V = sqrt(2gh) vs Bernouli equation contradiction?

[jeffp898]

#112 EK Physics review:

A spigot was opened at the bottom of a barrel full of water and the water was allowed to run through the spigot until the barrel was empty. Which of the following describes the speed of the water flowing through the spigot as the barrel emptied?

Answer: Always decreasing

V = sqrt(2gh)

Simple math, BUT according to Bernouli's as pressure decreases velocity increases, and since Pressure = density(g)👍 as y decreases as the water is drained from the barrel the Pressure decreases and the velocity should increase! Intuitively the answer makes sense but according to these equations it is the opposite? Where is my misconception?

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[Isoprop]

#112 EK Physics review:

A spigot was opened at the bottom of a barrel full of water and the water was allowed to run through the spigot until the barrel was empty. Which of the following describes the speed of the water flowing through the spigot as the barrel emptied?

Answer: Always decreasing

V = sqrt(2gh)

Simple math, BUT according to Bernouli's as pressure decreases velocity increases, and since Pressure = density(g)👍 as y decreases as the water is drained from the barrel the Pressure decreases and the velocity should increase! Intuitively the answer makes sense but according to these equations it is the opposite? Where is my misconception?

The pressure at the spigot is ambient, atmopheric pressure and not depth pressure. Since the spigot is exposed to the atmosphere, the pressure at that point is 1 atm or 101 kPa.

The equation is actually Bernoulli's principle. Take two points, the point at the surface on top of the barrel and the point on the spigot. Let the spigot be y = 0.

(surface) P + ρgy + ½ρv² = P + ρgy + ½ρv² (spigot)


Since the pressure is the same on both ends, the velocity of the water at the surface is close to zero, and the y at the spigot is defined at 0, we can cancel P on both sides and eliminate ½ρv² for the surface and ρgy for the spigot. Thus:

(surface) ρgy = ½ρv² (spigot)

Rearranging for velocity and canceling out the densities, we get the equation you cited.

 

[jeffp898]

Thanks 🙂