Chap. XVII.
THEORY or TIIE MOTION OF FLUIDS.
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of water. But when the surface meets the current, we must add their velocities together,and divide the square of the sum by 60.
When the force which moves the surface of water at rest is given, and it is requiredto find what velocity that force will produce ; first find the height of a prism of waterhaving the same surface for its base, and whose weight would be equal to the given force;then seek the velocity relative to a fall equal to the height of the prism, which will bethat required.
If the force given move a surface against a current, first seek, as in the preceding case,the velocity answering to the height of the prism of water, regarding it as the sum of thevelocities of the current and of the surface, from which subtracting that of the current, thedifference will be the velocity with which the surface will remount.
To find the Velocity of a Current, the rough method wasformerly adopted of throwing a piece of wood into the water,and observing the space which it went over in a certain time;to effect this more accurately, M. Pitot invented an instru-ment consisting of two glass tubes open at the ends; thefirst, A B, is straight, and the second, C I), has one extremitycurved and funnel-shaped, EFG D; the whole is enclosed ina prism of wood to preserve it from accident. ’Hie tube isdivided into equal parts, like a barometer, expressed in inchesand lines, and is plunged perpendicularly into the water, sothat the entrance to the funnel may be opposed to the direc-tion of the current, in order that it may enter the funnel ;the water then rises in the two tubes, but at different heights.
'Hie line III represents its level: it can only rise in the first,
A B, to the height G B, which dips in the water, having onlyits weight to compel its rise, while the water which enters thecurved tube C D will rise to a height M K proportionate tothe velocity of the current, which, being considered as ac-quired by a fall of a certain height, the water will ascend tothe same height, and be sustained there by the impulse of thisvelocity, which, acting on the entrance, 1) E, of the tube, willbe in equilibrio with the weight of a column M K. Caremust always be taken to direct the funnel in the most rapidthread of the water, remarking the point where it riseshighest, without regarding whether this thread be straightor oblique: if it sometimes happen that an eddy makes thewater rise above the level corresponding to its velocity,after some little time it will assume its natural level: a stillday should also be selected, as the wind prevents it rising toits proper height.
Motion of Water in Conduit Pipes and open Canals. — M. Eytelwein observes that ahead ofwater may be divided into two parts, the one employed in producing velocity, the otherin overcoming friction, and that the latter height, employed in overcoming the frictionmust be directly as the length of the pipe and the circumference of the section, or as thediameter of the pipe, and inversely as the content of the section, or the square of thediameter, viz. on the whole inversely as the diameter; this height must also vary, like thefriction, as the square of the velocity.
To determine the velocity of the discharge of a pipe, when the height of the water in thereservoir above the point of discharge, and the length and diameter of the pipe, are given :multiply 2500 times the diameter of the pipe in feet by the height in feet, and divide theproduct by the length in feet, and add 50 times the diameter ; the square root of thequotient will be the velocity of the discharge in feet per second. Suppose the diameter ofthe pipe to be *375 feet, the height of the water in the reservoir above the point of discharge51 5 feet, and the length of pipe 14637 feet: then
2500 x *375 x 51‘5 48281*25
1*1637 + 50 x *375 14655*75
the square root of which is 1*816, the velocity in feet per second.
To determine the quantity of water a pipe will discharge when the height of the reser-voir above the place of discharge, the length of the pipe, and the diameter are known,multiply the area of the pipe in feet by the velocity in feet, as found by the above rule, andthe result will be the discharge in cubic feet per second.
If from these rules the equation for the quantity discharged be formed, and that quantity
he called Q, we have
Q* (
/ + S0rf\ 51542A / *
from whence the diameter of the pipe to supply a
given discharge may be found.
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