Question

A constant-pressure \(R-134\) a vapor separation unit separates the liquid and vapor portions of a saturated mixture into two separate outlet streams. Determine the flow power needed to pass \(6 \mathrm{L} / \mathrm{s}\) of \(\mathrm{R}-134 \mathrm{a}\) at \(320 \mathrm{kPa}\) and 55 percent quality through this unit. What is the mass flow rate, in \(\mathrm{kg} / \mathrm{s}\), of the two outlet streams?

Short answer

Also, determine the mass flow rates of the two outlet streams: liquid and vapor. Answer: To calculate the flow power and mass flow rates, follow these steps: 1. Find the specific volume of the mixture entering the unit, \(v_{mix}\), using the given quality and saturated properties table of R-134a. 2. Calculate the mass flow rate of the system, \(\dot{m}\), using the given volumetric flow rate and the specific volume found in step 1. 3. Determine the enthalpy of the mixture entering the unit, \(h_{mix}\), using the given quality and saturated properties table of R-134a. 4. Calculate the flow power needed, \(P_{flow}\), using the mass flow rate and enthalpy found in steps 2 and 3. 5. Determine the mass flow rate of the separate outlet streams, \(\dot{m}_{liquid}\) and \(\dot{m}_{vapor}\), using the mass flow rate of the system and the given quality.

Step-by-step solution

Find specific volume of the mixture entering the unit

First, we need to find the specific volume of the mixture entering the unit (\(v_{mix}\)). This can be calculated using the formula: \(v_{mix} = (1-Q) v_f + Qv_g\) Where \(Q\) is the quality (0.55), \(v_f\) is the specific volume of the saturated liquid, and \(v_g\) is the specific volume of the saturated vapor. We can find \(v_f\) and \(v_g\) using the given pressure of 320 kPa by referring to the saturated properties table of R-134a.

Calculate mass flow rate

Now, we can calculate the mass flow rate of the system (\(\dot{m}\)) using the given volumetric flow rate (6 L/s) and the specific volume calculated in step 1: \(\dot{m} = \frac{V}{v_{mix}}\)

Determine enthalpy of mixture entering the unit

Before calculating the flow power, we need to find the enthalpy of the mixture (\(h_{mix}\)) entering the vapor separation unit. This can be calculated using the formula: \(h_{mix} = (1-Q)h_f + Qh_g\) Where \(Q\) is the quality (0.55) and \(h_f\) and \(h_g\) are the specific enthalpies of saturated liquid and saturated vapor, respectively. These values can be found using the given pressure of 320 kPa in the saturated properties table of R-134a.

Calculate flow power

Now that we have the actual mass flow rate and the enthalpy of the mixture, we can calculate the flow power needed: \(P_{flow} = \dot{m} \times h_{mix}\)

Determine mass flow rate of the separate outlet streams

Finally, to determine the mass flow rates of the two outlet streams, we can use the mass flow rate of the system and the given quality (0.55). Since liquid and vapor portions are separated, the mass flow rates will be proportional to the liquid and vapor mass fractions in the entering mixture: \(\dot{m}_{liquid} = (1-Q) \times \dot{m}\) \(\dot{m}_{vapor} = Q \times \dot{m}\)