Problem $9\mathrm{.}3\mathrm{.}22.$ Steam survey: In a plant where the value of energy is $$4/$GJ$,$ a survey of a steam system identified a $100$ m long bare $20$ mm diameter steam line and $50$ m of bare $10$ mm diameter steam line both operating at $10$ bar $($T $=180\backslash$deg C$).$ An additional $150$ m of bare $50$ mm diameter steam line operating at $5$ bar $($T $=151\backslash$deg C$)$ was found. Fibreglass $($k$=0\mathrm{.}03$ W$/$mK$)$ is available at a market price of $$20/$m$2$ including installation. The ambient temperature is $25\backslash$deg C and the heat transfer coefficient is h$=10$ W$/$m$2$K$\mathrm{.}1.$ Calculate $ savings resulting from the application of insulation$2.$ Find the thickness of insulation that reduces energy loss by $90\%3.$ Find the economic thickness of insulation of the $20$ mm steam pipe $4.$ Investigate the use of critical radius of insulation of each pipe