Hence it is obvious that, except for very small values of σ, the simpler equation (5) gives values sensibly identical with those of (8). When σ < 0.5 it is better to use equation (8) with values of c determined experimentally for the particular proportions of orifice which are in question.
| Fig. 44. |
§ 40. Large Jets having a Circular Section from Orifices in a Vertical Plane Surface.—Let fig. 44 represent the section of the jet, OO being the free surface level in the reservoir. The discharge through the horizontal strip aabb, of breadth aa = b, between the depths h1 + y and h1 + y + dy, is
dQ = b √ {2g (h1 + y) } dy.
The whole discharge of the jet is
Q = ∫d0 b √ { 2g (h1 + y) } dy.
But b = d sin φ; y = 1⁄2d (1 − cos φ); dy = 1⁄2d sin φ dφ. Let ε = d/(2h1 + d), then
Q = 1⁄2d2 √ { 2g (h1 + d/2) } ∫π0 sin2 φ √1 − ε cos φ dφ.
From eq. (5), putting ω = πd2/4, h = h1 + d/2, c = 1 when d is the diameter of the jet and not that of the orifice,
Q1 = 1⁄4πd2 √ {2g (h1 + d/2) },