442 APPLIED MECHANICS 
the levels of the mercury being indicated by cast-iron floats with vei 
rods attached to them. 
It may be left as an exercise to the student £6 show that the quantit; 
of water flowing through the main in a given time is equal to ea/i 
where ¢ is a constant for a given meter, and & is the head of me 
equivalent to the difference between the pressures in the main and in» 
throat of the meter. 
The diameter of the throat of the meter is frequently one-thi 
of the diameter of the main. 
In order that Bernoulli’s theorem may apply without sensible e 
it is necessary-that the interior of the Venturi tube lying between t 
annular pressure chambers should be as smooth as possible. In pre 
the error in the Venturi meter does not exceed 2 per cent. E 
It is usual to fit a recording apparatus to the Venturi meter, e 
sisting of a clock-driven drum, upon which a diagram is traced by a p 
actuated by one of the cast-iron floats mentioned above. The abscisses 
this diagram represent time, and the ordinates rate of flow, and the at 
of the diagram between any two ordinates represents the quantity 
water delivered in the time represented by the distance between these 
ordinates. A mechanical integrator operated by a clock and the se 
float is generally added ; this shows on a dial the total quantity of we 
delivered.* — 
Venturi meters are suitable for mains of almost any diamet 
and have been made for mains as large as 10 feet in diame 
They are, however, not suitable when the velocity of the water is ve: 
small. 
376. Radiating Current.—Fig. 720 shows two horizontal co-ax 
discs whose distance apart is a. At the centre of the lower dise there is” 
an opening into a pipe, from which water flows into the space between he 
discs. Consider the flow acrossa ——~~,—~~-—~-— f---—--- = 
section of the water between the 4 8, 
discs made by the surface of a hon, | 
cylinder of radius 7 whose axis’ 
coincides with the axis of the 
discs. Let the velocity of the 
water across this section be v, and 
let Q be the volume passing per 
unit of time, then Q = 27rav, and 
rv=Q/27a. But for all values 
of r the quantity Q is constant, 
therefore rv =a constant, and if r 
and v be plotted in a plane con- 
taining the axis of the discs, the 
resulting curve is a rectangular 
hyperbola. 
Let P be the pressure of the water at radius r, as show wn 
by @ pressure gauge, then the pressure head is P/w, and » 
kinetic energy per unit of weight is v?/2g.. Let A be the height of 
* For an illustrated description of the recording apparatus of a Venti vari 
meter, see Engineering, Feb. 22, 1907. 
