§ 50. Convergent Mouthpieces.—With convergent mouthpieces there is a contraction within the mouthpiece causing a loss of head, and a diminution of the velocity of discharge, as with cylindrical mouthpieces. There is also a second contraction of the stream outside the mouthpiece. Hence the discharge is given by an equation of the form
Q = cvccΩ √(2gh),
(4)
where Ω is the area of the external end of the mouthpiece, and ccΩ the section of the contracted jet beyond the mouthpiece.
Convergent Mouthpieces (Castel’s Experiments).—Smallest diameter of orifice = 0.05085 ft. Length of mouthpiece = 2.6 Diameters.
| Angle of Convergence. | Coefficient of Contraction, cc | Coefficient of Velocity, cv | Coefficient of Discharge, c |
| 0° 0′ | .999 | .830 | .829 |
| 1° 36′ | 1.000 | .866 | .866 |
| 3° 10′ | 1.001 | .894 | .895 |
| 4° 10′ | 1.002 | .910 | .912 |
| 5° 26′ | 1.004 | .920 | .924 |
| 7° 52′ | .998 | .931 | .929 |
| 8° 58′ | .992 | .942 | .934 |
| 10° 20′ | .987 | .950 | .938 |
| 12° 4′ | .986 | .955 | .942 |
| 13° 24′ | .983 | .962 | .946 |
| 14° 28′ | .979 | .966 | .941 |
| 16° 36′ | .969 | .971 | .938 |
| 19° 28′ | .953 | .970 | .924 |
| 21° 0′ | .945 | .971 | .918 |
| 23° 0′ | .937 | .974 | .913 |
| 29° 58′ | .919 | .975 | .896 |
| 40° 20′ | .887 | .980 | .869 |
| 48° 50′ | .861 | .984 | .847 |
The maximum coefficient of discharge is that for a mouthpiece with a convergence of 13°24′.
| Fig. 59. | Fig. 60. |
The values of cv and cc must here be determined by experiment. The above table gives values sufficient for practical purposes. Since the contraction beyond the mouthpiece increases with the convergence, or, what is the same thing, cc diminishes, and on the other hand the loss of energy diminishes, so that cv increases with the convergence, there is an angle for which the product cc cv, and consequently the discharge, is a maximum.