Hydromechanics; An Elementary Treatise Prepared for the Use of the Midshipmen at the United States Naval Academy (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ...within the vessel; the whole work done must be equivalent to the transfer of the surface layer to the orifice, and this must equal the energy of the escaping liquid, provided we can neglect losses of energy in overcoming friction and imparting velocity to the liquid remaining in the vessel, and experiments show that we can practically do this, if the orifice is small in comparison with the cross-section of the vessel. 60. It will be noted that in the first deduction of the formula v = J2gh, v, by hypothesis, is the velocity at a section of the issuing jet throughout which the pressure is the same as at its surface, and such uniformity of pressure can only occur where all the stream lines are parallel and the assumed section a normal one to the stream-tube. So also, in the second deduction of v = y/2gh, v, being merely that velocity which will account for the kinetic energy of the jet, can only be considered the true velocity of efflux if all parts of the jet have the same velocity. Actually, however, the escap ing liquid is made up of a great number of elementary streams converging towards the orifice, and so the motion is not parallel everywhere throughout the area of the orifice, but is more and more oblique to that area as we pass from its center to its boundary. This converging motion of the elementary streams must make the pressure at the orifice somewhat greater in the interior of the jet than at its surface, and consequently the velocity in the interior of the jet must be less than that at its surface. Mathematical analysis is incompetent to determine either the motions or the actual paths of the issuing particles of liquid, but experiment shows that at a distance beyond the orifice equal to about half its diameter the converging motion...