Hydraulic Performance of Sharp-Crested Side Slit Weirs

Abstract

A rectangular slit weir is used to measure small discharges (Q < 5 L/s) and contraction ratios (b/B $\le$ 0.25). Various discharge relationships were reported in the literature for calculating the discharge capacity of slit weirs in terms of frontal flow. However, this is not valid for lateral flow. In the current study, the side slit weir flow was investigated experimentally using piezometric heads over the weirs. The discharge coefficient was investigated for side slit weirs with different contraction ratios, which ranged from 0.075 to 0.25. Accordingly, the discharge coefficients were calculated using the Schmidt approach. Moreover, the outflow discharge of sharp-crested side slit weir was analyzed using the incomplete self-similarity theory (ISS) and dimensional analysis. The new discharge model was theoretically created based on the experimental results obtained from laboratory tests. The results of the current study indicated that the contraction ratio, dimensionless head over the weir, and Froude number were dominant parameters over the discharge of sharp-crested side slit weirs. Within this framework, slit weirs can be used laterally as water intake structures for small discharges. Furthermore, a nonlinear equation including all effective parameters is proposed to obtain the discharge capacity of sharp-crested side slit weirs with the highest accuracy.

Appendix

1.1 Schmidt Approach

To determine the discharge capacity of side weir for subcritical, Schmidt (1954) proposed an approach. The energy equation was given as follows:

$${S}_{\mathrm{o} }b+{y}_{1 }+{\alpha }_{1}\frac{{V}_{1}^{2}}{2g}={y}_{2 }+{\alpha }_{2}\frac{{V}_{2}^{2}}{2g}+\Delta {h}_{s}$$

(26)

$${S}_{o }b+p+{h}_{1}+{\alpha }_{1}\frac{{V}_{1}^{2}}{2g}={h}_{3}+p+{\alpha }_{2}\frac{{V}_{2}^{2}}{2g}+\Delta {h}_{s}$$

(27)

$${h}_{1}={h}_{3}+{\alpha }_{2}\frac{{V}_{2}^{2}}{2g}{-S}_{\mathrm{o} }b-{\alpha }_{1}\frac{{V}_{1}^{2}}{2g}+\Delta {h}_{s}$$

(28)

where $\Delta {h}_{s}$=friction loss. $\Delta {h}_{s}$ could be obtained from the Manning–Strickler formula as $\Delta {h}_{s}={S}_{E} b$. Schmidt (1954) assumed that the channel slope and energy grade line are nearly equal (${S}_{E}b\cong {S}_{0}b$). The slope of channel is very small (sinθ ≅ tanθ = S_o). Therefore, it is assumed that the specific energy is constant along the side weir.

Energy correction coefficients can be taken into account as ${\alpha }_{1}={\alpha }_{2}=1.1$ using the trial and error method. To verify the energy correction coefficients, $\xi$ was obtained experimentally. For $\Delta {h}_{s}={S}_{E}b\cong {S}_{0}b$, Eq. (28) is formulated as follows:

$${h}_{1}={h}_{3}- \xi \left[1.1\frac{{V}_{1}^{2}}{2g}-1.1\frac{{V}_{2}^{2}}{2g}\right]$$

(29)

in which $\xi$=correction coefficient for the Schmidt approach. Schmidt (1954) stated that Poleni’s equation was applied to this approach.

$$Q={C}_{d }\frac{2}{3} \sqrt{2g} b {h}_{a}^{3/2}$$

(30)

$${h}_{a }=\frac{1}{2} \left({h}_{1}+{h}_{2}\right)$$

(31)

or

$${h}_{a }=\frac{1}{3} \left({h}_{1}+{h}_{2}+{h}_{3}\right)$$

(32)

in which ${h}_{a}$=average piezometric head according to two points and three points, respectively. ${h}_{1},{h}_{2},{h}_{3}$ are piezometric heads over the weir at the upstream (C1), downstream (C2), and center (C3) sections of the side weir, respectively.

Friction loss was considered in the formula or theweir length in the Schmidt approach, where was much larger, Eq. (33) could be utilized instead of Eq. (29) (Ozbek 2009).

$$\xi =\frac{{h}_{2}-{h}_{1}}{1.1\frac{{V}_{1}^{2}}{2g}-1.1\frac{{V}_{2}^{2}}{2g}-\Delta {h}_{s}}$$

(33)