Question

Conical flow is rotational according to the result obtained from Crocco’s theorem.

(a) True

(b) False

This question was posed to me in semester exam.

My question is based upon Quantitative Formulation in division Linearized and Conical Flows of Aerodynamics

Answer 1

The correct choice is (b) False

The best I can explain: Based on Crocco’s theorem, for a steady floe the relation is given by

T∇s = ∇h0 – V × (∇ × V)

Therefore the vorticity is related to total enthalpy and gradient as (on rearranging the terms):

V × (∇ × V) = ∇h0 – T∇s

In a flow having a change in enthalpy or entropy would result in a rotational flow, but since for conical flow, the assumptions result in both change in entropy and enthalpy being zero, we get

V × (∇ × V) = 0

Since curl of velocity i.e. vorticity is zero, thus the flow is irrotational.