Problem $1$

The stage reaction is defined as

$R=\frac{h_1}{h_1+h_s}=\frac{h_1-h_2}{h_0-h_2}$

Where $h_r$ is entropy change across the rotor

$h_s$ is entropy change across the nozzle

Refer to the sketch shown, prove the velocity diagram is symmetric $($step by step$)$ and draw the velocity diagram when $R=\frac{1}{2}(50\%$ reaction turbine$).$

Problem $2$

A compressor has $12$ stages and overall pressure ratio is $15.$ If a compressor polytrophic efficiency is $0\mathrm{.}84$ and the compressor inlet temperature is $68F,$ determine the single stage pressure ratio.

Problem $3$

The combustor of a gas turbine has following information:

Fuel heat value LHV

$18,300$ Btu$/$lb

Stoichiometric fuel$-$air ratio $f$

$0\mathrm{.}0667$

Burner efficicency ${}_b,0\mathrm{.}95$

Spcific heat $c_p$

$0\mathrm{.}3$ But$/$lbo $R$

Compressor exit temp. $978R$

Turbine inlet temp. $1,095C$

Using the chart shown, determine the required fuel$-$air ratio for the comubstion.

$($show your work on the chart$)$