Question

Using EES (or other) software and the relations given in Table \(A-33\), generate the one-dimensional normal shock functions by varying the upstream Mach number from 1 to 10 in increments of 0.5 for air with \(k=1.4\).

Short answer

Question: Develop one-dimensional normal shock functions for air with a specific heat ratio of 1.4 using EES software, for upstream Mach numbers ranging from 1 to 10 with increments of 0.5. Present the results in a table or plot format. Answer: To create one-dimensional normal shock functions for air with a specific heat ratio of 1.4 using EES software, follow the steps outlined in the solution above. Input the necessary normal shock relations from Table A-33, define the variables, perform calculations using a loop for varying upstream Mach numbers, and output the results in a table or plot format. The resulting table or plot will provide the pressure ratio, temperature ratio, and density ratio values for the specified range of upstream Mach numbers, illustrating the normal shock functions for air with a specific heat ratio of 1.4.

Step-by-step solution

Understand the Table A-33 relations

Table A-33 lists the normal shock relations for different properties across the shock, such as Mach number, pressure, temperature, and density ratios. These relations are functions of the upstream Mach number (M1) and specific heat ratio (k).

Set up the software

For this exercise, we will assume that you have chosen to use EES software. Start by launching the EES software and create a new EES file. In the equations window, we will input the necessary relations from Table A-33 and define the variables.

Input the relations and define variables

In the EES equation window, input the normal shock relations from Table A-33, including the pressure ratio, temperature ratio, and density ratio equations. Since we are given the value of k as 1.4, use this value for k. Define M1 as an independent variable, M2 (downstream Mach number) as a dependent variable, and assign other dependent variables (pressure ratio, temperature ratio, and density ratio) accordingly.

Perform the calculations

Use a loop (e.g., FOR loop) to vary the upstream Mach number (M1) from 1 to 10 with a step size of 0.5. In each iteration of the loop, use the normal shock relations to calculate the downstream Mach number (M2) and other shock properties (pressure ratio, temperature ratio, and density ratio). Record these values in a table or matrix format for further analysis.

Output the results

After completing the calculations for all the upstream Mach numbers from 1 to 10 in increments of 0.5, present the results in a table or plot format. This can be done within EES using the built-in table and plot functions or exported to another software (such as Microsoft Excel) for further data manipulation and presentation. The table or plot should show the one-dimensional normal shock functions for the specified range of upstream Mach numbers and specific heat ratio of 1.4. In conclusion, by following these steps, you should now have successfully generated the one-dimensional normal shock functions using EES software for air with a specific heat ratio of 1.4 and a range of upstream Mach numbers from 1 to 10 with increments of 0.5. Make sure to draw the appropriate plots or present the numerical results in a clear and concise manner.