Mechanical Properties of Fluids · Question 1

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If H= ( 169 )h, then the ratio t1/t2 is .

A table tennis ball has radius (3/2) 10-2 m and mass (22/7) 10-3 kg. It is slowly pushed down into a swimming pool to a depth of d = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed v, without getting wet, and rises up to a height H. Which of the following option(s) is(are) correct? [Given: = 22/7, g = 10 m s-2, density of water = 1 103 kg m-3, viscosity of water = 1 10-3 Pa-s.]

1. The work done in pushing the ball to the depth d is 0.077 J.
2. If we neglect the viscous force in water, then the speed v = 7 m/s.
3. If we neglect the viscous force in water, then the height H = 1.4 m.
4. The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is 500/9.

A spherical soap bubble inside an air chamber at pressure P0 = 105 Pa has a certain radius so that the excess pressure inside the bubble is P = 144 Pa. Now, the chamber pressure is reduced to 8P0/27 so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure P in both the cases to be much smaller than the chamber pressure. The new excess pressure P in Pa is .