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 0.900 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 410 N up. Also, use g = 9.8 m/s2.

The height of water in the tube is  cm.

Explanation / Answer

given Diameter D = 80 cm or 0.8 m

then Radius r = D/2 = 0.8/2 = 0.4 m

radius of lid is too small and can be ignored.

Pressure P = Force/area = rho gh

rho is density of water = 1000 kg/m^3

g is accleration due to gravity = 9.8 m/s^2

h is height = ?

area = pi r^2

so

410/(3.14 * 0.4^2) = 1000* 9.81 *h
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            h = 0.0831 m or 8.31 cm is the height of water
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