Oftentimes, as when water is sold to a corporation or city, it is necessary to know the quantity of water coming down a stream. To measure this a device called a weir (Fig. 49) is constructed at the sides of the stream so as to form either a rectangular or angular opening through which the water flows. Where a large quantity of water is measured the opening is usually shaped in this way where the quantity is small the opening is V-shaped, as the flow of water may then be measured with greater accuracy.
The volume of the flow is measured by ascertaining the height of the water above the bottom of the notch. To do this a peg is driven into the bed of the stream as at E in Fig. 49. The top of this peg is exactly the same height as the bottom of the notch. A measuring scale inserted in the water as shown in the illustration then enables the exact height of the flow over the weir to be measured. The formula for determining the volume of flow is:
Q = 4K / 15 X B X
Where Q = cubic feet passing over the notch per second, K = .59, which is a constant, B is the breadth of the water in the notch, H is the height of the water in the notch, g = 32.2 (force of gravity).
The energy stored in the moving water is equal to the number of cubic feet passing down the stream per minute multiplied by the weight of a cubic foot of water, multiplied by the perpendicular distance this water falls. This equals the number of foot-pounds per minute. Weight of a cubic foot of water 62.5 lbs.
Fig. 49. - Measuring Water with a Weir.
The E. H. P., or estimated horse-power, stored in the moving water is expressed by the following formula:
E. H. P. = W X H / 33000----------
Where E. H. P. = estimated horse-power, W = weight of water passing per minute in pounds, H = height it falls in feet.