CHAPTER VIII. 



Pipe flow Experimental Formulae Darcy Hagen D'Aubuisson Prony Eyteiwein 

 Weisbach Kutter Rational formula for pipe flow Reynolds Unwin Lawton 

 Thrupp Tutton Values off and 6' for various pipes Fire hose Resistance with oil 

 Sand Mean velocity Distribution of velocity Measurement of discharge Pitot tube 

 Relation of pipe diameter to volume discharged Gradual and sudden stoppage of 

 motion in an uniform pipe Water hammer. 



ART. 63. PIPE FLOW. 



ONE very important effect of fluid friction is experienced in the resist- 

 ance to the flow of water through a pipe. This resistance can only be 

 overcome by a gradual fall of pressure in the liquid, in the direction of 

 motion, and, reasoning from analogy to the resistance experienced by a 

 plane surface moving through water, it might be inferred that, with 

 sinuous motion, the total resistance R would equal f 8 v n , 



f f depends chiefly on the surface of the pipe and to a smaller 



where J extent on viscosit y- 



I S = area of wetted surface. 



* n depends on the pipe surface, and is approximately equal to 2. 

 Putting A = sectional area of pipe in square feet. 

 P = length of perimeter of pipe. 



PI Pv = fell in pressure in Ibs. per square foot over a length 

 I feet of pipe. 

 This becomes 



(1) 



ean depth l and 

 commonly denoted by m, so that (1) may be written 



A 



Here = ; - is termed the hydraulic mean depth l and is 

 P perimeter 



77 r 2 r d ... 



In the case of a circular pipe m = = - ; == $ - - -^, so that, if in 



1 Tf the mass of water in the pipe be imagined as distributed over a horizontal surface of 

 the same area as the walls of the pipe, its depth will then be the same as the hydraulic mean 

 depth for the pipe. 



