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53:071 Principles of Hydraulics Laboratory Experiment #2

WEIR CALIBRATION Principle The discharge over a weir is a function of the weir geometry and of the head on the weir. Introduction A weir is an obstruction in an open channel over which liquid flows. The purpose of this experiment is to determine the head-discharge relationship of three different shapes of weirs, and to compare the experimental results with their corresponding analytical expressions. Consider a weir with an irregular cross-section, as shown in Figure 1.
Upstream level H h dh V= 2gh

Nappe Weir crest

P

Weir

Downstream level

L

4H

Figure 1. Definition sketch for a weir Applying Bernoulli’s equation along a streamline between a point upstream of the weir (where the velocity head is neglected) and a point in the plane of the weir, the velocity, V, at the weir is V ( h) = 2 gh (1) where g is the gravitational acceleration and h is the elevation of the streamline below the free surface. Assuming that the velocity is constant throughout the cross-section of the weir, the expression for the discharge, Q, over the weir becomes

1

Q = ∫ dQ = ∫ V ( h)dA = ∫ 2 ghb(h)dh = 2 g ∫ b(h) hdh (2) 0 0 A A where A is the cross-section of the weir and b(h) is the width of the weir at elevation h. Thus, the general expression for the weir head-discharge relationship is Q = kh n (4) where k is a flow coefficient and n is an exponent. Both k and n are dependent on the shape of the weir (e.g., rectangular, triangular, trapezoidal or parabolic) and flow conditions (velocity distribution in the approach section, fluid viscosity, surface-tension effects, contraction coefficient). Apparatus The experiment is conducted in 2-foot open channel flume facility located in Model Annex, Iowa Institute of Hydraulic Research (IIHR). The weir shapes subjected to measurements in this experiment are rectangular and triangular. The geometry of these weirs is sketched in the Figure 2. The weir shapes are cut