1.

Which of these assumptions is invalid for the linearized velocity potential equation?(a) \(\frac {u^{‘}}{V_∞}\) 1(d) \(\frac {w^{‘}}{V_∞}\)

Answer»

The CORRECT option is (c) \(\FRAC {W^{‘}}{V_∞}\) >> 1

Easy explanation: The perturbation velocity potential equation is given by:

(a^2 – (V∞ + ϕx)^2) ϕxx + (a^2 – ϕy^2) ϕyy + (a^2 – ϕz^2) ϕzz – (2(V∞ + ϕx) ϕy) ϕxy – (2(V∞ + ϕx) ϕz) ϕxz – (2ϕy ϕz) ϕyz

This relation is non – linear in nature and in ORDER to reduce to the linear form, an assumption is made i.e. the perturbations in uniform flow is very small. This results in u^‘, v^‘, w^‘ << V∞.



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