A cylinder with diameter, D, is filled with a liquid with density, p. A disk wit

Question

A cylinder with diameter, D, is filled with a liquid with density, p. A disk with the same diameter as the cylinder with a small hole in its middle is placed on top of the liquid. Immediately after the disk is placed on the liquid, a stream of liquid shoots out of the hole, and travels to a height, h, above the disk. What is the mass, M, of the disk? You can neglect the size of the hole compared to the diameter of the cylinder, and assume that no water slips between the walls of the cylinder and the edges of the disk.

Explanation / Answer

speed of the water from the hole, v = sqrt(2*g*h)

use Bernoulli's equation

P1 + (1/2)*rho*v1^2 = P2 + (1/2)*rho*v2^2

here P1 = Pa + Mg/A (just below the disk)
v1 = 0 (just below the disk)
P2 = Pa (at the hole)

v2 = v (at the hole)

so,

(Pa + M*g/A) + 0 = Pa + (1/2)*rho*v^2

M*g/(pi*D^2/4) = (1/2)*rho*(2*g*h)

4*M/(pi*D^2) = rho*h

M = rho*h*pi*D^2/4 <<<<<<------------Answer

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