$(10)$ Ans. $($a$)246\mathrm{.}75k\frac{g}{s}$; $($b$)2\mathrm{.}16$ m

Steam at $11032$kPa,$538C,$ and a velocity of $0\mathrm{.}6\frac{m}{s}$ enters a turbine operating at steady state. As shown in Fig., $22\%$ of the entering mass flow is extracted at $1103$kPa,$232C,$ with a velocity of $3\frac{m}{s}.$ The rest of the steam exits as a two$-$phase liquid$-$vapor mixture at $7$ kPa $,$ with a quality of $85\%$ and a velocity of $45\frac{m}{s}.$ The turbine develops a power output of $2\mathrm{.}6{10}^{5}kW.$ Neglecting potential energy effects and heat transfer between the turbine and its surroundings, determine

$($a$)$ the mass flow rate of the steam entering the turbine, in $k\frac{g}{h}.$

$($b$)$ the diameter of the extraction duct, in $m.$

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