426 
MR. J. H. MICHELL ON THE THEORY OF FREE STREAM LINES. 
An interesting special case is the flow from an aperture in the side of a rectangular 
vessel, of which the bottom is at a considerable distance from the aperture. 
For this case = 0, and, therefore, 
d V3 
7 = F,’ 
expressing the equality of inflow and outflow. 
So that 
= (iAJLAir. 
^ 2^3 + Vi ^ ^ 2 L 
4- 2'y3 — v-, 
^3 + ^’1 
or 
+ r*l % ^4^ + i ^ log to + A 4 - 
V., V, 
V., — V. 
^ 2?;3 + 
+ ill 2r?-Z , tt/. 
^ ^ I d) d — ^ 9 ^7 _L / “1~ 9 1^ /73) ’ 
d ^ ' 2 d -V L 
cV- 
which is the simplest exjiression for this case. 
The angle the jet makes with the bounding wall is 
cos 
, -1 
1 — ah 
or 
cos 
-1 1 + ^3 
in the general case, while in the particular case it is simply 
cos 
-] 1 Id 
