Chapter 3.9, Problem 18P

(A)

Interpretation Introduction

Interpretation:

The exiting velocity of the steam.

Concept Introduction:

The energy balance equation around the nozzle.

$\frac{d}{dt}\left\{M\left(\underset{\_}{U}+\frac{v^2}{2}+gh\right)\right\}={\dot{m}}_{in}\left({\underset{\_}{H}}_{in}+\frac{v_{in}^2}{2}+g{h}_{in}\right)-{\dot{m}}_{out}\left({\underset{\_}{H}}_{out}+\frac{v_{out}^2}{2}+g{h}_{out}\right)+{\dot{W}}_S+{\dot{W}}_{EC}+\dot{Q}$

Here, mass flow rate for inlet and outlet is ${\dot{m}}_{in}$ and ${\dot{m}}_{out}$, molar enthalpies of inlet and outlet is ${\underset{\_}{H}}_i$ and ${\underset{\_}{H}}_{out}$, heights at which streams enters and leave the system is $h_{in}$ and $h_{out}$, time taken is t, mass of the system is M, molar internal energy is $\underset{\_}{U}$, velocity is v, height is h, acceleration due to gravity is g, rate at which work is added to the system is ${\dot{W}}_{EC}$, rate of shaft work is ${\dot{W}}_S$, and the rate of heat addition to the system is $\dot{Q}$.

(B)

Interpretation Introduction

Interpretation:

The exiting velocity of the nitrogen.

Concept Introduction:

The modified steady state equation.

$0={\dot{m}}_{in}\left({\underset{\_}{H}}_{in}\right)-{\dot{m}}_{out}\left({\underset{\_}{H}}_{out}+\frac{v_{out}^2}{2}\right)$

Refer the Appendix table D.1, “Ideal gas heat capacity”, obtain the ideal gas heat capacity of a compound as a function of temperature.

$\begin{array}{l}\frac{C_P^{*}}{R}=A+BT+C{T}^2+D{T}^3+E{T}^4\\ C_P^{*}=R\left[A+BT+C{T}^2+D{T}^3+E{T}^4\right]\end{array}$

Here, constant pressure heat capacity on a molar basis for ideal gas is $C_P^{*}$ and constants are A, B, C, D, and E.

The expression to calculate the specific change in molar enthalpy for an ideal gas is.

$d\underset{\_}{H}=C_P^{*}dT$

Here, constant pressure heat capacity on a molar basis for ideal gas is $C_P^{*}$.

(C)

Interpretation Introduction

Interpretation:

The exiting velocity of the ideal gas.

Concept Introduction:

The expression to calculate the specific change in molar enthalpy for an ideal gas.

$d\underset{\_}{H}=C_P^{*}dT$

Here, constant pressure heat capacity on a molar basis for ideal gas is $C_P^{*}$.

The modified steady state equation for nozzle with negligible mass.

$\frac{v_{out}^2}{2}={\underset{\_}{H}}_{in}-{\underset{\_}{H}}_{out}$