HYDRAULICS.] HYDROMECHANICS 11 sider a mass of fluid flowing in contact with a solid surface also in motion, the motion of both fluid and solid being estimated relatively to the earth. Then the motion of the fluid may be resolved into two parts, one a motion equal to that of the solid, and in the same direc tion, the other a motion relatively to the solid. The motion which the fluid has in common with the solid cannot at all be influenced by the contact. The relative component of the motion of the fluid can only be altered in direction, but not in magnitude. The fluid moving in contact with the surface can only have a relative motion parallel to the surface, while the pressure between the fluid and Maximum surface veto citu = V= 1-3,5 2 Right bank 35-03 34-03 4-084-80 6-667-30 9-2* 9-80 11-8212-30 14- 4-1 li-80 16-92 17-30 19-57 19-80 22-15 22-30 24-80 27-30 Discharge per Second = Q = 14-1087 cu6>m> Curves of equal velocity. ormation ratio JO. 1 Heiahi scale solid, if friction is neglected, is normal to the surface. The pressure therefore can only deviate the fluid, without altering the magnitude ot the relative velocity. The unchanged common component and, combined with it, the deviated relative component give the resultant final velocity, which may differ greatly in magnitude and direction from the initial velocity. From the principle of momentum the impulse of any mass of fluid reaching the surface in any given time is equal to the change of momentum estimated in the same direction. The pressure between the fluid and surface, in any direction, is equal to the change of momentum in that direction of so much fluid as reaches the surface in one second. If P a is the pressure in any direction, m the mass of fluid impinging per second, ? a the change of velocity in the direction of P a due to impact, then P a = mv a . If r, (fig. 153) is the velocity and direction of motion before impact, v. 2 that after impact, then v is the total change of motion due to impact. The resultant pressure of the fluid on the surface is in the direction of v, and is equal to v multiplied by the mass im pinging per second. That is, putting P for the resultant pressure, P=ir. V Let P be resolved into two components, Fig. 153. N and T, normal and tangential to the .direction of motion of the solid on which the fluid impinges. Then N is a lateral force pro ducing a pressure on the supports of the solid, T is an effort which does work on the solid. If u is the velocity of the solid, Tu is the work done per second by the fluid in moving the solid surface. Let Q be the volume, and GQ the weight of the fluid impinging per second, and let v, be the initial velocity of the fluid before strik- f 1 ing the surface. Then iQ-i^ is the original kinetic energy of Q cubic feet of fluid, and the efficiency of the stream considered as an arrangement for moving the solid surface is Tit 140. Jet, deviated entirely in one Direction Geometrical Solution (fig. 154). Suppose a jet of water impinges on a surface ac with a velocity ab, and let it be wholly deviated in planes parallel to the d Fig. 154. figure. Also let ac be the velocity and direction of motion of tho
surface. Join cb ; then the water moves with respect to the sur-
