## Related questions with answers

Steam expands isentropically through a converging nozzle operating at steady state from a large tank at $1.83\ \text{bar}$, $280^{\circ} \mathrm{C}$. The mass flow rate is $2 \mathrm{~kg} / \mathrm{s}$, the flow is choked, and the exit plane pressure is $1\ \text{bar}$. Determine the diameter of the nozzle, in $\mathrm{cm}$, at locations where the pressure is $1.5\ \text{bar}$, and $1\ \text{bar}$, respectively.

Solution

VerifiedIn this problem we need to calculate the diameter the exit nozzle for two different exit pressures. For the calculation we will need the given temperature $T_0=280\,\text{\textdegree}\text{C}$ and pressure $p_0=183\,\text{kPa}$ to determine the enthalpy $h_0$ and entropy $s_0=s_2$.

$\begin{align*} h_0&=3030\,\frac{\text{kJ}}{\text{kg}} \\ s_0&=s_2=7.86\,\frac{\text{kJ}}{\text{kg K}} \\ \end{align*}$

The first pressure given is exit pressure $p_2=150\,\text{kPa}$. We can use that with the calculated entropy $s_2$ to determine the enthalpy $h_2$ and specific volume $V_2$.

$\begin{align*} h_2&=2980\,\frac{\text{kJ}}{\text{kg}} \\ V_2&=1.61\,\frac{\text{m}^3}{\text{kg}} \\ \end{align*}$

We can now calculate the exit velocity $v_2$ using the energy balance equation.

$\begin{align*} \frac{v_2^2}{2}&=h_0-h_2 \\ \frac{v_2^2}{2}&=3030000\,\frac{\text{J}}{\text{kg}} -2980000\,\frac{\text{J}}{\text{kg}}\\ v_2&=316.2\,\frac{\text{m}}{\text{s}} \\ \end{align*}$

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