Consider the nonlinear dynamics of an artery as modelled by the continuity and momentum equations ∂R/∂t + v ∂R/∂x + (1 /

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Consider the nonlinear dynamics of an artery as modelled by the
continuity and momentum equations
∂R/∂t + v ∂R/∂x + (1 /2) R ∂v/∂x = 0 ,
∂v/∂t + v ∂v/∂x = − (α /ρ) ∂R/∂x .
Show that both these partial differential equations become the
same linear unidirectional wave equation for “small” disturbances
if we prescribe that the blood velocity is directly dependent upon
R by the relation
v = 2√ (2α/ρ) (√ R − √ R∗) .
What is the wave speed of the small disturbances? (Small
disturbances are those for which the artery is almost at rest, R ≈
R∗, and the blood is slow, v ≈ 0).