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GENERAL PRINCIPLES OF HYDRAULICS 461 
surface of a body. The following, laws of fluid friction have been 
established on the results of numerous experiments by Froude* and 
others. (1) The frictional resistance is independent of the fluid pressure. 
(2) The frictional resistance depends on the amount of surface of 
‘contact between the fluid and the body, and in general it may be taken 
a8 proportional to the area of contact surface. (3) The frictional re- 
sistance is proportional to the mth power of the relative velocity of the 
- fluid and body, where » is equal to 1 for very small velocities, but for 
velocities which occur in practical hydraulics varies from about 1°7 to 
about 2°2, and has an average value of 2. (4) At very small velocities 
the frictional resistance is independent of the nature of the surface of the 
body, but at ordinary velocities the frictional resistance increases very 
rapidly with the roughness of the surface of the body. (5) The frictional 
resistance is proportional to the density of the fluid. 
401. Wetted Perimeter—Hydraulic Mean Depth.—That part of the 
_ boundary of the cross section of a channel or pipe which is in contact 
with the water in it is called the 
wetted perimeter, and the area of the 
cross section of the stream divided by 
the wetted perimeter is called the 
hiudraulic mean depth, or the hy- 
aiutic mean ae Ne or the hydraulic WIG. (66°, Wig, 15. Bea. 768 
radius. In this work the hydraulic mean depth, or hydraulic mean 
radius, will be denoted by m. For example, in a channel of rectangular 
section (Fig. 756), having a breadth } and depth of water d, ma ‘ 
In a circular pipe (Fig. 757) of diameter d, running full, m = "42/rd = 4 
In the same pipe, running half full (Fig. 758), m =? / 57 =5 as for the 
full pipe. 
Some writers restrict the term hydraulic mean depth to channels, and 
apply the term hydraulic mean radius to circular pipes. 
402. Usual Velocities of Water in Pipes.—'The usual velocity in 
water mains is less than 5 feet per second. Unwin gives the formula 
v=1'45d+2 as the expression of a fair rough rule for the velocity of 
water in pipes used in town’s supply, where v is the velocity of the water 
in feet per second, and d is the diameter of the pipe in feet. A velocity 
of 10 feet per second is fairly common in the pipes of centrifugal pumps. 
Velocities greater than 15 feet per second are very unusual in pipes. 
High velocities involve great loss of energy in friction when the pipes are 
long, and since the loss of energy per lb. of water delivered is greater the 
smaller the pipe, the velocity should be lower the smaller the pipe. 
403. Critical Velocity of Water in Pipes.—Professor Osborne 
Reynolds made most interesting experiments on the flow of water in 
pipes with apparatus roughly shown in Fig. 759. AB is a tank 6 feet 
long, 18 inches deep, and 18 inches wide, containing water. CD is a 
glass tube provided with a trumpet-shaped mouthpiece at C, and pro- 
* For the results of Froude’s experiments see British Association Reports, 
