TGPSC HMWSSB Manager 2015 Paper 2 · Question 47
Question 47 of the TSPSC Manager (Engineering), HMWSSB, 2015: Paper 2 (Civil Engineering) (1 November 2015). Try it first, then open the answer and explanation.
The stream function for a potential flow field is given by ψ=x²-y², the corresponding potential function (Φ), assuming zero potential at the origin is
- x²+y²
- 2xy
- x²-y²
- x-y
Show answer
Answer: (2) 2xy
From ψ = x² − y², u = ∂ψ/∂y = −2y and v = −∂ψ/∂x = −2x. With u = −∂Φ/∂x and v = −∂Φ/∂y this gives Φ = 2xy (zero at the origin); Φ and ψ are harmonic conjugates, and the opposite sign convention only changes the sign to −2xy.