According to your equation, what is the functional relationship between the height of the water h_1 and the speed of the flow v_2 at Point 2

This question is incomplete, the complete question is;

Starting with the full Bernoulli’s equation, simplify the equation for the case diagrammed below, where Point 1 is at the top of the water at height h1, with negligible flow speed v1=0, and Point 2 is at height h2=0. Both Point 1 and Point 2 are open to the atmosphere so P1 = P2 = Patm.

According to your equation, what is the functional relationship between the height of the water h1 and the speed of the flow v2 at Point 2?

the functional relationship between  the height of the water h1 and the speed of the flow v2 at Point 2 is v2 = √2gh1

Explanation:

Gravitational acceleration = g

Density of water = P

Pressure of the water at point 1 = p1 = patm

Speed of the water at point 1 = v1 = 0 m/s

Height of point 1 = h1

Pressure of the water at point 2 = p2 = patm

Speed of the water at point 2 = v2

Height of point 2 = h2 = 0 m

Now, Using Bernoulli's equation at point 1 and 2,

p1 + Pv1²/2 + Pgh1 = p2 + Pv2²/2 + Pgh2

patm + P(0)²/2 + Pgh1 = patm + Pv2²/2 + Pg(0)

Pgh1 = Pv2²/2

gh1 = v2²/2

v2² = 2gh1

v2 = √2gh1

Therefore the functional relationship between  the height of the water h1 and the speed of the flow v2 at Point 2 is v2 = √2gh1

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