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## Main Question or Discussion Point

Consider two cylindrical containers of the same diameter. Fill them with a liquid to different levels. We all know that the liquid can be "siphoned" from one container to the other using a thin hose, which we will consider to be thin and of uniform diameter.

Bernoulli's Equation can be used to derive the flow rate (which is essentially the same as Torricelli's Theorem).

However, consider applying Bernoulli's Equation to the free surface of each container.

P1 + pgh1 + 1/2 p v1^2 = P2 + pgh2 + 1/2 p v2^2

Because the cylinders have the same diameter, v1 = v2.

Because a free surface is at atmospheric pressure, P1 = P2.

Bernoulli's Equation then reduces to h1 = h2, which makes no sense.

Does anyone have any insight to why Bernoulli's Equation does not work in this case?

Bernoulli's Equation can be used to derive the flow rate (which is essentially the same as Torricelli's Theorem).

However, consider applying Bernoulli's Equation to the free surface of each container.

P1 + pgh1 + 1/2 p v1^2 = P2 + pgh2 + 1/2 p v2^2

Because the cylinders have the same diameter, v1 = v2.

Because a free surface is at atmospheric pressure, P1 = P2.

Bernoulli's Equation then reduces to h1 = h2, which makes no sense.

Does anyone have any insight to why Bernoulli's Equation does not work in this case?