Final answer:
To determine the diameter of the evaporator flow channel, use the equation of continuity. To determine the velocity at the exit, use the ideal gas law and the equation of continuity.
Step-by-step explanation:
To determine the diameter of the evaporator flow channel, we can use the equation of continuity. The equation states that mass flow rate is equal to the product of density, velocity, and cross-sectional area. Since the velocity and mass flow rate are given, we can rearrange the equation to solve for the cross-sectional area, which can then be used to calculate the diameter. The mass flow rate is 0.1 kg/s, the velocity is 7 m/s, and the density can be determined using the saturation pressure at -4°C. Once the density is determined, we can calculate the cross-sectional area, and finally the diameter of the evaporator flow channel.
To determine the velocity at the exit, we can use the ideal gas law to calculate the final state of the refrigerant. The initial and final temperatures are given as -4°C, which can be converted to Kelvin. Since the refrigerant is a saturated vapor at the exit, we can use the saturation pressure at -4°C to determine the final density. Once the final density is determined, we can use the equation of continuity to solve for the final velocity at the exit by equating the cross-sectional area of the evaporator flow channel to the product of velocity and density at the exit.