d of the the pisto pressure fic e valve br cation betwe Dre steam f the m he lap may the rar 25, by the counting a motion, to steame rics, que te direc of the eccentrics are turned towards the link. In the case of new arrangements of engine, it is advisable to make a skeleton model in paper of the link and its connexions, so as to obtain full assurance that it works in the best way. VELOCITY OF WATER IN RIVERS, CANALS, AND PIPES, When a river runs in its bed with a uniform velocity, the gravitation of the water down the inclined plane of the bed, is just balanced by the friction. In the case of canals, culverts, and pipes, precisely the same action takes place. The head of water, therefore, which urges the flow through a pipe, may be divided into two parts, of which one part is expended in giving to the water its velocity, and the other part is expended in overcoming the friction. If water be let down an inclined shoot, its motion at the top will be slow, but will go on accelerating until the friction generated by the high velocity will just balance the gravitation down the plane, and after this point has been attained, the shoot may be made longer and longer without any increase in the velocity of the water taking place. In the case of a ball falling in the air or in water, the velocity of the descent will go on increasing until the resistance becomes so great as to balance the weight; and, in the case of a steam vessel propelled through the water, the speed will go on increasing until the resistance djust balances the tractive force exerted by the engines, when the is shifte of the ther end Centr ther speed of the vessel will become uniform. In all these cases the The resistance which is occasioned by the friction of water friction does not increase quite so rapidly at high velocities as the square of the speed. It is easy to determine the friction in lbs. per square foot of any given pipe or conduit, with any given velocity of the stream, when the slope or declivity of the surface of the water is known. For as the gravitation down the inclined plane of the conduit just balances the friction, the friction in the whole length of the conduit will be equal to the whole weight of the water in it, reduced in the same proportion as any other body descending an inclined plane. Thus, if the conduit be 2,000 feet long, and have 1 foot of fall in that length, the total friction will be equal to the total weight of the water divided by 2,000, and the friction per square foot will be equal to this 2000th part of the weight of the water divided by the number of square feet exposed to the water in the conduit. The friction will in all cases vary as the rubbing surface, or, what is the same thing, as the wetted perimeter As a cylindrical pipe has a less perimeter than any other form, it will occasion less resistance than any other form to water passing through it. In like manner, a canal or a ship with a semicircular cross section will have the minimum amount of friction. The propelling power of flowing water being gravity, the amount of such power will vary with the magnitude of the stream; but the resisting power being friction, which varies with the amount of surface, or in any given length with the wetted perimeter, it will follow that the larger the area is relatively with the wetted perimeter, the less will be the resistance relatively with the propelling power, and the greater will be the velocity of the water with any given declivity. Now, as the circumference or perimeter of a pipe increases as the diameter, and the area as the square of the diameter, it is clear, that with any given head, water will run more swiftly through large pipes than through small; and in like manner with any given proportion of power to sectional area, large vessels will pass more swiftly than small vessels through the water. The sectional area of a pipe or canal divided by the wetted perimeter, is what is termed the hydraulic mean depth, and this depth is what would result if we suppose the perimeter to be bent out to a velocities quare foot of the stra ter is kno the co length of th ater in it escending ng, and by equal to th frictio eight or t to the the ra perize her form terpa straight line, and the sectional area to be spread evenly over it, TO DETERMINE THE MEAN VELOCITY WITH WHICH WATER WILL RULE.-Multiply the hydraulic mean depth in feet by twice the Example.