Chapter 4.8, Problem 31P

(A)

Interpretation Introduction

Interpretation:

The physical state of the fluid at the exit of the valve

Concept Introduction:

Write the steady state energy balance equation for throttling valve.

$\frac{d}{dt}\left\{M\left(\widehat{U}+\frac{V^2}{2}+gh\right)\right\}=\left[\begin{array}{l}{\dot{m}}_{in}\left({\widehat{H}}_{in}+\frac{V_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\widehat{H}}_{out}+\frac{V_{out}^2}{2}+g{h}_{out}\right)\\ +{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}\end{array}\right]$

Here, total mass is $M$, specific internal energy is $\widehat{U}$, velocity is $V$, time taken is $t$, acceleration due to gravity is $g$, height is $h$, initial mass flow rate is ${\dot{m}}_{in}$, initial specific enthalpy is ${\widehat{H}}_{in}$, rate of heat is added or removed from the system is $\dot{Q}$, initial velocity is $V_{in}$, initial height of the gas is $h_{in}$, final mass flow rate is ${\dot{m}}_{out}$, final height of the gas is $h_{out}$, rate of shaft work is added to the system is ${\dot{W}}_{\text{S}}$, and rate of work is added to the system through expansion or contraction of the system is ${\dot{W}}_{\text{EC}}$.

(B)

Interpretation Introduction

Interpretation:

The entropy generation rate per unit mass of steam.

Concept Introduction:

Write the expression for entropy balance of throttling valve.

$\frac{d\left(M\widehat{S}\right)}{dt}={\displaystyle \sum _{j=1}^{j=J}{\dot{m}}_{j,in}{\widehat{S}}_j}-{\displaystyle \sum _{k=1}^{k=K}{\dot{m}}_{k,out}{\widehat{S}}_k}+{\displaystyle \sum _{n=1}^{n=N}\frac{{\dot{Q}}_n}{T_n}}+{\dot{S}}_{gen}$

Here, time taken is t, mass of the system is M, specific entropy of the system is $\widehat{S}$, mass flow rates of individual streams entering and leaving the system are ${\dot{m}}_{j,in}$ and ${\dot{m}}_{k,out}$, specific entropies of streams entering and leaving the system are ${\widehat{S}}_j$ and ${\widehat{S}}_k$, actual rate at which heat is added to or removed from the system at one particular location is ${\dot{Q}}_n$, the temperature of the system at the boundary where the heat transfer labeled n occurs is $T_n$, and the rate at which entropy is generated within the boundaries of the system is ${\dot{S}}_{gen}$.

(C)

Interpretation Introduction

Interpretation:

Maximum work produced when 1 kg of steam enters the turbine.

Concept Introduction:

Write the expression for entropy balance of throttling valve.

$\frac{d\left(M\widehat{S}\right)}{dt}={\displaystyle \sum _{j=1}^{j=J}{\dot{m}}_{j,in}{\widehat{S}}_j}-{\displaystyle \sum _{k=1}^{k=K}{\dot{m}}_{k,out}{\widehat{S}}_k}+{\displaystyle \sum _{n=1}^{n=N}\frac{{\dot{Q}}_n}{T_n}}+{\dot{S}}_{gen}$

Here, time taken is t, mass of the system is M, specific entropy of the system is $\widehat{S}$, mass flow rates of individual streams entering and leaving the system are ${\dot{m}}_{j,in}$ and ${\dot{m}}_{k,out}$, specific entropies of streams entering and leaving the system are ${\widehat{S}}_j$ and ${\widehat{S}}_k$, actual rate at which heat is added to or removed from the system at one particular location is ${\dot{Q}}_n$, the temperature of the system at the boundary where the heat transfer labeled n occurs is $T_n$, and the rate at which entropy is generated within the boundaries of the system is ${\dot{S}}_{gen}$.

Write the expression for quality using the entropy relation $\left(q\right)$.

${\widehat{S}}_{out}=\left(1-q\right){\widehat{S}}^L+q{\widehat{S}}^V$

Here, specific entropy in liquid phase is ${\widehat{S}}^L$, and specific entropy in vapor phase is ${\widehat{S}}^V$.

(D)

Interpretation Introduction

Interpretation:

Compare the physical state of the fluid at the turbine exit as given in part C and the state of fluid at the value exit as given in part A

(E)

Interpretation Introduction

Interpretation:

Compare the answers with problem 4-30.