THE HYDRAULIC BRAKE 



789 



while if F = resistance in Ibs. due to mechanical friction and to effect of 

 counterweights, &c., 



62'4 F 2 f fl] A 3 

 R=pA+F= -1+/J1-4- + F. (2) 



m 



Brake with Uniform Resistance. With uniform resistance the retardation 



Fi 2 

 of the moving body is uniform, and will be given by ->- feet per 



second per second, where FI is the velocity at impact, so that the velocity 

 at any point distant x feet from the beginning of the stroke is given by 



= ^( I -L)' 



By equating the work done on the brake to the loss of K. E. by the 

 moving body we get 



EL- 2^- 



(3) 



W ' 



and 



Inserting this value in (2) above, we get 



which finally reduces to 



w 



ffl" = 



w 



(4) 



giving the passage area for any value of x, when the form of the orifice is 

 known. 



If it be assumed that mechanical friction is equivalent to 5 per cent. 



of the force on the piston, and if the term f 1 + J be taken as unity 



(i.e., if fluid friction be neglected), this simplifies to 



65-7 L A 



EXAMPLE. 



Buffer stop piston, 12J inches diameter, provided with two slots of 

 total area 4/75 square inches 3 J-inch rod length of stroke 4 feet. 

 Weight of train = 100 tons. 



