Chapter 2, Problem 2.16P

Interpretation Introduction

(a)

Interpretation:

To show: The given equation gives reasonable results for h=0, h=r and h=2r

Concept introduction:

The mathematical expression for the volume of benzene in the drum is given by:

$V=L\left[r^2{\cos }^{-1}\left(\frac{r-h}{r}\right)-(r-h)\sqrt{r^2-{(r-h)}^2}\right]$

Where,

$V$ = Volume of benzene $L$ =Length of the drum $r$ =Radius of the drum $h$ =Level of the benzene in the drum

Interpretation Introduction

(b)

Interpretation:

The mass of the benzene in the tank for the given case.

Concept introduction:

The expression for the volume of benzene in the drum is given as,

   $V=L\left[r^2{\cos }^{-1}\left(\frac{r-h}{r}\right)-(r-h)\sqrt{r^2-{(r-h)}^2}\right]$

Where,

$V$ = Volume of benzene $L$ = Length of the drum $r$ = Radius of the drum $h$ = Level of the benzene in the drum

In addition, Density is defined as,

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

Where,

$\text{ρ=Density}\text{m=Mass}$

V = volume

Interpretation Introduction

(c)

Interpretation:

A relationship between the mass of benzene and the liquid height of benzene in the tank by plotting graph between mass of benzene and level of benzene.

Concept introduction:

On combining the density formula and expression for the volume of benzene in the drum we get:

$\begin{array}{l}m=\rho \times V\\ =\rho \times L\left[r^2{\cos }^{-1}\left(\frac{r-h}{r}\right)-(r-h)\sqrt{r^2-{(r-h)}^2}\right]\end{array}$