HYDRAULICS 351 



HYDRAULICS 



GENERAL PRINCIPLES 



Hydraulics treats of liquids in motion, particularly of the flow 

 of water through orifices, pipes, and channels. 



The quantity of water, in cubic feet, flowing through a 

 channel or a pipe in 1 sec. is called the discharge of the channel 

 or the pipe in cubic feet per second and is denoted by Q. It is 

 equal to the mean, or average, velocity of flow through the 

 given section multiplied by its area, or 



Q = t/A, 



in which v is the mean velocity, in feet per second, and A the 

 area, in square feet. If the area of the channel or pipe varies, 

 the mean velocities vary inversely as the corresponding cross- 



A. i, 



sections; or, = , 



i>b Aa. 



A a , v a and A^, v& denoting, respectively, areas ,and correspond- 

 ing velocities at two different cross-sections. 



Hydrostatic Head and Pressure Head. When water con- 

 tained in any vessel or pipe discharges freely into the atmos- 

 phere, the velocity of discharge v, in feet per second, if frictional 

 and other resistances are neglected, is equal to 



v= ^2gh 



in which h is the vertical distance in feet of the point of dis- 

 charge from the level of the water, and g = 32. 16. This velocity 

 is produced by the pressure due to the weight of a column of 

 .water of the height h, the latter being called the static or 

 hydrostatic head. 



The water in the pipe or vessel may be subjected to an 

 external pressure, thus giving an intensity of pressure greater 

 than that due to the static head, or owing to losses during the 

 flow, it may have an intensity of pressure which is smaller than 

 that due to the static head. Let p be the intensity of pressure 

 in pounds per square inch, and v' the velocity due to this pres- 

 sure; then, 



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