A gauging structure is to be built across an artificial drainage channel in order to measure discharges. Designers have settled on a contracted sharp crested rectangular weir. The channel cross section is trapezoidal in shape, with a bed width of 3m and side slopes of 1 Vertical to 3 Horizontal. The bed and wall of the channel is covered with grass with an estimated Manning's n of 0.045. Along the length of the channel the bed drops by an average of 2.5 metres every kilometre. Historic accounts indicate that the maximum flow of water in the channel prior to the construction of the gauging structure was 1.4 m. As the channel cross section is relatively consistent over its length we can assume that in the absence of the gauging structure that water flows at normal depth. The general equation for flow over a weir is given by:
d ideal Q = C ×Q
Where Q is the actual flow rate, Qideal is the discharge estimated from conservation of energy principles and Cd is an experimentally derived coefficient which is dependent on the shape of the weir and the depth of water flow. In the calculations for flow over the weir you are instructed to account for the approach velocity to calculate the value of Qideal. In order to measure discharge an ultrasonic senor is to be located just upstream of the weir. The selected sensor has a maximum range of 1m, i.e. (max reading) - (min reading) = 1.0m
Weir Design Criteria:
To avoid submergence the crest of the weir must be at least 0.05 m above the downstream water depth. Here we can assume that the depth downstream is equal to the normal depth. To simplify calculations we will assume that Cd = 0.7 Water depth over the weir will be restricted by the range of the sensor.
Tasks:
a) Design the weir structure in order to accommodate the design max flow and maximise the use of the electronic sensor. Design variables include weir width and height of crest above the bed.
b) Use the direct step method to determine water profile upstream of the weir as a result of the weir. Plot the longitudinal bed, water surface and energy profiles over the length of this profile.