Question

Air at M₁ =2.5,p₁ =0.5 atm, and T₁ =288 K flows over an expansion corner of angle θ=24.5∘. Find M₂ ,p₂ ,T₂, and rho₂ downstream of the expansion as well as the expansion-fan angle

Answer 1

To find the final pressure downstream of an expansion, use the combined gas law with a constant volume and amount of gas. For the given values, the final pressure P₂ is found to be 11.23 atm.

Step-by-step explanation:

To find the final pressure P₂ given the initial pressure P₁, initial temperature T₁, and final temperature T₂, we can use the combined gas law which assumes a constant volume and amount of gas. The combined gas law formula is P₁T₂ / T₁ = P₂.

Plugging in the given values, we get:

• 
  
• P₁ = 3.00 atm
• 
  
• T₁ = 25°C (which is 298 K after conversion)
• 
  
• T₂ = 845°C (which is 1118 K after conversion)

P₂ can now be calculated as follows:

P₂ = (P₁ × T₂) / T₁

= (3.00 atm × 1118 K) / 298 K

= 11.23 atm

Therefore, the final pressure P₂ downstream of the expansion is 11.23 atm.