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A two-dimensional incompressible frictionless flow field is given by u = xî − yĵ. If ρ is the density of the fluid, the expression for pressure gradient vector at any point in the flow field is given as

1. ρ (xî + yĵ)
2. −ρ (xî + yĵ)
3. ρ (xî − yĵ)
4. −ρ (x²î + y²ĵ)

Correct answer: −ρ (xî + yĵ)

Solution

The correct option is derived from the application of the Euler's equation for inviscid flow, which states that the pressure gradient is equal to the negative of the density times the velocity vector. Since the velocity vector is given as u = xî − yĵ, the pressure gradient vector is thus calculated as −ρ (xî + yĵ).

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