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Question 4.2: For the velocity potential Φ = x²— y² , find the velocity co......

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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