A cylindrical barrel is completely full of water and sealed at the top except fo

Question

A cylindrical barrel is completely full of water and sealed at the top except for a narrow tube extending vertically through the lid. The barrel has a diameter of 80.0 cm, while the tube has a diameter of 1.10 cm. You can cause the lid to pop off by pouring a relatively small amount of water into the tube. To what height do you need to add water to the tube to get the lid to pop off the barrel? The lid pops off when the vector sum of the force of the atmosphere pushing down on the top of the lid and the force of the water pushing up on the bottom of the lid is 390 N up. Also, use g = 9.8 m/s2.

What is the height of water in the tube in cm?

Explanation / Answer

The lid has a diameter of 80cm, so its radius = 0.4m.
Lid's area (ignoring the hole) = r² = x 0.4² = 0.503m²
(The area of the 1cm diameter hole is negligible compared to the lid's area).

P = F/A. So a force difference of 390N on the lid means a pressure difference of 390/0.503
=775Pa

This pressure difference is due to the extra pressure produced by the column of water in the narrow tube:
height, h, of water in the narrow tube
density of water, = 1000kg/m³
g = 9.8m/s²

P = gh
775 = 1000 x 9.8 x h
h = 0.0790m
= 7.9cm (to 2 significant figures)

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