Chapter 3, Problem 3.59P

Interpretation Introduction

(a)

Interpretation:

The height of mercury above the bottom of the manometer in the arm connected to the pipe is to be calculated.

Concept introduction:

The gauge pressure $\left(P_{\text{g}}\right)$ is the difference between the actual pressure $\left(P\right)$ and atmospheric pressure $\left(P_{\text{a}}\right)$. Since the gas manometer is not flowing, the manometer equation is expressed as,

$\begin{array}{c}{P}_{\text{g}}-P_{\text{m}}=0\\ P_{\text{g}}-{\rho }_{\text{m}}g\Delta h=0\left(\because P_{\text{m}}={\rho }_{\text{m}}g\Delta h\right)\\ \Delta h=\frac{P_{\text{g}}}{{\rho }_{\text{m}}g}\end{array}$

Interpretation Introduction

(b)

Interpretation:

The value of gas pressure, if the gas is flowing at the given mercury level is to be calculated.

Concept introduction:

The gauge pressure $\left(P_{\text{g}}\right)$ is the difference between the actual pressure $\left(P\right)$ and atmospheric pressure $\left(P_{\text{a}}\right)$. Since the gas is flowing, the manometer equation is expressed as,

$\begin{array}{c}{P}_{\text{g}}+{\rho }_{\text{m}}g{h}_1-{\rho }_{\text{m}}g\left[h-\left(H+h_1\right)\right]=0\\ P_{\text{g}}={\rho }_{\text{m}}g\left[h-\left(H+h_1\right)\right]-{\rho }_{\text{m}}g{h}_1\\ ={\rho }_{\text{m}}g\left[h-H-h_1-h_1\right]\\ P_{\text{g}}={\rho }_{\text{m}}g\left[h-H-2h_1\right]\end{array}$