SECT, x.] OF STEAM NAVIGATION. 



613. Now if c be the perimeter of the section in contact with the fluid, and 

 a its area, / the length of the vessel, and F = 64 times the friction when the sur- 

 face is 1, we have, 



the head equal to the friction being nearly as the square of the velocity directly, 

 and the area inversely, and the friction being as the surface of the fluid put in 

 motion, or the rubbing surface of the vessel. 



These two values of x must therefore be equal, hence 



, _ 1-5 t> _ /c F v- 

 ~64~ = 64 a ' 



or the whole head is, 



, _ 1-5 t> 2 / c F p 

 ~~ ~~ 



But the resistance being usually estimated in Ibs., we have for sea water 64 ha 

 = that resistance, = t? (1'5 a + /cF) = R, the resisting force; and the power 

 required is as the force and velocity = v 3 (1'5 a + / c F) = the Ibs. raised one 

 foot per second, when F is in Ibs. 



614. For fresh water put 1*45 in the place of 1'5, but the correction is not 

 necessary in practice. The coefficient F is 0*0032 Ibs. found from experiment. 



615. If the body have a simple angular prow, and an after body of the same 

 figure, and a be the angle the prow forms with the direction of its motion, and 3 

 the angle of the after part, then the pressure on its surface depends on the velocity 

 of the surface, in a direction perpendicular to itself. This velocity before is v sin. a ; 

 and behind v sin. ; being to the velocity of the vessel as the sine of the angle 

 is to radius ; and therefore the resistance would be, 



., 2 /2 a sin. 'a +a8in. a /3 + /cF \ 



The effect of this head in the direction of the motion of the vessel is as the sine 

 of a to radius at the prow, but the quantity of fluid required to fill the void behind 

 is constant for the same angle ; hence the resistance is, 



^asin.aq + asin.^ + ^^ = R> 



and, 

 v , ^arin.a+gin.0 + / c F ) = the power in Ibs. raised one foot per second. 



This gives the resistance when the vessel is of a wedge shape at both ends, or of 

 any regular pyramidal form, a being the angle the slant side of the pyramid makes 



