Question

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

Answer 1

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?

Answer:

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