HYDRODYNAMICS. 



Of the Discharge of Fluids through Apertures in the Bottom and 

 Sides of Vessels. 



476. If a fluid be made to pass through a canal or tube of 

 variable bore, kept constantly full, and the velocity be the same 

 in every part of the same section, since for any given time the 

 same quantity of fluid must pass through every section, this 

 quantity must be equal to the area of the section multiplied by 

 the velocity, rf, rf', being the areas of two sections, and t>, i/, the 

 velocities at these sections, we shall have 



6 -o = tf' i>', 

 and hence 



6 : 6' :: ^ : v, 



lhat is, the velocities in different sections are inversely as* the areas of 

 the sections. 



The case here supposed is purely theoretical, and can never 

 occur in practice, since on account of friction, the velocity is 

 always greatest at the surface in a canal, and at the axis in a 

 tube. 



477. Let MNOP represent a vessel filled with a fluid 



to G#, CD an aperture, very small compared with the bottom 

 MP, CIKD, the column of fluid directly above the aperture, and 

 CABD the lowest lamina or stratum of this fluid, immediately 

 contiguous to the aperture. Also let v denote the velocity ac- 

 quired by a heavy body in falling freely through BD, the height 

 of the stratum, and u the velocity which the same stratum would 

 Mech. 47 



