GATE XE (Engineering Sciences) 2023 - Question 27

Section: Fluid Mechanics | Marks: 1

An inviscid steady incompressible flow is formed by combining a uniform flow with velocity 𝑈∞ and a clockwise vortex of strength 𝐾 at the origin, as shown in the figure. Velocity potential (𝜙) for the combined flow in polar coordinate (𝑟, 𝜃) is

• A. 𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 cos 𝜃
• B. 𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 sin 𝜃
• C. 𝜙= 𝐾ln 𝑟+ 𝑈∞𝑟 cos 𝜃
• D. 𝜙= −𝐾ln 𝑟+ 𝑈∞𝑟 sin 𝜃

Answer: A. 𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 cos 𝜃