Quizwork 6

Dr. Elle Wroblewski AE 312 Spring 2024 AE 312 Quizwork 6 Due: 03/20/2024 Problem Solution Format (you will be graded on these procedures):  Draw the diagram or correctly determine the diagram from provided description, add station labels.  State “Given” and “Unknown” property value s that you are using or finding.  As you use them in your solution, or before beginning, state your Assumptions  Draw a coordinate frame indicating positive direction for vector values.  In your solution describe your approach to the problem and any equations you use to solve it.  As you determine your unknowns, please circle them .  Use the online calculator or tables to speed up solution approaches to these problems.  When uploading to Gradescope: select the pages your problems correspond to. 1. Air is flowing at a Mach number of 0.5 in a two-dimensional channel at a location where the area is 1 ft 2 . At this location the static pressure is 10 psia, and the static temperature is 500ºR. a. Calculate the mass flow rate through the channel and the stagnation pressure and temperature at this location. b. What percent reduction in area would be necessary to increase the flow Mach number to 0.75? What would the static pressure and temperature be at this location? Percent reduction: ( A A ¿ ) M = 0.5 − ( A A ¿ ) M = 0.75 ( A A ¿ ) M = 0.5 × 100 c. What reduction in area would be necessary to reach a Mach number of 1.0, and what would be the corresponding static conditions? d. What would happen if the area were reduced to a value smaller than that in part (c)? 2. A converging nozzle has an exit area of 10 i n 2 . Nitrogen stored in a reservoir is to be discharged through the nozzle to an ambient pressure of 14.7 psia. Assume isentropic flow and that the reservoir temperature is 520 ° R . Determine which operating regime the nozzle is in as well as the mass flow rate through the nozzle for: a. A reservoir pressure of 20 psia b. A reservoir pressure of 40 psia c. A reservoir pressure of 100 psia 3. A Mach 2.5 air flow with a stagnation temperature of 400 K and a mass flow rate of 0.72 kg/s encounters a normal shock wave at a location with an area of 10 cm 2 . The flow then enters a diverging section whose exit area is 20 cm 2 . The flow may be assumed to be isentropic except across the normal shock wave. Find the Mach number, velocity, static pressure, stagnation pressure, static temperature, and stagnation temperature at the exit of the diverging section. 1