Question

How would you use Bernoulli's and continuity eqn to find force lifting bird up?

Please explain.

Answer 1

The required force lifting the bird is

P = F/A

F = PA

here p is pressure

from the Bernoulis equation

P1 + 1/2 rho v1^2 + rho g h1 = P2 + 1/2 rho v2^2 + rho gh2

h1 = h2

P1 - P2 = 1/2 rho v2^2 - 1/2 rho v1^2

from the equation of continituty

A1 v1 = A2 v2

v2 = A1v1/A2

P1 - P2 = 1/2 rho ( v2^2 - v1^2) = 1/2 rho ((A1v1/A2)^2 - v1^2

           then force

F = ( P1- P2) A

   = (1/2 rho ((A1v1/A2)^2 - v1^2) A