Question

air at 500 kpa and 400 k enters an adiabatic nozzle at a velocity of 30 m/s and leaves at 300 kpa and 350 k. determine the isentropic efficiency and the entropy generation.

Answer 1

To determine the isentropic efficiency (\(\eta_{\text{isentropic}}\)) and the entropy generation (\(\Delta S_{\text{gen}}\)) of the adiabatic nozzle, we can use the following equations:

1. **Isentropic Efficiency (\(\eta_{\text{isentropic}})\):**

`\[ \eta_{\text{isentropic}} = \frac{h_{\text{inlet}} - h_{\text{outlet actual}}}{h_{\text{inlet}} - h_{\text{outlet isentropic}}} \]`

2. **Entropy Generation (\(\Delta S_{\text{gen}})\):**

`\[ \Delta S_{\text{gen}} = s_{\text{outlet actual}} - s_{\text{outlet isentropic}} \]`

where:

- h is the specific enthalpy,

- s is the specific entropy,

- Subscripts "inlet" and "outlet" refer to the inlet and outlet states,

- Subscripts "isentropic" refer to the ideal (isentropic) process.

To find the specific enthalpies (h) and specific entropies (s), you can use steam tables or any other relevant tables for air properties.

Given:

Steps:

1. **Determine the Inlet State (\(h_{\text{inlet}}, s_{\text{inlet}}\)):**

Use the given pressure and temperature to find the specific enthalpy and entropy of air at the inlet state.

2. **Determine the Ideal (Isentropic) Outlet State (\(h_
`- \(P_{\text{inlet}} = 500 \ \text{kPa}\),- \(T_{\text{inlet}} = 400 \ \text{K}\),- \(V_{\text{inlet}} = 30 \ \text{m/s}\),- \(P_{\text{outlet}} = 300 \ \text{kPa}\),- \(T_{\text{outlet}} = 350 \ \text{K}\).`{\text{outlet isentropic}}, s_{\text{outlet isentropic}}\)):**

Use the given outlet pressure and the inlet entropy to find the specific enthalpy and entropy assuming an isentropic process.

3. **Determine the Actual Outlet State (\(h_{\text{outlet actual}}, s_{\text{outlet actual}}\)):**

Use the given outlet pressure and temperature to find the specific enthalpy and entropy of air at the actual outlet state.

4. **Calculate Isentropic Efficiency (\(\eta_{\text{isentropic}})\):**

Substitute the values into the isentropic efficiency formula.

5. **Calculate Entropy Generation (\(\Delta S_{\text{gen}})\):**

Substitute the values into the entropy generation formula.

Performing these calculations will give you the isentropic efficiency and entropy generation for the given adiabatic nozzle process.