508 HYDROMECHANICS [HYDRAULICS, The objection to this is that the motion of the stream is interfered with, and it is no longer certain that the velocity in front of the orifice is exactly the velocity of the unobstructed stream. Darey preferred to make the mouth of the tube very small, partly to avoid interference with the stream, partly to check oscillations of the eolumn. In that case he found the difference of level of two tubes, such as A and B, to be almost exactly One objection to the Pitot tube in its original form was the great difficulty and inconvenience of reading the height /tin the immediate neighbourhood of the stream surface. This is obviated in the Darcy gauge, which cnn be removed from the stream to be read. Fig ] 47 shows a Dairy gauge. It consists of two Pitot tubes having their mouths at right angles. In the instrument shown, the two tubes, formed of copper in the lower part, are united into one for strength, and the mouths of the tubes open vertically and horizontally. The upper part of the tubes is of glass, and they are provided with a brass scale and two verniers b, b. The whole instrument is supported on a vertical rod or small pile AA, the fixing at B permitting the instrument to be adjusted to any height on the rod, and at tlie same time allowing free rotation, so that it can be held parallel to the current. At c is a two-way cock, which can be opened or closed by cor>ls. If this is shut, the instrument can be lifted out of the stream for reading. The glass tubes are connected at top by a brass fixing, with a stop cock a, and a flexible tube and mouthpiece m. The use of this is as follows. If the velocity is required at a point near the surface of the stream, one at least of the water columns would be below the level at which it could be read. It would be in the copper part of the instrument. Suppose then a little air is sucked out by the tube m, and the cock a closed, the two columns will be forced up an amount corresponding to the difference between atmospheric pressure and that in the tubes. But the difference of level will remain unaltered. When the velocities to be measured are not very small, this instru ment is an admirable one. It requires observation only of a single linear quantity, and does not require any time observation. The law connecting the velocity and the observed height is a rational one, and it is not absolutely necessary to make any experiments on the coefficient of the instrument. If we take then it appears from Darcy s experiments that for a well-formed instrument k does not sensibly differ from unity. It gives the velocity at a definite point in the stream. The chief difficulty arises from the fact that at any given point in a stream the velocity is not absolutely constant, but varies a little from moment to moment. Darcy in some of his experiments took several readings, and deduced the velocity from the mean of the highest and lowest. 132. Hydrodynamometer of M. Perrodil. This consists of a frame abed (fig. 148) placed vertically in the stream, and of a height not less than the stream s depth. The two vertical members of this frame are connected by cross bars, and united above water by a circular bar, situated in the vertical plane and carrying a horizontal graduated circle ef. This whole system is movable round its axis, being suspended on a pivot at g connected with the fixed support mn. Other horizontal arms serve as guides. The central vertical rod gr forms a torsion rod, being fixed at r to the frame abed, and, passing freely upwards through the guides, it carries a horizontal needle moving over the gradu ated circle ef. The support g, which carries the apparatus, also receives in a tubular guide the end of the torsion rod gr and a set screw for fixing the upper end of the torsion rod when necessary. The impulse of the stream of water is received on a circular disk x, in the plane of the torsion rod and the frame abed. To raise and lower the rig. no. n ; apparatus easily, it is not fixed directly to the rod mn, but to a tube M sliding on mi. Suppose the apparatus arranged so that the disk x is at that level in the stream where the velocity is to be determined. The plane abed is placed parallel to the direction of motion of the water. Then the disk x (acting as a rudder) will place itself parallel to the stream on the down stream side of the frame. The torsion rod will be unstrained, and the needle will be at zero on the graduated circle. If then the instrument is turned by pressing the needle, till the plane abed of the disk and the zero of the graduated circle is at right angles to the stream, the torsion rod will be twisted through an angle which measures the normal impulse of the stream on the disk x. That angle will be given by the distance of the needle from zero. Observ ation shows that the velocity of the water at a given point is not constant. It varies between limits more or less wide. When the apparatus is nearly in its right position, the set screw at g is made to clamp the torsion spring. Then the needle is fixed, and the apparatus carrying the graduated circle oscillates. It is not then difficult to note the mean angle marked by the needle. Let r be the radius of the torsion rod, I its length from the needle over ef to r, and a the observed torsion angle. Then the moment of
the couple due to the molecular forces in the torsion rod is
