In working out his principle, Pascal showed dramatically how force can be multiplied with fluid pressure. He placed a long, thin tube of radius r =0.30 cm vertically into a wine barrel of radius R =21 cm, Fig. 10-62. He found that when the barrel was filled with water and the tube filled to a height of 12 m, the barrel burst. Calculate (3) the mass of water in the tube, and (6) the net force exerted by the water in the barrel on the lid just before rupture.

Solution 20P:

We have to calculate the mass of the water inside the tube and the force exerted by the water in the barrel on the lid just before rupture.

Step 1 of 3</p>

Concept:

The ratio of the mass of a substance to its volume is always constant, and it is known as the density of the substance. Mathematically, …(1)

Pressure on the body is defined as the force applied per unit cross-sectional area of the body. Mathematically, …(2)

Pressure due to liquid of density having its column height , is given as

…(3)

Step 2 of 3</p>

A] Using the above relation (1) between density, volume and mass of the water in the tube, we get,

Thus the mass of the water inside the tube is .