Q35 of 81 Page 273

Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel (figure 13-E11)?


The height of the vessel is H. Let the height of the hole be h.


The height of water above the hole is H-h.


therefore, the velocity with which water exits is


Let the time of flight be t



The horizontal distance travelled is



Now we need to maximize this function.





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31

Water flows through a tube shown in figure (13-E8). The areas of cross section at A and B are 1 cm2 and 0.5 cm2 respectively. The height difference between A and B is 5 Cm. If the speed of water at A is 10 cm s-1, find (a) the speed at B and (b) the difference in pressures at A and B.


 32

Water flows through a horizontal tube as shown in figure (13-E9). If the difference of heights of water column in the vertical tubes is 2 cm, and the areas of cross section at A and B are 4 cm2 and 2 cm2 respectively, find the rate of flow of water across any section.


 33

Water flows through the tube shown in figure (13-E10). The areas of cross section of the wide and the narrow portions of the tube are 5 cm2 and 2 cm2 respectively. The rate of flow of water through the tube is 500 cm3 s-1. Find the difference of mercury levels in the U-tube.


 34

Water leaks out from an open tank through a hole of area 2 mm2 in the bottom. Suppose water is filled up to a height of 80 cm and the area of cross section of the tank is 0.4 m2. The pressure at the open surface and at the hole are equal to the atmospheric pressure. Neglect the small velocity of the water near the open surface in the tank. (a) Find the initial speed of water coming out of the hole. (b) Find the speed of water coming out when half of water has leaked out. (c) Find the volume of water leaked out during a time interval dt after the height remained is h. Thus find the decrease in height dh in terms of h and dt. (d) From the result of part (e) find the time required for half of the water to leak out.