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It uses a combination of the energy, momentum, and continuity equations to determine water depth with a given a friction slope (), channel slope (), channel geometry, and also a given flow rate. In practice, this technique is widely used through the computer program HEC-RAS , developed by the US Army Corps of Engineers Hydrologic Engineering ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
The slope a measures the rate of change of the output y per unit change in the input x. In the graph, moving one unit to the right (increasing x by 1) moves the y-value up by a: that is, (+) = +. Negative slope a indicates a decrease in y for each increase in x.
In this case, the equation governing the beam's deflection can be approximated as: = () where the second derivative of its deflected shape with respect to (being the horizontal position along the length of the beam) is interpreted as its curvature, is the Young's modulus, is the area moment of inertia of the cross-section, and is the internal ...
The gradient can also be used to measure how a scalar field changes in other directions, rather than just the direction of greatest change, by taking a dot product. Suppose that the steepest slope on a hill is 40%. A road going directly uphill has slope 40%, but a road going around the hill at an angle will have a shallower slope.
Here, is a free parameter encoding the slope at =, which must be greater than or equal to because any smaller value will result in a function with multiple inflection points, which is therefore not a true sigmoid.
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
The Bruun rule is a formula for estimating the magnitude of the retreat of the shoreline of a sandy shore in response to changes in sea level. Originally published in 1962 by Per Bruun, [ 1 ] the Bruun rule was the first to give a relationship between sea level rise and shoreline recession . [ 2 ]