A barrel with a diameter of 40 cm can hold water as high as 3m before its bottom

Question

A barrel with a diameter of 40 cm can hold water as high as 3m before its bottom bursts.

The barrel on the right has the same bottom construction but is only 85 cm high.

It has a small opening of diameter of only 5 mm in the lid with a thin tube of the same diameter attached to it.

How high can one fill the water in the tube without bursting at the barrel?

The picture:   http://imgur.com/IJjjYQ8

A barrel with a diameter of 40 cm can hold water as high as 3m before its bottom bursts. The barrel on the right has the same bottom construction but is only 85 cm high. It has a small opening of diameter of only 5 mm in the lid with a thin tube of the same diameter attached to it. How high can one fill the water in the tube without bursting at the barrel?

Explanation / Answer

From Pressure = F/A, we can find the force

In the first barrel

F = PA

P = pgh

F = (1000)(9.8)(3)(pi)(.2)^2

F = 3694.5 N

For the second barrel, we need the same force

The force from the barrel water = pghA = (1000)(9.8)(.85)(pi)(.2)^2 = 1046.8 N

We need an additional amount (3694.5 - 1046.8) = 2647.7

F = pghA

2647.7 = (1000)(9.8)(h)(pi)(2.5 X 10^-3)^2

h = 13760 m

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