Chapter 4, Problem 1P

To determine

To write:

A MATLAB program in a script file that calculates heat index $HI$.

Answer to Problem 1P

Solution:

The calculated value of heat index is $122$.

Explanation of Solution

Given $T=90°\text{F}$

$R=90\%$

The equation used by national weather service for the calculation of heat index $HI$

is given by,

$\begin{array}{c}HI=-42.379+2.04901523T+10.14333127R-6.83783\times {10}^{-3}{T}^2\\ -5.481717\times {10}^{-2}{R}^2+1.22874\times {10}^{-3}{T}^{2}R+8.5282\times {10}^{-4}T{R}^2-1.99\times {10}^{-6}{T}^2{R}^2\end{array}$

Where,

► $T$ is the temperature in degrees $\text{F}$.

► $R$ is the relative humidity in integer percentage.

Substitute the given values of temperature and relative humidity in the above equation.

$\begin{array}{c}HI=-42.379+2.04901523\times 90+10.14333127\times 0.9-6.83783\times {10}^{-3}\times {90}^2\\ -5.481717\times {10}^{-2}\times {\left(0.9\right)}^2+1.22874\times {10}^{-3}\times {90}^2\times 0.9\\ +8.5282\times {10}^{-4}\times 90\times {\left(0.9\right)}^2-1.99\times {10}^{-6}\times {90}^2\times {\left(0.9\right)}^2\\ =122\end{array}$

Write the MATLAB program that calculates the heat index $HI$ using the given values of temperature and relative humidity.

MATLAB Code:

%MATLAB Program that calculates the heat index by using the given values of temperature and relative humidity.

Temp = input('Enter the temperature in deg F: ');%Temperature

RH = input('enter the relative humidity in percentage: ');%Relative humidity

HI = -42.379+2.04901523*Temp+10.14333127*RH-0.22475541*RH*Temp-6.83783*10^-3*Temp^2-5.481717*10^-2*RH^2+1.22874*10^-3*Temp^2*RH+8.5282*10^-4*Temp*RH^2-1.99*10^-6*Temp^2*RH^2;

fprintf('\nThe Heat Index Temperature is: %.0f\n',HI)

Save the MATLAB Script with the name, Chapter4_29864_4_1P.m in the current folder.

Execute the script by typing the script name at the command window to get the code that gives the relative heat index by using the given values of temperature and relative humidity.

Result:

Conclusion:

Therefore, the calculated value of heat index is $122$.