There are several well-known formulas used to compute the discharge over 90° V-notch weirs. The accuracy of measurements obtained with Cipolletti weirs and these formulas is inherently not as great as that obtained with suppressed rectangular or V-notch weirs.6 It is, however, acceptable where no great precision is required. H = head on weir, ft (m) L = length of weir, ft (m)
Where Q = discharge neglecting velocity of approach, ft3/s (m3/s) Q' = discharge considering velocity of approach, ft3/s (m3/s) The formula including velocity of approach is in USCS units Q' = 3.367L(H + 1.5h )3/2 (6) The Cipolletti formula, in which the Francis coefficient is increased by about 1% and velocity of approach is neglected, is in USCS units Q = 3.367LH3/2 (5) However, Cipolletti has compensated for the reduction in discharge due to end contractions by sloping the sides of the weir sufficiently to overcome the effect of contraction. The Cipolletti weir is a contracted weir and must be installed as such to obtain reasonably correct and consistent discharge measurements. No tests have been made to determine the applicability of these formulas to weirs less than 4 ft (1.2 m) in length. The coefficient of discharge was obtained by Francis from the same general set of experiments as those used for the contracted rectangular weir. In these formulas, the letters have the same significance as in the formulas for contracted rectangular weirs. The Francis formula for the standard suppressed rectangular weir neglecting velocity of approach in in USCS units Q = 3.33LH3/2Īnd that including velocity of approach is in USCS units Q' = 3.33L In the Smith formulas for suppressed weirs, as for contracted weirs, coefficients of discharge vary with weir head and length therefore, these formulas are not convenient for use in computations without tables or coefficients. The principal formulas used for computing the discharge of the standard suppressed rectangular weir were also proposed by Smith and Francis. A table of § powers that provides values of H3'2, h3'2, and (H + h)3'2 for convenience in computing discharge with the Francis formulas may be found in hydraulic handbooks. Note that the Francis formulas contain constant discharge coefficients that allow computation without the use of tables. H = head due to velocity of approach (v2/2g), ft (m) Where Q = discharge neglecting velocity of approach, ft3/s (m3/s) Q' = discharge considering velocity of approach, ft3/s (m3/s) H = head on weir, ft (m) L = length of weir, ft (m) For this type of weir operating under favorable conditions as prescribed in preceding paragraphs, the Francis formula when velocity of approach is neglected is in USCS units Q = 3.33H/2(L - 0.2H) (1)Īnd the formula when velocity of approach is included is in USCS units Q' = 3.33(L - 0.2H) Consequently, the Smith formulas are somewhat inconvenient to use, although they are accurate for the ranges of coefficients usually given. Two widely used sets of formulas for computing discharge over standard contracted rectangular weirs are those of Smith4 and Francis.5 The formulas proposed by Smith require the use of coefficients of discharge that vary with the head of water on the weir and with the length of the weir. A staff gage (Figure 15) having a graduated scele with the zero placed at the same elevation as the weir crest is usually provided for the head measurements. This distance should be at least four times the maximum head on the weir, and the same gage point should be used for lesser discharges. The head H must be measured at a point on the water surface in the weir pond beyond the effect of the drawdown. This curved surface, or drawdown, extends upstream a short distance from the weir notch. The discharge of the standard 90° V-notch weir is determined directly by the head on the bottom of the V notch.Īs the stream passes over the weir, the top surface curves downward. Head H in feet (meters) and the crest length L in feet (meters).
Centrifugal Pumps FIGURE 13 Standard contracted weirs and temporary bulkhead with contracted rectangular weir discharging at free flowĪir vent- FIGURE 14 Typical suppressed weir in a flume drop FIGURE 15 Standard weir, or staff, gage
0 kommentar(er)
