Spring $2023$

B$3[15$ Marks in Total$]$

Methane at $25$degC is compressed at a rate of $0\mathrm{.}0085k\frac{g}{s}$ from $100$kPa to $1500$kPa. A staged centrifugal compressor is to be used. Take $R=518\frac{J}{k}gK,$ and $=1\mathrm{.}31.$

$[$Note:

$H_{\text{a}\text{d}\text{i}\text{a}\text{b}\text{a}\text{t}\text{i}\text{c}}=NR{T}_1(\frac{}{-1})[(\frac{P_2}{P_1}{)}^{\frac{-1}{NN}}-1]$

where $H_{\text{a}\text{d}\text{i}\text{a}\text{b}\text{a}\text{t}\text{i}\text{c}}$ is the adiabatic head in $N\frac{m}{k}g,R$ is the gas constant for the fluid, $$ is the ratio of specific heats, $N$ the number of stages, and $P$ and $T$ refer to pressure and temperature respectively $]$

Determine how many stages would be required

$[4$ Marks$]$