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The steady velocity field in an inviscid fluid of density 1.5 is given to be V = (y² - x²)î + (2xy)ĵ. Neglecting body forces, the pressure gradient at (x = 1, y = 1) is __________.

1. 10ĵ
2. 20î
3. −6î − 6ĵ
4. −4î − 4ĵ

Correct answer: −6î − 6ĵ

Solution

For steady inviscid flow, grad p = -rho*(V.grad)V. With V=(y^2-x^2, 2xy) the acceleration is (2x(x^2+y^2), 2y(x^2+y^2)); at (1,1) that is (4,4). Times -rho=-1.5 gives grad p = -6 i - 6 j, which is option 2, not -4i-4j.

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