. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 370 THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. [Dec. WORKING STEAM EXPANSIVELY. When a steam-engine is working at any given speed, the pressure on the prank-pin is equal to the pressure on the piston resolved into the direction of the length of the connecting-rod, minus the force of inertia of the re- ciprocating parts when their velocity is increasing, or plus the via insita of those parts when their velocity is decreasing :âit is required to ascertain the amount of this + p
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. 370 THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. [Dec. WORKING STEAM EXPANSIVELY. When a steam-engine is working at any given speed, the pressure on the prank-pin is equal to the pressure on the piston resolved into the direction of the length of the connecting-rod, minus the force of inertia of the re- ciprocating parts when their velocity is increasing, or plus the via insita of those parts when their velocity is decreasing :âit is required to ascertain the amount of this + pressure. If the square of the velocity of any mass of matter increases in an ele- mentary space n times as much as it would increase by falling through that space,âthen the force for that point or elementary space must be n times the force of gravity, or n times the weight of the mass; that is, putting V = the velocity due to falling a given space, and V = the actual velocity, VrfV as d V- ⢠dv'', or as V(/V : vdv ''. n\\, or â âzâ â¢= n ; van but v' â = 2r/s, and differentiating vdv = gds, VrfV , -VdV , and for the destruction of motion gds Let : = the angle passed through by the crank; r = the length of the crank j s -= the space travelled by the piston; ds V .= the velocity of the piston â = â; d i V = the velocity of the crank-pin in the arc z â gds rdz ~di ' C = the length of the connecting-rod ; Q c = the value of C in terms of the length of the crank; r n = the force of inertia or insita in terms of the weight; P = the pressure on the crank-pin caused by the insita or inertia, or the value of n reduced to the mechanical conditions. -e-. The space described by the piston is = ab; .â¢. s = r I ver ; + c â {(p â sia'z)- \ ; rdz / sin 2 cos z \ -r- X I sin I -h TTTi I ⢠dt \ (e-'-sin=z)5/ ds differentiating r-. therefore, V dV = V cos 2 dz + V sin z + V sin r cos z - J and differentiating (c2-sin2i)5 (jsing2r + cos 2z (c°-sin°;) >v (e2- sm-
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