GATE XE (Engineering Sciences) 2023 - Question 32

Section: Fluid Mechanics | Marks: 2

A two-dimensional incompressible flow field is defined as, 𝑉⃗⃗(𝑥, 𝑦) = (𝐴𝑥𝑦) 𝑖̂ + (𝐵𝑦2) 𝑗̂ where, 𝐴 and 𝐵 are constants. The dynamic viscosity of the Newtonian fluid is 𝜇. In the absence of body force, which among the following expressions represents the pressure gradient at the location (5, 0) in the concerned flow field?

• A. 𝜇𝐴(5 𝑖̂ + 𝑗̂)
• B. 𝜇(−5𝐵 𝑖̂ + 𝐴 𝑗̂)
• C. 𝜇𝐴(−𝑗̂)
• D. 𝜇𝐴(5 𝑖̂)

Answer: C. 𝜇𝐴(−𝑗̂)