Week 5 Q2 (ENGR5003)

Week 5 Q2Exercise sheetCurrent spec2:135 min

Consider a Rankine cycle, where 5 kg of saturated water ( $x = 0$ ) at 0.05 bar and $32.87\ ^\circ\mathrm{C}$ is compressed to 50 bar. The water is heated under constant pressure until it is converted into dry saturated steam. The pressurised steam is forced through a turbine, allowing the pressure to drop back to 0.05 bar.

Formulas you may need

Wet steam: $s = (1 - x)s_f + xs_g$ , and the same for $v$ , $h$ (on the formula sheet)
SFEE per component: $w_T = h_3 - h_4$ , $w_P = h_2 - h_1$ , $q_{in} = h_3 - h_2$ (on the formula sheet)
Pump work for an incompressible liquid: $w_P = v_f(p_2 - p_1)$ (learn this)
Isentropic efficiencies: $\eta_P = \dfrac{h_{2s} - h_1}{h_2 - h_1}$ , $\eta_T = \dfrac{h_3 - h_4}{h_3 - h_{4s}}$ (learn this, Lecture 13)
Back work ratio $r_{bw} = \dfrac{w_{in}}{w_{out}}$ ; $\eta_{th} = \dfrac{w_{net}}{q_{in}}$ (on the formula sheet)

(a)
Determine the entropy, pressure, temperature and volume of the water at each state of the cycle, assuming that the compression and expansion processes are isentropic.
s1 (= s2) =kJ/(kg K)
T3 =C
s3 (= s4) =kJ/(kg K)
v3 =m^3/kg
x4 =
v4 =m^3/kg
V4 (5 kg) =m^3
(b)
Determine the entropy, pressure, temperature and volume of the water at each state of the cycle, assuming that the compression and expansion processes have isentropic efficiencies 0.75 and 0.8 respectively.
h2 =kJ/kg
h4 =kJ/kg
x4 =
s4 =kJ/(kg K)
v4 =m^3/kg
(c)
What is the back work ratio and thermal efficiencies for the isentropic assumption and assuming the isentropic efficiencies stated in part b)?
r_bw isentropic =
eta isentropic =
r_bw real =
eta real =