. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Ship Waves. 5 The quantity H^ â Y^ is monotonic and decreases to an asymptotic value 2/7C. The symmetrical terms in (14) represent the local disturbance, becoming infinite near the origin like x~^. The last term in (14) represents the wave disturbance in the rear. The expressions are easily calculated from tables of the functions, and fig. 1 shows the two parts of the rio. 1. It wiU be seen that there is discontinuity at the origin, but that arises from extending this part
. The collected papers of Sir Thomas Havelock on hydrodynamics. Ship resistance; Water waves; Hydrodynamics. Ship Waves. 5 The quantity H^ â Y^ is monotonic and decreases to an asymptotic value 2/7C. The symmetrical terms in (14) represent the local disturbance, becoming infinite near the origin like x~^. The last term in (14) represents the wave disturbance in the rear. The expressions are easily calculated from tables of the functions, and fig. 1 shows the two parts of the rio. 1. It wiU be seen that there is discontinuity at the origin, but that arises from extending this particular distribution right up to the free surface. If we retain the quantity d used at the beginning of this section, it is easily seen that the discontinuity is associated with the last term of (14); for any finite value of d, this part of the disturbance is zero at the origin. 4. Consider now a imiform distribution over a finite length of the vertical plane y = 0, extending over the range âIKxKl- This might be deduced from the previous section by integrating with suitable precautions to allow for the discontinuities in those expressions; but we shall use the general formida (4). Suppose in the first place that the distribution extends from a depth d to an infinite depth ; then we have TtMj-i Jd J-:r Jo K â KoS( tf + inTS' CqScc^ 8 + t[isec 9 For the elevation along the line e/ = 0, this gives 4iM r'^ r. J/^ r e-"^ le'" '*-^' ""^ * â e*'' ^'^+^' â¢' ^1 , I spp. HrtH I i ^dK. l^^n^i secede â KU Jo Jo K ~ Kq s&c? e + i[i. sec e (15) (16) We may put c? = 0 in (16). Further, the disturbance separates into equal and opposite disturbances associated with the front and rear of the system, or, as we may call them, into bow and stern systems. Writing q-^ for x â I, we have to evaluate the real part of iir/2 /â¢Â« secede - 0 Jo K piKQi cos 6 KjSec^ e + i[xsec 6 -dK. (17) 351. Please note that these images are extracted from scanned page images that may
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