Of course, the horse power to be obtained from a stream determines the size of the paddle wheel or turbine which can be run by it.  It would be possible to construct a turbine so large that the stream would not suffice to turn the wheel; for this reason, the power of a stream is carefully determined before machine construction is begun, and the size of the machinery depends upon the estimates of the water power furnished by expert engineers.

A rough estimate of the volume of a stream may be made by the method described below:—­

Suppose we allow a stream of water to flow through a rectangular trough; the speed with which the water flows through the trough can be determined by noting the time required for a chip to float the length of the trough; if the trough is 10 feet long and the time required is 5 seconds, the water has a velocity of 2 feet per second.

[Illustration:  FIG. 123.—­Estimating the quantity of water which flows through the trough each second.]

The quantity of water which flows through the trough each second depends upon the dimensions of the trough and the velocity of the water.  Suppose the trough is 5 feet wide and 3 feet high, or has a cross section of 15 square feet.  If the velocity of the water were 1 foot per second, then 15 cubic feet of water would pass any given point each second, but since the velocity of the water is 2 feet per second, 30 cubic feet will represent the amount of water which will flow by a given point in one second.

175.  Quantity of Water Furnished by a River.  Drive stakes in the river at various places and note the time required for a chip to float from one stake to another.  If we know the distance between the stakes and the time required for the chip to float from one stake to another, the velocity of the water can be readily determined.

The width of the stream from bank to bank is easily measured, and the depth is obtained in the ordinary way by sounding; it is necessary to take a number of soundings because the bed of the river is by no means level, and soundings taken at only one level would not give an accurate estimate.  If the soundings show the following depths:  30, 25, 20, 32, 28, the average depth could be taken as 30 + 25 + 20 + 32 + 28 / 5, or 27 feet.  If, as a result of measuring, the river at a given point in its course is found to be 27 feet deep and 60 feet wide, the area of a cross section at that spot would be 1620 square feet, and if the velocity proved to be 6 feet per second, then the quantity of water passing in any one second would be 1620 x 6, or 9720 cubic feet.  By experiment it has been found that 1 cu. ft. of water weighs about 62.5 lb.  The weight of the water passing each second would therefore be 62.5 x 9720, or 607,500 lb.  If this quantity of water plunges over a 10-ft. dam, it does 607,500 x 10, or 6,075,000 foot pounds of work per second, or 11,045 H.P.  Such a stream would be very valuable for the running of machinery.