Find the speed of fluid using bernoulli

[songoku]

Homework Statement

Find v

Homework Equations

Bernoulli

The Attempt at a Solution

Here's what I've done

I took the surface of water as first reference and the right-end of the pipe as second reference, so:

P₁ + 1/2 ρV₁² + ρgh₁ = P₂ + 1/2 ρV₂² + ρgh₂

P₁ = P₂ = P_atm and I assumed v₁ = 0 and h₁ = 0, then the equation became:
0 = 1/2 ρV² - ρgh
v = √(2gh) ---> ta daa, I'm finished with degree of confidence 0.5 % that my answer is correct.

Do I get it right? Thanks

 

[emailanmol]

It is 100% correct.

However to build up your confidence let's just clear up how we got here.

After applying the equations, we realized two things.Pressure at surface and Pressure at exit are same as they are open to atmosphere.

Then we made velocity zero.
That was using equation of continuity as surface area of water is much greater than that of pipe.

 

[songoku]

Ah I get it. Thanks for the help