The following experiment is interesting. Two cisterns provided with converging pipes were placed so that the jet from one was exactly opposite the entrance to the other. The cisterns being filled very nearly to the same level, the jet from the left-hand cistern A entered the right-hand cistern B (fig. 31), shooting across the free space between them without any waste, except that due to indirectness of aim and want of exact correspondence in the form of the orifices. In the actual experiment there was 18 in. of head in the right and 201⁄2 in. of head in the left-hand cistern, so that about 21⁄2 in. were wasted in friction. It will be seen that in the open space between the orifices there was no pressure, except the atmospheric pressure acting uniformly throughout the system.
| Fig. 30. |
| Fig. 31. |
§ 32. Venturi Meter.—An ingenious application of the variation of pressure and velocity in a converging and diverging pipe has been made by Clemens Herschel in the construction of what he terms a Venturi Meter for measuring the flow in water mains. Suppose that, as in fig. 32, a contraction is made in a water main, the change of section being gradual to avoid the production of eddies. The ratio ρ of the cross sections at A and B, that is at inlet and throat, is in actual meters 5 to 1 to 20 to 1, and is very carefully determined by the maker of the meter. Then, if v and u are the velocities at A and B, u = ρv. Let pressure pipes be introduced at A, B and C, and let H1, H, H2 be the pressure heads at those points. Since the velocity at B is greater than at A the pressure will be less. Neglecting friction
H1 + v2/2g = H + u2/2g,
H1 − H = (u2 − v2) / 2g = (ρ2 − 1) v2 2g.
Let h = H1 − H be termed the Venturi head, then
u = √ { ρ2.2gh / (ρ2 − 1) },
from which the velocity through the throat and the discharge of the main can be calculated if the areas at A and B are known and h observed. Thus if the diameters at A and B are 4 and 12 in., the areas are 12.57 and 113.1 sq. in., and ρ = 9,
u = √ 81/80 √ (2gh) = 1.007 √ (2gh).