Problem #$1$:

Steam at $1600l\frac{b_f}{i}{n}^2,1000F,$ and a velocity of $2\mathrm{.}0f\frac{t}{s}$ enters a turbine operating at steady state. Show in the following figure, $22\%$ of the entering mass flow is extracted at $160lb\frac{f}{i}{n}^2,450F,$ with a velocity of $10\mathrm{.}0f\frac{t}{s}.$ The rest of the steam exits as a two$-$phase liquid$-$vapor mixture at $1\mathrm{.}0l\frac{b}{i}{n}^2,$ with a quality of $85\%$ and a velocity of $150f\frac{t}{s}.$ The turbine develops a power output of $9{10}^{8}Bt\frac{u}{h}.$ 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 lb$/$h$.$

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

Problem #$1$:

Steam at $1600l\frac{b_f}{i}{n}^2,1000F,$ and a velocity of $2\mathrm{.}0f\frac{t}{s}$ enters a turbine operating at steady state. Show in the following figure, $22\%$ of the entering mass flow is extracted at $160lb\frac{f}{i}{n}^2,450F,$ with a velocity of $10\mathrm{.}0f\frac{t}{s}.$ The rest of the steam exits as a two$-$phase liquid$-$vapor mixture at $1\mathrm{.}0l\frac{b}{i}{n}^2,$ with a quality of $85\%$ and a velocity of $150f\frac{t}{s}.$ The turbine develops a power output of $9{10}^{8}Bt\frac{u}{h}.$ 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 lb$/$h$.$

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