Mr Watts’ Observations on ihe Resistance of Fluids. - 317 
of a prism of the fluid, whose base is equal to 5, and whose 
height is equal to h : thus, when the fluid escapes into air, the 
pressure at the orifice o, will be equal to g^hli only; because 
the pressure g^hh\ which is transmitted to the surface 6, by the 
intervention of the different strata of the fluid, is balanced by 
an equal and opposite pressure of the atmosphere acting with- 
out the orifice o. In this case, therefore, we have 
P=gibh (1). 
The same reasoning holds good, when we suppose that the 
small surface o is immersed to the depth h below the upper 
surface of a stagnant fluid, and moved through it with the ve- 
locity V ; for when the velocity is very great, so that a perfect 
vacuum is left behind the small surface o, we shall have 
p = gghh ^ ; 
but when the fluid does not escape into a perfect vacuum, or 
any thing like it, but into a mixture of air and water, the pres- 
sure at the depth Ji below the upper surface will be, nearly, 
p z=: g^hh, as before. 
I have been more particular on this head than I should other- 
wise have been, with a view to meet an objection that has been 
advanced against this part of the subject. 
Now, it is well known, that when the pressure is the same at 
the upper surface of the fluid and at the orifice o, or at the an- 
terior and posterior surfaces of the base h, the water will flow 
out with the velocity u = sj^gh ; whence we deduce = ^gK 
and/i=~. 
If we substitute this value uf li in the equation (1), we shall 
have 
Let us now suppose the elementary surface o to move with the 
velocity v ; then the fluid would meet it either with the velocity 
w -f- 1 ;, or u — V, according as it moves in the direction opposite 
to that of the efiluent fluid ; or in the same direction with it : 
and, by substituting (tt i vf instead of u in the preceding equa- 
tion, we shall obtain 
