GATE XE (Engineering Sciences) 2023 - Question 35

Section: Fluid Mechanics | Type: MSQ | Marks: 2

In a steady two-dimensional compressible flow, 𝑢 and 𝑣 are the 𝑥- and 𝑦- components of flow velocity, respectively and 𝜌 is the fluid density. Among the following pairs of relations, which one(s) perfectly satisfies/satisfy the definition of stream function, 𝜓, for this flow?

• A. 𝑢= 𝜕𝜓 𝜕𝑦 and 𝑣= − 𝜕𝜓 𝜕𝑥
• B. 𝑢= − 𝜕𝜓 𝜕𝑥 and 𝑣= − 𝜕𝜓 𝜕𝑦
• C. 𝜌𝑢= 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= − 𝜕𝜓 𝜕𝑥
• D. 𝜌𝑢= − 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= 𝜕𝜓 𝜕𝑥

Answer: C. 𝜌𝑢= 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= − 𝜕𝜓 𝜕𝑥; D. 𝜌𝑢= − 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= 𝜕𝜓 𝜕𝑥