How do you determine the volume of water passing through a weir?  R 

If the speed of the water were uniform as it passes through the opening, you could measure that speed and multiply it by the crosssection of the weir to obtain the volume of water passing through the weir each second. However, since the flow is faster near the center of the flow, it's difficult to calculate the volume flowing each second. Your best bet is probably to divide the opening into a number of regions and then to measure the water's velocity at the center of each region. Multiply each velocity by the crosssectional area of that region and then sum up all the products to obtain the overall volume flow per second.