GATE XE (Engineering Sciences) 2025 - Question 27

Section: Fluid Mechanics | Marks: 1

Conservation of mass for a steady axisymmetric flow field in the cylindrical (r, z) coordinates is: 1 𝑟 𝜕(𝑟𝑉𝑟) 𝜕𝑟 + 𝜕𝑉𝑧 𝜕𝑧= 0 Here, 𝑉𝑟 and 𝑉𝑧 are radial and axial components of velocity, respectively. Which one of the following options is correct if 𝜓 is the stream function?

• A. 𝑉𝑟= 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟
• B. 𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟
• C. 𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= 1 𝑟 𝜕𝜓 𝜕𝑟
• D. 𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 𝜕𝜓 𝜕𝑟

Answer: B. 𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