Normal Shock Problem 3 - Compressible Fluid Flow - Fluid Mechanics 1

TL;DR

Calculate the conditions immediately downstream from a compression shock in an air flow with given upstream conditions.

Transcript

hello students let's start with a new topic that is problem based on shockwave from the chapter compressible fluid flow the problem states conditions immediately upstream from a compression shock in an air flow are given as follows p is equal to 34.3 kilo newton per meter square absolute t is equal to 0 degree celsius and v is equal to 1000 meter p... Read More

Key Insights

• 🤭 Upstream conditions: P = 34.3 kN/m², T = 0°C, and V = 1000 m/s.
• 😀 Downstream conditions: velocity downstream = 331.3 m/s, pressure downstream = 359.3 kN/m³, and temperature downstream = 738 K.
• #️⃣ Mach number upstream = 3.02, Mach number downstream = 0.474.
• 👌 The equation for pressure downstream is Pd / Pu = 2 * K * M² - K - 1 / K + 1.
• 👌 The equation for temperature downstream is Td / Tu = (2 * K * M² - K - 1) / (K + 1) * (K - 1 * M² + 2) / (K + 1 * M²).
• 👌 Density downstream can be calculated using the equation ρd / ρu = (K + 1) * M² / (K - 1) * M² + 2.
• 🫢 The given constant values are k = 1.4 and the gas constant = 287 J/kg Kelvin.

Questions & Answers

Q: What are the given upstream conditions in the problem?

The given upstream conditions are P = 34.3 kN/m², T = 0°C, and V = 1000 m/s.

Q: How do you calculate the velocity downstream?

The velocity downstream is calculated using the equation M = V / C, where M is the Mach number and C is the speed of sound. In this case, M = 3.02 and C = 331.3 m/s.

Q: What is the formula for calculating pressure downstream?

The formula is Pd / Pu = 2 * K * M² - K - 1 / K + 1, where Pd is the pressure downstream and Pu is the pressure upstream. In this case, Pd / Pu = 359.3 kN/m³ / 34.3 kN/m².

Q: How do you determine the temperature downstream?

The equation for calculating temperature downstream is Td / Tu = (2 * K * M² - K - 1) / (K + 1) * (K - 1 * M² + 2) / (K + 1 * M²). In this case, Td = 738 K and Tu = 273.15 K.

Summary & Key Takeaways

• Conditions upstream from a compression shock: P = 34.3 kN/m², T = 0°C, and V = 1000 m/s.

• Calculate downstream conditions: velocity downstream = 331.3 m/s, pressure downstream = 359.3 kN/m³, and temperature downstream = 738 K.