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 
2 
= '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 to 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 
p A V A Y (1 - n) 
a ~ 4-5 / V 86*5 n (459 + t‘) ~ 42 ^ n (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 he reduced from V to 
a 
Y 
in passing n obstructions. For the loss of velocity at the first obstruction must he — ; hence it 
will be reduced to 
Y / 1\ 
y — — = y (1--); 
a \ a / 
aud this quantity will he similarly reduced in the same proportion at each contraction. 
To calculate the amount of such a succession of diminutions, we have 
log. V + n log. ^ 1 — — j = the logarithm of the reduced velocity.