Question

For a two dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression  δ ( u 2 ) δ x + δ ( u v ) δ y can be simplified to

Options :

  1. u δ u δ x + u δ v δ y

  2. u δ u δ x + v δ u δ y

  3. 2 u δ u δ x + u δ v δ y

  4. 2 u δ u δ x + v δ u δ y

Show Answer

Answer :

u δ u δ x + v δ u δ y

Solution :

δ ( u 2 ) δ x + δ ( u v ) δ y

After differentiating we get,

2 u δ u δ x + u δ v δ y + v δ u δ y

u δ u δ x + u [ δ u δ x + δ v δ y ] + v δ u δ y

According to continuity equation for 2D incompressible flow  δ u δ x + δ v δ y = 0

∴  u δ u δ x + v δ u δ y

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