-What is the mean velocity of a river falling a foot in the mile, and of which the mean hydraulic depth is 8 feet? Here 8 x 216, the square root of which is 4, and this multiplied by 55: = 220, which will be the mean velocity of the stream in feet per minute. In cylindrical pipes running full, the hydraulic mean depth is one-fourth of the diameter. For the hydraulic mean depth being the area divided by the wetted perimeter,it is •7854d2 d 3.1416d * 4 } *The surface, bottom, and mean velocities of rivers have fixed relations to one another. Thus, if the surface velocity in inches per second be denoted by V, the mean velocity will be (V + 0·5)~/V and the bottom velocity by (V + 1) −2 V. With surface velocities therefore of 4, 16, 32, 64, and 100 inches per second, the corresponding mean velocities will be 2-5, 12.5, 26-8, 56-5, and 90.5 inches per second, and the corresponding bottom velocities will be 1, 9, 21-6, 49, and 81 inches per second. The common rule for finding the number of cubic feet of water delivered each minute by a pipe of any given diameter is as follows:-Divide 472 times the square root of the fifth power of the diameter of the pipe in inches by the square root of the quotient obtained by dividing the length of the pipe in feet by the head of water in feet. Hawksley's rule for ascertaining the delivery in gallons per hour is as follows:-Multiply 15 times the fifth power of the diameter of the pipe M. Prony has shown by a comparison of a large number of experiments that if H be the head in feet per mile required to balance the friction, V the velocity of the water through the pipe in feet per second, and D the diameter of the pipe in feet, then This equation is identical with that which has been used by Boulton and Watt in their practice for the last half century, and which is as follows: If I be the length of the main in miles, V the velocity of the water in the main in feet per second, D the diameter of the pipe in feet, and 2.25 a constant, This equation put into words gives us the following Rule: TO DETERMINE THE HEAD OF WATER THAT WILL BALANCE THE FRICTION OF WATER RUNNING WITH ANY GIVEN VELOCITY THROUGH A PIPE OF A GIVEN LENGTH AND DIAMETER. RULE.-Multiply 2.25 times the length of the pipe in miles by the square of the velocity of the water in the pipe in feet per second, and divide the product by the diameter of the pipe in feet. The quotient is the head of water in feet that will balance the friction. The law indicated by this Rule is expressed numerically in the Tables on pp. 204, 205. in inches by the head of water in feet, and divide the product by the length of the pipe in yards. Finally, extract the square root of the quotient, which gives the delivery in gallons per hour. The annual rain-fall in England varies from 20 to 70 inches, the mean being 42 inches, and it is reckoned that about ths of the rain-fall on any given area may be collected for storage. A cubic foot of water is about 62 gallons, and it is found in supplying towns with water that about on the average 16 gallons per head per day are required in ordinary towns, and 20 gallons per head per day in manufac turing towns, but the pipes should be large enough to convey twice this quantity. In the rainy districts of England collecting reservoirs should contain 120 days' supply, and in dry districts 200 days' supply. Service reservoirs are usually made to contain 8 days' supply. The mean daily evaporation in England is '08 of an inch, and the loss from the overflow of storm water is reckoned to be about 10 per cent. e number d e required ngh the p feet, then ANCE TE VELOCIT Explanation of the Tables.-The top horizontal row of figures represents either the diameter of a cylindrical pipe, or four times the area of any other shaped pipe divided by the circumference, or four times the area of the cross section of a canal, divided by the sum of all its sides, or bottom and sides, all being in inches. The first vertical column indicates the slope of the pipe or canal, that is, the whole length of the pipe or canal, divided by the perpendicular fall. Any number in any other column indicates the velocity, in inches per second, with which water would run through a pipe of such a diameter as the number at the head of such column expresses, having such a slope as that number in the first column expresses which is horizontally against such velocity. Example 1.-With what velocity will water run through a pipe of 16 inches diameter, its length being 8,000 feet, and fall 16 feet? Here the slope manifestly is 8,000+16=500. Against 500 in the first column, and under 16, the diameter in the top row of figures, the number 29.8 is found, which is the velocity in inches per second. Example 2.-With what velocity will water pass through a pipe of 21 inches diameter, having a slope of 900? 21 is not found in the head of the Table, in which case such a number must be found in the top row as will bear such proportion to 21 as some other two numbers in the top row bear to each other, and these latter numbers should be as near to 21 as they can be found. In this case it will be seen that 18 is to 21 as 6 is to 7, or (for compliance with the indication just mentioned) rather as 12 to 14, or still better as 24 to 28. Then say as the velocity (against 900, the slope) under 24 is to 28 (287), so is the velocity under 18 (227) to that of 21 (viz. 24-7) the velocity in inches per second. By the same process may the velocity for slopes be found or assigned, which are not to be found in the first column of the Table, proceeding with proportions found in the vertical column instead of the horizontal rows; the first vertical column |