74 MECHANICS 



Velocity of Flow. If a hole is made in the side of a tank 

 filled with water, the water will issue therefrom with a velocity 

 depending on the head of water above the opening. 



When water flows in a pipe, a ditch, or a channel of any 

 kind, the velocity is not the same at all points, because the 

 cross-section of the channel is not the same at all points, and 

 also because of friction. In such cases, the mean velocity is 

 taken in all calculations. The mean velocity is that velocity 

 which, being multiplied by the area of the cross-section of 

 the stream, will equal the total quantity discharged. 



Flow of Water in Pipes. For straight cylindrical pipes of 

 uniform diameter, the mean velocity of discharge may be calcu- 

 lated by the formula 



in which V m = mean velocity of discharge in feet per second ; 

 h = total head in feet = vertical distance between 

 the level of water in reservoir and the point 

 of discharge; 



I = length of pipe, in feet; 

 d = diameter of pipe, in inches; 

 / = coefficient of friction. 



The head is always taken as the vertical distance between 

 the point of discharge and the level of the water at the source, 

 or point from which it is taken, and is always measured in 

 feet. It matters not how long the pipe is, whether vertical or 

 inclined, whether straight or curved, nor whether any part of 

 the pipe goes below the level of the point of discharge or not; 

 the head is always measured as stated above. 



EXAMPLE. What is the mean velocity of efflux from a 

 C-in. pipe, 5.780 ft. long, if the head is 170 ft.? Take /=. 021. 

 SOLUTION. Substituting in formula 1, 



F m = 2.315 \/ -- =6.69 ft. per sec. 



\.021X5,780+(.125X6) 



When the pipe is very long compared with the di 

 as in the foregoing example, use may be made of the formula 



iameter, 

 y be made of the 



fu 

 V? 



V m = '-'.:; I >\ .. (2) 



