gradient
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GC: n

CT: The significance of slope or gradient.
17. In simple cases, you can assume that the bottom of the canal will slope downstream. In fact, water will flow in canals as long as the water level is higher at the upstream end than the downstream end. If a canal has a horizontal floor, the gradient can be taken as the difference in head between upstream and downstream. The slope S of the canal bottom is expressed as metres of head per metre of canal length, for example S = 0.01 or 1 percent. The greater the value of S, the greater the flow.
18. Note that for steady, even flow and to minimize the risk of sedimentation, the canal should be built so that its bottom slope follows the overall gradient, i.e. the depth remains constant. Because they are easier to construct, however, canal bases are often made horizontal..

S: FAO – http://www.fao.org/tempref/FI/CDrom/FAO_Training/FAO_Training/General/x6708e/x6708e08.htm (last access: 13 December 2019)

N: 1. “steep slope of a road or railroad,” 1835, principally in American English, probably from grade (n.) by analogy of quotient, etc. (Oxford English Dictionary). It was used 17c. as an adjective, of animals, “characterized by walking;” in that case it is probably from Latin gradientem, present participle of gradi “to walk.”
2. The rate of regular or graded ascent or descent : inclination. A part sloping upward or downward.
2 : change in the value of a quantity (such as temperature, pressure, or concentration) with change in a given variable and especially per unit distance in a specified direction
3. Design of canals. All canals should be well designed to have the required water carrying capacity. The canals are designed using formulas that relate the carrying capacity of the canal to its shape, its effective gradient or head loss, and the roughness of the canal sides. The most commonly used formula incorporating all these factors is the Manning equation:
v = (1 ÷ n) (R2/3(S1/2)
where
v = water velocity in the canal;
n = roughness coefficient of the canal sides;
R = hydraulic radius of the canal;
S = effective slope.
4. Some other points to remember. In many cases you may have several choices of width, depth, gradient, side slope, etc. Some other practical factors may help you define your choice:

  • If the water carries silt, too low a velocity will encourage the silt to settle out. You may wish to design an area specifically for this purpose.
  • If you need to cross the canal, it may be better to make it narrower at this point, possibly by lining the walls.
  • If there are difficult or permeable soils at lower levels, you may wish to keep canals wide and shallow.
  • If there are standard tools available for construction and maintenance, such as a bulldozer blade or a backhoe shovel, you may prefer to base canal sizes on these. Similarly, if you are using sheet polythene or concrete slabs* to line the canal, you may wish to size the canals to suit standard dimensions.
  • Remember to allow sufficient capacity for floodwater likely to reach the canal.

5. Gradient, in mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables. The symbol for gradient is ∇. Thus, the gradient of a function f, written grad f or ∇f, is ∇f = ifx + jfy + kfz where fx, fy, and fz are the first partial derivatives of f and the vectors i, j, and k are the unit vectors of the vector space. If in physics, for example, f is a temperature field (giving the temperature at every point in a space), ∇f is the direction of the heat-flow vector in the field

S: 1. OED – https://www.etymonline.com/search?q=gradient (last access: 13 December 2019). 2. MW – https://www.merriam-webster.com/dictionary/gradient (13 December 2019). 3 & 4. FAO – http://www.fao.org/tempref/FI/CDrom/FAO_Training/FAO_Training/General/x6708e/x6708e08.htm (last access: 13 December 2019). 5. EncBrit – https://www.britannica.com/science/gradient-mathematics (last access: 13 December 2019).

SYN: slope (depending on context)

S: FAO – http://www.fao.org/tempref/FI/CDrom/FAO_Training/FAO_Training/General/x6708e/x6708e08.htm (last access: 13 December 2019)

CR: geothermal gradient, hydraulic gradient, ocean’s thermal gradient.