DISTRIBUTION OF VELOCITY IN PIPE 211 



of loose material which may be carried in suspension, at moderate 

 velocities of flow the material is rolled along the bottom of the pipe or 

 channel, with comparatively great loss of head. As the velocity increases, 

 at a certain point, depending on the size and weight of the particles, 

 these are picked up and carried in suspension in the water. Experiments 

 on sand, having grains varying from '16 m.m. to '75 m.m. in diameter 

 show that for a 1-inch pipe this velocity is about 3*5 feet per second, 

 while for a 3-inch pipe it is about 4 feet per second, and for a 32-inch 

 pipe about 9 feet per second. 1 With grains of approximately uniform 

 size the minimum resistance is attained with this velocity. With grains 

 of widely varying size the minimum resistance is attained with a velocity 

 somewhat less than is necessary to pick up the larger grains. With fine 

 sand the additional loss of head is about 25 per cent, of that due to the 

 water alone, for each 1 per cent, of added sand. For velocities higher 

 than are necessary to cause suspension, the proportion of solid matter 

 which may be carried is approximately independent of the velocity. 

 Experiments show that the proportion of sand to water may exceed 

 50 per cent. Where a sand ejector is used this proportion depends 

 largely on the form of ejector. 1 This is on similar lines to the ordinary 

 jet pump, and is situated at the bottom of the sand hopper, the sand 

 being carried into suspension by means of a number of small water jets 

 surrounding the inlet to the ejector 



Mixtures of Water and Air. See Art. 189. 



ART. 67. VARIATION OF VELOCITY OVER THE CROSS- SECTION OF A 

 CYLINDRICAL PIPE. 



Experiments show that with sinuous motion through a pipe the 

 velocity of flow is much greater at 

 the centre than near the walls. wmw 

 From experiments on pipes with 

 diameters ranging from 8 inches 

 to 19 inches Darcy deduced the 

 formula 



(1) 



FIG. 95. 

 as giving the velocity v at any 



radius x of a pipe of radius a. When the unit of length is the metre, 

 k = 11-8, and when the foot, & = 20'4. The volume of the solid of 



1 " Transactions American Society Civil Engineers," Vol. 57, 1906. 



p 2 



