Page:Encyclopædia Britannica, Ninth Edition, v. 12.djvu/523

507 HYDRAULICS.] HYDROMECHANICS 507 vane is shown at WH. The galvanic current acts on the electro magnet m, which is fixed in a small metal box containing also the battery. The magnet exposes and withdraws a coloured disk at an opening in the cover of the box. H Fig. 144. Moore s Current Meter. The difficulties in using the ordinary current meter have been overcome to a great extent by an arrange ment of another kind, invented by Mr B. T. Moore (Proc. Just. Si ize. Scale - Full Fig. 145. Civil Eng., xlv. 220). This instrument (fig. 145) can be lowered into the water to any required depth by a light cord or chain. The counting arrangement inside the meter can be started or stopped at any instant. The instrument consists of a light brass frame carry ing an ogival head, and long rudder, cross-shaped in section. The frame is suspended in & stirrup, and if necessary a lead weight can be suspended below the meter. A rotating cylinder with screw blades is placed behind the ogival head. The centre of gravity of the instrument is accurately in the intersection of the axis of the stirrup-bearings and the longitudinal axis of the instrument. The rotating cylinder is started by releasing a spring by a cord. The recording mechanism is inside the rotating cylinder. The instru ment is put in motion by a very small force. Some experiments made by towing it in still water gave the following equations : For speeds giving more than sixty rotations per minute, -y = l 2R, where v is_the velocity of the water relatively to the instrument in feet per minute, and R the number of rotations per minute. Fol lower speeds, It would appear therefore that the instrument will record velocities down to 12 feet per minute. Mr Moore states that a velocity at any depth down to 20 feet can be taken in five minutes, the meter being raised and lowered much more easily than when it is attached to a rod. Determination of the Coefficients of the Current Meter. Suppose a series of observations have been made, by towing the meter in still water, at different speeds, and it is required from these to ascertain the coefficients of the meter. A formula must be assumed to con nect the observed velocities v with the number of rotations per second n. Then, in determining the coefficients of the formula from the given observations, the condition to be fulfilled is that the sum of the squares of the differences between the observed results and those given by the formula should be a minimum. Let the formula assumed be of the form v=an + & ........ (1). Then the difference in any case between the observed and calcul ated quantity is v - an - ft ; and therefore 2(r - an - ) 2 is to be a minimum. The coefficients being independent, we must equate separately to zero the differential coefficients of the expression with respect to the two coefficients. 2 [ (v - an - ft}n ] = ; whence from which a and $ are easily determined. Exner has shown (Zcitschrift fitr Bauicescn, 1875) that the relation between the velocity of the water and the number of rota tions of the meter is better expressed by the formula than by that generally used. r is sensibly equal to the velocity at which the meter just ceases to revolve ; and a is a constant deter mined by experiments at different speeds. Other expressions have been given, but they are more complicated and not more accurate than (1) and (2). 131. Darcy Gauge or Modified Pitot Tube. A very old instrument for measuring velocities, invented or used by Pitot, consisted simply of a vertical glass tube with a right- angled bend, placed so that its mouth was normal to the direction of flow (fig. 146). The impact of the ^ ^ stream on the mouth of the tube balances a column in the tube, the height of which - -gc3__ is approximately v C 11&quot; &=, where v is Fig. 146. 20 the velocity at the depth x. Placed with its mouth parallel to the stream the water inside the tube is nearly at the same level as the surface of the stream, and turned with the mouth down v 2 stream, the fluid sinks a depth ^ =o~ near ty&amp;gt; though the tube in that case interferes with the free flow of the liquid and somewhat modifies the result. Pitot expanded the mouth of the tube so as to- form a funnel or bell mouth. In that case he found by experiment