Flow rate

“ The advancing end of a flood wave may, while the 152 wave is rising and being formed, travel rapidly, but when the wave has been formed it travels at the ordinary rate of flow of the risen stream. The advancing end of a trough may, while it is being formed, travel rapidly, but after formation it travels at the ordinary rate of the fallen stream (Hydraulics, Chap. IX., Arts. 3 and 4) . Thus the rate at which a change in water-level travels down a stream depends at first on the amount of the rise or fall, but afterwards on the water-level of the risen or fallen stream. ”

“ Temperature gradient affects conduction rate Physical factors operate to control the rate of heat conduction much as they do to control the rate of water flow. Suppose we have a water tank with a smooth, open-ended pipe connected to the bottom. Provided the water level in the tank is maintained at a fixed point, the water pressure at the pipe inlet remains constant, and the water flows through and out of the pipe at a constant rate. ”

“ The relation between gradient and velocity is evident; that between volume and velocity is illustrated by every stream in time of flood, when its rate of flow is greatly increased. The relation between velocity and load is less obvious, but none the less definite. Every particle of sediment carried by a stream makes a draught on its energy, and energy expended in this way reduces the velocity. The draught on a stream’s energy of a particle carried in suspension is measured by its mass into the distance it would fall in a unit of time in still water. ”

“ It is difficult to set any definite figure for the percentage which the maximum rate of flow is of the average. Fluctuations above and below the average are greater the smaller the tributary population. ”

“ Moreover, he can be equally sure that his friend is sauntering up-stream, if the corks come past with a common interval exceeding three feet; and that he is sauntering down-stream, if the common interval is less than three feet. And, if, by some process of measuring, he can find out exactly how much greater or how much less than three feet the interval is, he can tell exactly how fast his friend is sauntering up-stream or down-stream. It would not matter how far down-stream the observer might be, so long as the stream's rate of flow remained unchanged ”

“ But in determining the capacity of reservoirs intended to yield a supply of water equal to the mean flow of two, three or more years, the error, though on the safe side, caused by assuming the evaporation to be proportional to the rainfall, is too great to be neglected. The evaporation slightly increases as the rainfall increases, but at nothing like so high a rate. Having determined this evaporation for the second driest consecutive year and deducted it from the rainfall—which, as above stated, cannot be less than 87% of the mean of 50 years—we may, as shown on fig. ”

“ Various formulæ for determining the rate of flow under varying conditions have been devised, but it will be sufficient for our present purpose to remark that the average velocity of water in sands does not appear to be more than 3 or 4 kilometres a year. ”

“ If there is no supply, it quickly runs out. If a small stream of water be let in at the top, a small supply of water may be maintained in the vessel. If a larger stream be admitted, the depth of water in the vessel will at once begin to increase, but at the same time the pressure on the bottom, and consequently the rapidity of the outward flow through the aperture, increases, and outflow and inflow soon come into equilibrium. If the supply be diminished, the level of the water sinks till the hydrostatic pressure causes the outflow to again equal the inflow. ”

“ If an ordinary pipe, connecting reservoirs open to the air, rises at any joint above the line of virtual slope, the pressure at that point is less than the atmospheric pressure transmitted through the pipe. At such a point there is a liability that air may be disengaged from the water, and the flow stopped or impeded by the accumulation of air. If the pipe rises more than 34 ft. above the line of virtual slope, the pressure is negative. ”

“ It is not probable that the subject of heat transfer in boilers will ever be on any other than an experimental basis until the mathematical expression connecting the quantity of fluid which will flow through a channel of any section under a given head has been found and some explanation of its derivation obtained. Taking the simplest possible section, namely, a circle, it is found that at low velocities the loss of head is directly proportional to the velocity and the fluid flows in straight stream lines or the motion is direct. ”

“ Again, the energy of a clear stream is entirely consumed in the friction of flow; and the friction bears a direct relation to its velocity. But if detritus be added to the water, then a portion of its energy is diverted to the transportation of the load; and this is done at the expense of the friction of flow, and hence at the expense of velocity. As the energy expended in transportation increases, the velocity diminishes. If the detritus be composed of uniform particles, then we may also say that as the load increases the velocity diminishes. ”

“ Since the rate at which water is supplied from the pump will always be proportional to the velocity of the machine, it follows that every fluctuation in this velocity will be indicated by the rising or subsiding of the level of the water in the cistern, and that level never can remain stationary, except at that exact velocity which supplies the quantity of water discharged by the pipe. ”

“ When the variation of pressure is very small, it is no longer safe to neglect the variation of level of the pipe. For that case we may neglect the work done by expansion, and then
precisely equivalent to the equation for the flow of water, z0 and z1 being the elevations of the two ends of the pipe above any datum, p0 and p1 the pressures, G0 and G1 the densities, and v the mean velocity in the pipe. This equation may be used for the flow of coal gas.
§ 92. Distribution of Pressure in a Pipe in which Air is Flowing.—From equation (7a) it results that the pressure p, at l ft. ”

“ In actual fluids, such as water or air, we know in fact that it is not so. It would, however, appear that in the ideal fluid of hypothesis any form of motion generated by an impulse in this manner will persist without change of form, and therefore the field of force and system of pressure by which the flow is generated may be taken as defining the form of flow for the steady state. ”

