Velocity of water in a water tank

[dherr12]

Homework Statement

Take into account the speed of the top surface of the tank and shown that the speed of fluid leaving the opening at the bottom is v₁=sqrt(2gh/(1-(A²₁/A²₂))
P=Atmospheric pressure
d=density
v=velocity
g=gravity
h=height
A=Area

Homework Equations

P₁+1/2dv²+dgh=P₂+1/2dv²+dgh
v₁A₁=v₂A₂

The Attempt at a Solution

Atmospheric pressures cancel, densities cancel.
I substituted v₁A₁/A₂ into Bernoulli's equation.
I reduced and ended up with A₂/A₁(1+sqrt(2gh))=v₁

I cannot seem to reduce it to the correct answer.

Thank you!

 

[fzero]

You seem to have missed one of the velocity terms. You should be solving

$$\frac{1}{2}dv_2^2+dgh=\frac{1}{2}dv_1^2.$$