cr = 1 / cv2 − 1.
(5a)
Thus if cv = 0.97, then cr = 0.0628. That is, for such an orifice about 61⁄4% of the head is expended in overcoming frictional resistances to flow.
| Fig. 15. |
Coefficient of Contraction—Sharp-edged Orifices in Plane Surfaces.—When a jet issues from an aperture in a vessel, it may either spring clear from the inner edge of the orifice as at a or b (fig. 15), or it may adhere to the sides of the orifice as at c. The former condition will be found if the orifice is bevelled outwards as at a, so as to be sharp edged, and it will also occur generally for a prismatic aperture like b, provided the thickness of the plate in which the aperture is formed is less than the diameter of the jet. But if the thickness is greater the condition shown at c will occur.
When the discharge occurs as at a or b, the filaments converging towards the orifice continue to converge beyond it, so that the section of the jet where the filaments have become parallel is smaller than the section of the orifice. The inertia of the filaments opposes sudden change of direction of motion at the edge of the orifice, and the convergence continues for a distance of about half the diameter of the orifice beyond it. Let ω be the area of the orifice, and ccω the area of the jet at the point where convergence ceases; then cc is a coefficient to be determined experimentally for each kind of orifice, called the coefficient of contraction. When the orifice is a sharp-edged orifice in a plane surface, the value of cc is on the average 0.64, or the section of the jet is very nearly five-eighths of the area of the orifice.
| Fig. 16. |
Coefficient of Discharge.—In applying the general formula Q = ωv to a stream, it is assumed that the filaments have a common velocity v normal to the section ω. But if the jet contracts, it is at the contracted section of the jet that the direction of motion is normal to a transverse section of the jet. Hence the actual discharge when contraction occurs is
Qa = cvv × ccω = cccvω √(2gh),
or simply, if c = cvcc,