# Power System

 Question 1
Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure.
The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:

??$P_1=100kPa, \rho _1=1.2kg/m^3,u_1=400m/s$

The duct cross-sectional area at Location 2 is given by $A_2=2A_1$, where$A_1$ denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity $u_2$ and pressure $P_2$ at Location 2 is TRUE?

 A $u_2 \lt u_1, P_2 \lt P_1$ B $u_2 \lt u_1, P_2 \gt P_1$ C $u_2 \gt u_1, P_2 \lt P_1$ D $u_2 \gt u_1, P_2 \gt P_1$
GATE ME 2023   Thermodynamics
Question 1 Explanation:
Step -1: First identify type of flow - Subsonic or Supersonic by finding out Mach number

Mach no at start of flow
$M_a=\frac{u_1}{C_1},\; where, \; C_1=\sqrt{\gamma RT_1}$
$u_1$ is velocity of gas
$C_1$is velocity of sound

\begin{aligned} P_1 &=\rho _1RT_1 \\ T_1&= \frac{P_1}{\rho _1R}=\frac{100}{1.2 \times 0.287}=290.36K\\ C_1 &=\sqrt{1.4 \times 287 \times 290.36} \\ &= 341.56 m/sec\\ Ma_1 &=\frac{400}{341.56}=1.017 \end{aligned}
Flow is supersonic flow. Hence, diverging duct is nozzle so $u_2 \gt u_1$ and $P_2 \lt P_1$.
 Question 2
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).
 A 2624.37 B 1225.36 C 3625.25 D 1475.36
GATE ME 2022 SET-1   Thermodynamics
Question 2 Explanation:

\begin{aligned} W_{HPT}&=400kJ/kg\\ W_{LPT}&=850kJ/kg\\ W_{P}&=15kJ/kg\\ \eta &=0.35=\frac{W_{net}}{Q_S}\\ Q_S&=3859.375 kJ/kg\\ \therefore \; W_{net}&=Q_S-Q_R\\ Q_R&=3859.375-1235\\ Q_R&=2624.37 kJ/kg \end{aligned}

 Question 3
Consider the open feed water heater (FWH) shown in the figure given below:

Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater (at location 5) is 100 kg/s then the mass flow rate of steam at location 2 will be kg/s (round off to one decimal place).
 A 25.2 B 45.6 C 62.3 D 18.4
GATE ME 2021 SET-2   Thermodynamics
Question 3 Explanation:

\begin{aligned} 100 h_{5}+(x-100) h_{2} &=x h_{6} \\ 100 \times 226.7+(x-100) 2624&=708.6 x \\ 22670+2624 x-262400 &=708.6 x \\ 2624 x-708.6 x &=239730 \\ 1915.4 x &=239730 \\ x &=125.159 \simeq 125.2 \mathrm{~kg} / \mathrm{s} \end{aligned}
Mass flow rate at state $2(x-100)=25.2 \mathrm{~kg} / \mathrm{s}$
 Question 4
Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high pressure turbine is 750 kJ/kg. The work output from the low pressure turbine is 1500 kJ/kg. The thermal efficiency of the cycle is 50 %. The enthalpy of saturated liquid and saturated vapour at condenser pressure are 200 kJ/kg and 2600 kJ/kg, respectively. The quality of steam at the exit of the low pressure turbine is ________ % (round off to the nearest integer).
 A 45 B 68 C 98 D 93
GATE ME 2021 SET-1   Thermodynamics
Question 4 Explanation:

\begin{aligned} h_{f} &=200 \mathrm{~kJ} / \mathrm{kg} \\ h_{g} &=2600 \mathrm{~kJ} / \mathrm{kg} \\ w_{p} &=20 \mathrm{~kJ} / \mathrm{kg}=h_{6}-h_{5} \\ h_{1}-h_{2} &=750 \mathrm{~kJ} / \mathrm{kg} \\ h_{3}-h_{4} &=1500 \mathrm{~kJ} / \mathrm{kg} \\ \eta &=0.5=\frac{W_{\mathrm{NET}}}{Q_{s}}=\frac{W_{T}-W_{P}}{Q_{s}}\\ 0.5 &=\frac{750+1500-20}{Q_{S}} \\ Q_{S} &=4460 \mathrm{~kJ} / \mathrm{kg} \\ \eta &=1-\frac{Q_{R}}{Q_{S}} \\ \frac{Q_{R}}{Q_{S}} &=0.5 \\ Q_{R} &=2230 \mathrm{~kJ} / \mathrm{kg} \\ Q_{R} &=h_{4}-h_{5} \\ 2230 &=h_{4}-200 \\ h_{4} &=2430 \mathrm{~kJ} / \mathrm{kg} \\ h_{4} &=h_{f}+x\left(h_{g}-h_{f}\right) \\ 2430 &=200+x(2600-200) \\ x &=0.9291 \\ x &=93 \% \end{aligned}
 Question 5
The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are $h_1$ and $h_3$ respectively. The enthalpy at the stator outlet (or, rotor inlet) is $h_2$. The condition $(h_2-h_1)=(h_3-h_2)$ indicates that the degree of reaction of this stage is
 A zero B 50% C 75% D 100%
GATE ME 2020 SET-2   Thermodynamics
Question 5 Explanation:
As enthalpy across stator and rotor is equal it is 50% reaction stage.

There are 5 questions to complete.