A gauging structure is to be built across an artificial channel in order to measure discharges. Designers have settled on a contracted sharp crested rectangular weir The channel cross section is rectangular in shape,with a bed width of 4 m and Manning n of 0.022. The bed drops by an average of 4.2metres every kilometre. The maximum flow in the channel is equal to 7 m3/s. The channel is uniform over its length so it can be assumed that the flow is normal in absence of the gauging structure. The general equation for flow over a weir is given by: Q = Cd ´Qideal 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 sensor is to be located just upstream of the weir. The selected sensor has a maximum range of 0.8 m, i.e. (max reading) - (min reading) = 0.8m Weir Design Criteria: - To avoid submergence the crest of the weir must be at least 0.1 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. You may increase the width of the channel in the vicinity of the weir if required.
b) Construct a rating curve for the weir from Q = 0 to 7 m3/s accounting for approach velocity
Qideal = 2/3*b*sqrt(2g*[(h1+u2/2g)3/2-(u2/2g)3/2])