SECT, ii.] PROPERTIES OF STEAM. 91 



we have no experiments by which the effect of these causes of diminution can be 

 estimated with accuracy, but we may endeavour to allow for them on the principles 

 which operate in similar circumstances. For this purpose let the part of the pipe 

 from whence the change of figure takes place, be considered a vessel with an aper- 

 ture of the kind nearest resembling the figure of the branching pipe, and the loss 

 of motion at the place equal to that which such an aperture would cause. 



Thus when the angle is a right angle, the loss of velocity may be considered half 

 that which takes place when a pipe is inserted in the side of a vessel, as the dimi- 

 nutions in the exterior half of the aperture will not be so great in this case ; there- 

 fore the loss will be 



1-000 -813 



_ = -094 nearly ; 



and may be allowed for by diminishing the velocity one-tenth, for each right-angled 

 bend. 



The same allowance for loss should be made when one pipe branches at right 

 angles from another. 



143. In a pipe formed to a regular curve, or bent only to an obtuse angle, the 

 reduction will not exceed that which happens with a conical mouth-piece, which is 

 about THT of the velocity. 



If a pipe be terminated in a valve box, the allowance of two-tenths should be 

 made for the loss of velocity in passing the valve. 1 



144. Few engines have less than three obstructions equivalent to passing so 

 many different apertures, which together may be expected to reduce the velocity so 

 as to require the number 6'5 to be reduced to 4'5 ; consequently, the formula may 



be stated 



^A V A V (1 - ) 



a = 



4-5 / >/ 86-5 (459 + t') 42 V (459 + t') 



1 When a series of obstructions of the same kind occur in a pipe, the reduction for the first 



being , the velocity will be reduced from V to 

 1 



(1 \ n 

 1 - -j 



y 



in passing n obstructions. For the loss of velocity at the first obstruction must be ; hence it 



will be reduced to 



a 



a 



and this quantity will be similarly reduced in the same proportion at each contraction. 

 To calculate the amount of such a succession of diminutions, we have 



log. V + log. ( 1 ) = the logarithm of the reduced velocity. 



