For the velocity potential Φ = x²— y² , find the velocity components at point (4, 5).

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Given: Φ = x²— y²

We know that

\frac{\pmb{\delta} \phi }{\pmb{\delta}x }=u=2x

Hence, value of u at (4, 5) is:

u = 2x

= 2 × 4 = 8 units

Again, we know that

\frac{\pmb{\delta} \phi }{\pmb{\delta}y } = – v

= −(−2y) = 2y

Or v = −2y

= −2 × 5 = −10 units

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