$$ All problems in this assignment are to be done using MATLAB.

$$ You will submit two script $(*.$m$)$ files and two function $(*.$m$)$ files, named appropriately and

each containing appropriate comments, containing the solutions to all problems.

a$.$ Script files should be named in the following format: HWxPx$.$m

b$.$ Function files must be named the same as the function.

$$ Only files with $*.$m extensions will be accepted.

$$ It is your responsibility to make sure that your script $(*.$m$)$ file works properly and is free from

errors by utilizing the resources at your disposal.

a$.$ DO NOT use the clear command in your code.

b$.$ All final answers, and ONLY final answers, should be output to the command window, i$.$e$.$

make sure you use the $$;$$ to suppress output of each line that does not need to be

displayed to the command window.HW$2$P$4(13$ points$)$

Ocean water can be approximated as an incompressible fluid for which the equation of state relates the

density to the salinity and the temperature. The equation of state can be written

$(S,T)={}_0[1+(T_0-T)+(S-S_0)]$

where $,T$ and $S$ are the density, temperature and salinity, respectively. The parameters $$ and $$ are

the thermal expansion coefficient and the haline contraction coefficient, respectively. The

thermodynamic state at Standard Temperature and Pressure $($STP$)$ and salinity from Gill ${1982}^{[1]}$ is

given by $({}_0,T_0,S_0).$ The values of parameters are given below

Furthermore, the pressure at a given depth is given by

$p=p_a+gh$

where $p_a=101325Pa$ is the atmospheric pressure, $g=9\mathrm{.}81m{s}^{-2}$ is the acceleration due to gravity

and $h$ is the depth below the surface in meters. The formulae for density and pressure are given in kg

$m^{-3}$ and Pa respectively. Convert the density to grams per $cc(1(g)c{c}^{-1}=1000(kg)m^{-3})$ and the pressure

to bar $({10}^5(Pa)=\frac{1}{b}ar).$ You are required to calculate the density and pressure for given salinity,

temperature and depth.

Write a function file $[,p]=$EoS$(S,T,h)$ which takes $S,T$ and $h$ as input arguments and returns $$

and $p$ as output arguments. The function should assign local values to all constants. Use$/$call the

function to return and determine the values of $$ and $p$ in the command window for all inputs of the

table above.

Use the first several lines of your script$/$functions to describe the problem you are solving in the

comments.