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Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.5. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.5. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Nitrogen enters a duct with varying flow area at 400 K, 100 kPa, and a Mach number of 0.5. Assuming a steady, isentropic flow, determine the temperature, pressure, and Mach number at a location where the flow area has been reduced by 20 percent.

Expert Solution
Step 1

Given data:

  • The temperature at the inlet of the duct, T1 = 400 K.
  • The pressure at the inlet of the duct, P1 = 100 kPa.
  • Mach number at the inlet of duct, Ma1 = 0.5.
  • Area reduced by 20% compared to the inlet area.

Draw a schematic diagram.

Mechanical Engineering homework question answer, step 1, image 1

From the table of Mach number and parameter ratios for isentropic flow, the area, Temperature, and pressure ratios at a Mach number of 0.5 are,

A1A*=1.3398P1Po=0.8430T1To=0.9524

The available area at location 2 is,

A2=100%-20%100%A1A2=0.8A1

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