2.  More Fluids 
November 30, 2010

4. MC Question
In the figure, a tall cylindrical empty tank with a small side hole of square shape near its bottom is shown. The area of the hole is A. Water flowing with a velocity ‘v’ through a pipe of circular cross section having the same area A (as that of the hole) starts falling vertically down in to the tank. Which one of the following statements is correct?
(a) No water can remain in the tank
(b) The height of water column in the tank will go on increasing
(c) The height of water column in the tank will increase initially and will remain steady at v/2g
(d) The height of water column in the tank will increase initially and will remain steady at √(v/2g)
(e) The height of water column in the tank will increase initially and will remain steady at v2/2g.

7. MC Question
Water is flowing steadily out through the end of a vertical pipe (fig) with a velocity of 4 ms–1. At what distance from the end of the pipe will the area of cross section of the stream of water be (2/3)A where A is the area of cross section of the pipe?
(a) 0.5 m
(b) 1 m
(c) 1.5 m
(d) 2.2 m
(e) 2.5 m

8. An underground pipe carries water of density 1000 kg/m3 to a fountain at ground level, as shown above. At point A, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0 x 10-4 m2 . At ground level, the pipe has a cross-sectional area of 0.50 x 10-4 m2 . The water leaves the pipe at point B at a speed of 8.2 m/s.
(a) Calculate the speed of the water in the pipe at point A.
(b) Calculate the absolute water pressure in the pipe at point A.
(c) Calculate the maximum height above the ground that the water reaches upon leaving the pipe vertically at ground level, assuming air resistance is negligible.
(d) Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60∞ from the level ground, assuming air resistance is negligible.