“ The natural curve which the sewage would follow in its downward path as it flowed out from the end of the sewer can then be drawn out for the various depths, taking into account the fact that the velocity at the invert and sides of the sewer is less than the average velocity of flow. ”

“ Streams are moving masses of indefinite length, completely or incompletely bounded laterally by solid boundaries. When the solid boundaries are complete, the flow is said to take place in a pipe. When the solid boundary is incomplete and leaves the upper surface of the fluid free, it is termed a stream bed or channel or canal.
(2) A stream bounded laterally by differently moving fluid of the same kind is termed a current.
(3) A jet is a stream bounded by fluid of a different kind.
(4) An eddy, vortex or whirlpool is a mass of fluid the particles of which are moving circularly or spirally. ”

“ Green says, "the flow was increased because the channel was increased, and the resultant of the natural forces with it." But if the resultant increases with the distance from the center of the earth, then why could he not increase the flow still more by running the tube to a great height above the fountain instead of below it? But even Mr. Green would hardly expect to increase the flow by such means. For it is well known that by confining the water of an artesian well to a tube in which it must rise above the ground, the natural flow is rapidly diminished as the height of the tube increases. ”

“ Rivers and pipes have their metres, so that now the velocity and volume of rivers and streams are measured and controlled, and floods prevented. The supplies for cities and for families are estimated, measured and recorded as easily as are the supplies of illuminating gas, or the flow of food from elevators. ”

“ Now, for any one customer the size and length of pipe will remain constant, but the flow of gas along the line will vary from hour to hour, consequently the pressure at his house may be expected to vary from hour to hour. ”

“ Many physicists who have investigated the laws of natural hydraulics maintain that, in consequence of direct obstruction and frictional resistance to the flow of the water of rivers along their banks, there is both an increased rapidity of current and an elevation of the water in the middle of the channel, so that a river presents always a convex surface. ”

“ The minimum velocity when full should therefore be about 2 feet per second. Under this condition, the velocity of 1 foot per second is not reached until the sewer is less than 18 per cent full. The velocity in small sewers should be made somewhat faster than in large sewers since the velocity of flow for small depths in small pipes is less than for the same proportionate depth in large pipes. The maximum permissible velocity of flow is fixed at about 10 feet per second in order to avoid excessive erosion of the invert. ”

“ The former part of the volume is occupied with discussion of the laws that govern stream-flow, rainfall, evaporation, ground storage, surface storage, and surface or flood flows. Gauging flows and the method of computing them are next considered. The local water systems are then described. The latter part of the book is devoted to generalizations as to water supply, chemical analyses, public water supplies, water power, evaporation, ground storage, effects of vegetation, and stream-flow; and a list of the developed water powers and the drainage systems is given in the appendix. ”

“ CHAPTER VI. GAUGING FLOW IN SEWERS. A method frequently adopted to gauge the flow of the sewage is to fix a weir board with a single rectangular notch across the sewer in a convenient manhole, which will pond up the sewage; and then to ascertain the depth of water passing over the notch by measurements from the surface of the water to a peg fixed level with the bottom of the notch and at a distance of two or three feet away on the upstream side. ”

“ To illustrate: the different countries may be compared to several tanks connected at the bottom by pipes, and containing water, the level of which, representing money value,62 is continually fluctuating with the amounts of water added to or drawn from each of the tanks. If the water rises higher in one tank than in others, a flow will set in from the higher to the lower until all are again on a level; but if the cause of the rise in the one tank continues, or if the cause extends to all the other tanks, the level in all the tanks may be greatly changed. ”

“ If the channel down which they flow after union has also the same declivity, then the joint stream will have a greater velocity than its branches, its capacity for transportation will be more than adequate for the joint load, and it will corrade its bottom. By its corrasion it will diminish the declivity of its bed, and consequently its velocity and capacity for transportation, until its capacity is equal to the total capacity of its tributaries. When an equilibrium of action is reached, the declivity of the main stream will be less than the declivities of its branches. ”

“ Computation of Flood Flow by Rational Method.—The rational method for the computation of storm-water run-off is described in Chapter III. An example of its application to storm sewer design is given here for the district shown in Fig. 25. [34] The computations are shown in Table 21. As in the preceding designs the table has been filled in from left to right and line by line. Computations have started at the upper end of laterals tributary to each junction. ”

“ If running water be employed, the outlet of the jacket is so disposed that the water gushes out immediately on leaving the cylinder, and that the flow is visible and accessible, in order that the temperature may be tested by the hand. ”

“ The rate of travel of the currents varies in accordance with the time they have been running. Directly after the turn there is scarcely any movement, but the speed increases until it reaches a maximum about three hours later and then it decreases until the next turn, when dead water occurs again. ”

“ The difference of pressure which creates the flow of air then is
The head, , which creates the velocity of flow, is equal to the height of a column of air of temperature which would give the pressure , or
By the laws governing the flow of fluids the theoretical velocity with which the current of air would move through is where is, as above, the head producing the flow. ”

“ It is unwise to place much reliance upon an estimated flow where this is the case. The formula may be used with confidence where the layers are artificially made, and where there is no uncertainty regarding the uniform character of the material. In most natural channels there are distinct lines of flow, and under considerable hydrostatic head or pressure these lines of flow would surely enlarge. There is a wide difference between permissible and dangerously excessive percolation through an earth [Pg 58] embankment. ”