Water enters a $\backslash (2\mathrm{.}0-\backslash$mathrm$\{$cm$\}\backslash )-$diameter circular tube, whose surface temperature is maintained at $\backslash (90^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ at $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and leaves at $\backslash (60^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ If the entering velocity is $\backslash (1\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ calculate the length of tube required to accomplish the desired heating and the pressure drop across the tubelength

$($a$)$ using the Hausen or Gnielinski correlation $($depending on whether the flow is laminar or turbulent$)$ to calculate the convective heat transfer coefficient