~192 T. Guerin on the delivery of water from conduit pipes. 
. nothing; while the omnes 9 from A will increase until 
becomes a maximum as soon as the orifice at N is equal to 
ths section of the p 
It follows then, that when j a branch is inserted in a conduit, 
the effect will be to increase the discharge from the reservoir, 
but at the same time to diminish the quantity delivered at the 
point of distribution; and the sum of such increase and dimi- 
nution will be the exact quantity carried off by the branch. 
To be able to ascertain this increase and diminution separately, 
the exact quantity delivered at the point B, is 
manifestly of the greatest importance in laying a system. of 
water pipes; and although writers on hydra ulics have investi- 
pear to have been hitherto discussed. ime a solution of 
this question, I submit the following investigati 
On reference to D’ Aubuisson’s Hydraulics, ag by Ben- 
nett, we find in chapter 3, No. 186, 
H—-0251817% = = ‘0006769 3+ (Q2-4" 141724QD2). 
This is a general formula employed for the solution of ques- 
tions relating to the motion of water in conduit pipes; Q denotes 
the quantity flowing per second een the pipe; r its length; 
, its diameter, and H, the head on the orifice of efflux ; the 
denominations of all these hasanh ae being feet 
The second member of the equation is the aha of hig resis- 
tance from friction occasioned by the sides of the 
7 1s this equation we obtain general values for i and Q 
as follows 
t= 0251817 oooe769 5 (Q?+4-141724QD?) 
Q—— 070862LD2 + te TEDEae Phe y 
L-+37-20D \ L+37:20D 
L-+-37:20D 
Let us assume Q=the quantity delivered at B, 
fe mee carried off ie branch, 
en 
[= eae AN 
H=height of reservoir above B, 
D=diamete 
a rata oP ANB. 
On reference to the general value of H, it will appear that 
the head which forces the amount to tho e point tN, will be 
