Question

Steam enters a nozzle at 800 kPa and 553.15 K (280°C) at negligible velocity and discharges at a pressure of 525 kPa. Assuming isentropic expansion of the steam in the nozzle, what is the exit velocity and what is the cross-sectional area at the nozzle exit for a flow rate of 0.75 kg/s?

Answer 1

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Step-by-step explanation:

To determine the exit velocity and cross-sectional area at the nozzle exit, we can use the principles of isentropic flow and the mass flow rate equation.

1. Calculate the initial specific volume:

- The specific volume (v) of the steam can be calculated using the ideal gas law: v = R_specific * T / P, where R_specific is the specific gas constant and T is the temperature in Kelvin.

- Given that the steam enters at 553.15 K (280°C) and 800 kPa, we need to convert the temperature to Kelvin: 280°C + 273.15 = 553.15 K.

- The specific gas constant for steam is approximately 0.4615 kJ/kg·K.

- Therefore, the initial specific volume is v = (0.4615 kJ/kg·K * 553.15 K) / 800 kPa = 0.3186 m³/kg.

2. Calculate the final specific volume:

- Since the expansion is assumed to be isentropic, the specific entropy remains constant.

- Using the steam tables or other appropriate references, we can determine the specific volume at the final pressure of 525 kPa (corresponding to the specific entropy of the initial state).

- Let's assume the final specific volume is 0.546 m³/kg.

3. Calculate the exit velocity:

- The exit velocity (V_exit) can be determined using the equation for isentropic flow: V_exit = sqrt(2 * (h_initial - h_final)), where h is the specific enthalpy.

- The specific enthalpy (h_initial) at the initial state can be obtained from the steam tables or other references.

- Similarly, the specific enthalpy (h_final) at the final state can also be obtained.

- Substituting the values into the equation, we can calculate the exit velocity.

4. Calculate the cross-sectional area at the nozzle exit:

- The cross-sectional area (A_exit) can be calculated using the mass flow rate equation: m_dot = A_exit * v_exit, where m_dot is the mass flow rate and v_exit is the exit specific volume.

- The mass flow rate is given as 0.75 kg/s.

- Substituting the values into the equation, we can calculate the cross-sectional area.

Please note that the specific enthalpy values and specific volume values used in steps 2 and 3 are not provided in the question, so you would need to refer to appropriate references to obtain those values.

Answer 2

The student's question involves using thermodynamic principles to calculate the exit velocity and cross-sectional area of a nozzle for isentropic steam flow. Using the first law of thermodynamics and conservation of mass, one can determine both quantities after an isentropic expansion process.

Step-by-step explanation:

The question involves the calculation of the exit velocity and cross-sectional area for steam flowing isentropically through a nozzle, given the inlet pressure and temperature, the exit pressure, and the mass flow rate. To solve this problem, one would apply the principles of thermodynamics, specifically the first and second laws, and the conservation of mass.

To find the exit velocity, we need to use the energy balance equation for isentropic flow through a nozzle, which is a derivation of the first law of thermodynamics. Since the inlet velocity is negligible, we can ignore its kinetic energy. The energy release as steam expands allows us to calculate the exit velocity. The second step involves finding the cross-sectional area at the nozzle exit, which can be determined from the exit velocity and mass flow rate using the continuity equation and the ideal gas law to account for the change in density.

Applying these equations in combination with steam table data for specific enthalpies and entropy, we can find the desired quantities. In practice, additional factors such as nozzle efficiency might be considered, but for an isentropic process, these complexities are not included in the calculations.