When a pipe flow suddenly expands, low$-$speed recirculating eddies appear in the corners and the flow gradually expands to $A_2$ downstream. Use the suggested control volume for incompressible steady flow and assume that $p_2$~~$p_1$ on the corner annular ring as shown to show that the downstream pressure is given by

$p_2$~~$p_1+V_1^2\frac{A_1}{A_2}(1-\frac{A_1}{A_2})$

Is this the same as what you would expect from the Bernoulli equation?