| K = ρ ( 1.176 | ρ | − 1 ) | 2 | . |
| ρ − 1 |
| ρ = | K = |
| 1 | ∞ |
| 2 | 3.66 |
| 3 | 1.75 |
| 4 | 1.29 |
| 5 | 1.10 |
| 10 | .94 |
| 50 | 2.00 |
| 100 | 3.50 |
The assumption that the coefficient of contraction cc is constant for different values of ρ is probably only true when ρ is not very large. Further, the increase of K for large values of ρ is contrary to experience, and hence it may be inferred that the assumption that all the filaments have a common velocity v1 at the section A1A1 and a common velocity v at the section A2A2 is not true when the stream is very much larger than the plane. Hence, in the expression
R = KGωv2 / 2g,
K must be determined by experiment in each special case. For a cylindrical body putting ω for the section, cc for the coefficient of contraction, cc (Ω − ω) for the area of the stream at A1A1,
v1 = vΩ / cc (Ω − ω); v2 = vΩ / (Ω −ω);
or, putting ρ = Ω/ω,
v1 = vρ / cc (ρ − 1), v2 = vρ / (ρ − 1).
Then
R = K1Gωv2 / 2g,