(a) A weir is used to measure water discharge in an open channel. Use dimensional analysis with ρ, g,h as the recurring

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(a) A weir is used to measure water discharge in an open channel. Use dimensional analysis with ρ, g,h as the recurring set, to show that the discharge per unit width, q, relates to head over the weir, h, (Figure Q1) through q=CD​g​h3/2, where ρ is water density, g is acceleration due to gravity, and CD​ is the weir discharge coefficient, which depends on h/hw​, where hw​ is the weir height. [5 marks] (b) A model weir with height 0.1 m was tested in a 1.2 m-wide laboratory flume. Measurements of the total discharge in the flume and the head over the weir yielded the following data: Calculate and plot the dependence of the discharge coefficient on h/hw​ for this weir. [5 marks] (c) A 1.5 m-high weir that is geometrically similar to the model weir tested in the laboratory flume in Part (b) spans the full width of a 25 m-wide river. What is the discharge in the river if the measured head over the weir in the river is 2.25 m ? [4 marks] (d) For the weir in Part (c), what is the head over the weir for a discharge in the river of 27.5 m3/s ?