Conservation of Mass: ConcepTest and Example Problem
Try to answer this ConcepTest and solve the example problem before using this module. Studies show that trying to answer the questions before studying material improves learning and retention. We suggest that you write down the reasons for your answers. By the end of this module, you should be able to answer these on your own. Answers will be given at the end of this module.
Example Problem 1
Air flows steadily through this nozzle. The nozzle has an inlet diameter of \(D_1\) = 0.1 m and an outlet diameter of \(D_2\) = 0.04 m. The density of the air decreases from \(\rho_1\) = 1 kg/m3 at the inlet to \(\rho_2\) = 0.5 kg/m3 at the outlet. The average speed of the air at the inlet is \(V_1\) = 12 m/s.
1. What is the average speed of the air leaving the nozzle, \(V_2\), in units of m/s?
2. What is the mass flow rate of the air leaving the nozzle, \(\dot{m}_2\), in units of kg/s? Is it smaller than, equal to, or greater than the mass flow rate of air entering the nozzle, \(\dot{m}_1\)?
3. What is the volumetric flow rate of the air leaving the nozzle, \(Q_2\), in units of m3/s? Is it smaller than, equal to, or greater than the volumetric flow rate of air entering the nozzle, \(Q_1\)?
