460 APPLIED MECHANICS 
Taking the height of the water barometer at 34 feet, then, whe 
h' = 34 feet, there will be a perfect vacuum round the jet at AB, and for 
aX St = 454 feet. For a greater value of 4 than 
this the jet will break up, and the mouthpiece will not discharge full — 
bore. 
399. Borda’s Mouthpiece.—The reason for the contraction of a jet — 
issuing from an orifice being that the water entering .the orifice flows — 
towards it in various directions inclined to the axis of the orifice, it is” 
obvious that the greater the angle between the extreme stream lines, the — 
greater the contraction of the jet. In the case of a simple orifice in a 
flat plate the angle between the extreme stream lines is 180°. Evidently 
the maximum contraction will oceur when the * 
angle between the extreme stream lines is 
360°, which is the case in Borda’s mouth- 
piece. This mouthpiece consists of a thin 
tube projecting into a tank, as shown in 
Fig. 755. The jet contracts within the 
mouthpiece to a diameter LN. Let A be 
the area of the section of the mouthpiece, and 
a the area of the contracted section of the 
jet. Let XX, the free surface of the water 
in the tank, be at a height h above the axis [| . 
of the mouthpiece. The entrance to the Fra. 755. 
mouthpiece being removed from the walls of 
the tank, it may be assumed that the motion of the water does not — 
affect the pressure on the walls, which will therefore follow the hydro- — 
static law, and, excepting the portion EF of the wall exactly opposite to — 
the mouthpiece, the horizontal pressures on the walls will balance one 
another. The resultant pressure on EF is whA, and this will also be the 
resultant horizontal force on the water entering the mouthpiece. 
Consider the mass of water between XX and LN. Let this mass 
move into the position X’X’L’N’ in ¢ seconds, then since the momentum 
of the mass X’X’LN does not alter, the change in the momentum of the 
mass considered is the difference in the momenta of the masses XXX‘X’ 
and LNN’L’. But the momentum of XXX’X’ is entirely vertical, therefore 
the change in momentum in a horizontal direction is equal to the momen- 
tum of LNN’L’, and this is due to the action of the force whA. 
2 
The mass of LNN’L’ is oo and its momentum is 22 
this condition “2= 
, where v is 
g $ 
the velocity of the water in the contracted jet. The impulse of the 
force whA is whAt. Hence equating impulse to change of momentum 
whAt = avtw 
, therefor one But v?=2gh very nearly, therefore 
in 4, or the coefficient of contraction for Borda’s mouthpiece is $. 
Various authorities have obtained values of a/A by direct experiment 
varying from 0°515 to 0°555, which confirms the foregoing theory. — 
400. Fluid Friction.—Fluid friction is the resistance experienced 
when a body moves through a fluid, or when a fluid moves ‘over the 
