authorized. C2017] A: Basic Channel Parameters and Stream Discharge Stream disch
ID: 116623 • Letter: A
Question
authorized. C2017] A: Basic Channel Parameters and Stream Discharge Stream discharge (Q) is simply the volume of water that passes a particular point along a stream in a given amount of time. Discharge is equal to the product of cross-sectional channel area and water velocity (assuming water velocity is uniform across the stream and with depth, an assumption that can be a good first-order approximation but is never strictly valid). That is, Q=A * v where Q = discharge (m3/s); A cross-sectional channel area (m2); v = velocity (m/s). For a simple channel with a rectangular cross-section, the cross-sectional area is simply equal to the product of channel width and channel depth. That is, where A = cross-sectional channel area (m2); w = channel width (m), h-channel depth 10 H Figure 1 Cross-sectional area of a simple channel. The area of the channel in "a" is 30 , whereas the area of the channel in "b" is 90 (w.H. Freeman and Company).Explanation / Answer
Answer for 2a:
The channels with rectangular cross sections are homogeneous but the non rectangular channels are not homogeneous, their properties are not same. They vary timely and spatially. The non rectangular channels are generally deeper, and one depth observation to calculate the cross section area will not give accurate results.
Answer for 2b:
The deepest point is at depth h. The width is w, so the cross section area would be wh. It assumes that the depth is h at every point. But in real, the depth is less than in in surroundings. It implies a high cross sectional area that it is in real.By having multiple sections, we are dividing the section into equally spaced rectangular cross sections, we get depth at each section, the cross sections for each division will be arrived, summing them will give appropriate results.
Answer for Q3a,b,c:
Formula for Cross section = Width * Depth
5
So these are the cross sections at each depth. On summing all these we have 256.25 cross sectional area. If we want to measure the same by a single observation, let us suppose at 11m depth(as it is the deepest for the section), the cross section would be 11 * 50 (depth - 11, width 5*10 = 50) which is 550 sqkm. This shows a severe variation. It misleads that the whole section has a depth of 11mts. But in real it has a depth profile. By doing multiple sections, we are considering each depth at the specified interval and calculating the cross sections. The accuracy can even be improved if we subdivide it more.
S.No Width Depth Cross SectionalArea 1 5 0.75 3.75 (5*0.75) 2 5 1.5 7.5 3 5 4 20 4 5 8 40 5 5 11 55 6 5 9 45 7 5 7 35 8 5 6 30 9 5 3 15 10 5 1
5
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