Question 16.2: Determine the pressure ratio developed and the specific work...

The impeller tip speed

= 183.26 m/s

With the help of Eqs (16.6) and (16.7), we can write

$\frac{T_{2 t}}{T_{1 t}}=\frac{T_{3 t}}{T_{1 t}}=1+\frac{\Psi \sigma U_{2}^{2}}{c_{p} T_{1 t}}$ (16.6)

$\begin{aligned}\frac{p_{3 t}}{p_{1 t}} &=\left(\frac{T_{3 t}^{\prime}}{T_{1 t}}\right)^{\frac{\gamma}{\gamma-1}} \\&=\left[1+\frac{\eta_{c}\left(T_{3 t}-T_{1 t}\right)}{T_{1 t}}\right]^{\frac{\gamma}{\gamma-1}}\end{aligned}$ (16.7)

Pressure ratio $=\left[1+\frac{U_{2}^{2}}{c_{p} T_{1 t}}\right]^{\frac{\gamma}{\gamma-1}}$

= 1.46

From Eq (16.3), specific work input $=U_{2}^{2}=\frac{(183.26)^{2}}{1000}=33.58$ kJ/kg

$w=\Psi \sigma U_{2}^{2}$ (16.3)