Principles of the Mechanics of Machinery and Engineering

§ 345. Prismatic Vessels.-If a cistern from which water flows through an orifice at the side or bottom, has no influx to it from any other side, a gradual sinking of the surface of ,vater will take place, and the cistern at last empty itself. If, further, the quantity of influx Q, be greater or less than the quantity of efflux ,.,. F ✓ 2 g '1., the sttrface of water will then rise or fall until the head of water h = _!__ ( Q ) 2 , and after this the head of water and the velocity of 2g ,.,. F efflux will remain unaltered. Our problem, then, is to find how the time, the rise and fall of the water, and the emptying of vessels of given form and dimensions, depend on each other. The efflux from a prismatic vessel presents the most simple case when it takes place through an opening in the bottom, and when there is no efflux from above or below. If x is the variable head of water FG1, F the area of the orifice, and G the transverse section of the vessel .11.C, Fig. 473, we have then the theoretical velocity of efflux v = ✓ 2 g x, the theo• Fig. 479. retical velocity of the falling surface of the water F F = G v = G ✓ 2 gx, and the eff ective velocity "' F v1 = ✓ 2 gx. At the commencement: G x = FG = h, and at the end of the efflux x = O, therefore, the initial velocity is: