Chapter 10, Problem 10.1P

Hurricane Irma (2017) had a central pressure of 914 mbar, the lowest recorded for an Atlantic hurricane. Calculate the pressure in units of mm Hg.

Interpretation Introduction

Interpretation:

The pressure of $914\text{ mbar}$ is to be expressed in $\text{mm Hg}$.

Concept introduction:

Atmospheric pressure is defined as average pressure that is exerted at the sea level. This is equivalent to exactly equivalent to $\text{760 mm Hg}$ column.

The relation between $\text{Pa}$ and $\text{atm}$ is as follows:

$\text{1 atm}=101325\text{ Pa}$

The conversion factor to convert $\text{atm}$ to $\text{mm Hg}$ is as follows:

$1\text{ atm}=\text{760 mm Hg}$

The conversion factor to convert $\text{mbar}$ to $\text{bar}$ is as follows:

$1\text{ mbar}={10}^{-3}\text{ bar}$

Answer to Problem 10.1P

The pressure is $685.55\text{ mm Hg}$.

Explanation of Solution

Given information:

Central pressure is given as $914\text{ mbar}$.

The conversion factor to convert $\text{mbar}$ to $\text{bar}$ is as follows:

$1\text{ mbar}={10}^{-3}\text{ bar}$

Therefore $914\text{ mbar}$ is converted to $\text{atm}$ as follows:

$\begin{array}{c}\text{Pressure}=\left(914\text{ mbar}\right)\left(\frac{{10}^{-3}\text{ bar}}{1\text{ mbar}}\right)\\ =914\times {10}^{-3}\text{ bar}\end{array}$

The conversion factor to convert $\text{bar}$ to $\text{atm}$ is as follows:

$1\text{ bar}=0.986923\text{ atm}$

Therefore $914\times {10}^{-3}\text{ bar}$ is converted to $\text{atm}$ as follows:

$\begin{array}{c}\text{Pressure}=\left(914\times {10}^{-3}\text{ bar}\right)\left(\frac{0.986923\text{ atm}}{1\text{ bar}}\right)\\ =902.04\times {10}^{-3}\text{ atm}\end{array}$

The conversion factor for conversion of $\text{atm}$ to $\text{mm Hg}$ is as follows:

$1\text{ atm}=\text{760 mm Hg}$

Therefore $902.04\times {10}^{-3}\text{ atm}$ is converted to $\text{mm Hg}$ as follows:

$\begin{array}{c}\text{Pressure}=\left(902.04\times {10}^{-3}\text{ atm}\right)\left(\frac{\text{760 mm Hg}}{1\text{ atm}}\right)\\ =685.55\text{ mm Hg}\end{array}$