho$

The volume can be calculated using the following formula:

$V=\frac{\pi r^{2}L}{2}$

Interpretation Introduction

(c)

Interpretation:

The flowrate into the tank should be estimated when h has an approximate value of 50 cm, and (dh/dt) =1cm/min.

Concept introduction:

Mass balance equation is as follows:

$\text{Accumulation= Input – Output + Generation – Consumption}$

Chain rule is as follows:

$\frac{dV}{dt}=\frac{dV}{dh}\times \frac{dh}{dt}$

Interpretation Introduction

(d)

Interpretation:

To explain the reason for the drum to provide better performance than feeding a signal proportional to the flowrate directly to the control valve that would cause the valve to close if the flowrate drops below the set point and to open if the flowrates rises above that point.