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,