## What is the trapezoidal approximation formula?

We apply the trapezoidal rule formula to solve a definite integral by calculating the area under a curve by dividing the total area into little trapezoids rather than rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.

**What is the formula for the area of a trapezoidal channel?**

The hydraulic radius for flow in a trapezoidal open channel can be expressed in terms of y, b, and z, as follows: i) The cross-sectional area of flow, A, is the area of the trapezoid in Figure 4: A = y(b + B)/2 = (y/2)(b + B)

### How do you approximate area with the trapezoidal rule?

Trapezoidal rule approximates area under the curve With this method, we divide the given interval into n subintervals, and then find the width of the subintervals. We call the width Δx. The larger the value of n, the smaller the value of Δx, and the more accurate our final answer.

**What is a trapezoidal sum approximation?**

The Trapezoidal Rule is the average of the left and right sums, and usually gives a better approximation than either does individually. Simpson’s Rule uses intervals topped with parabolas to approximate area; therefore, it gives the exact area beneath quadratic functions.

## What is Manning’s equation used for?

The Manning equation is a widely used and very versatile formula in water resources. It can be used to compute the flow in an open channel, compute the friction losses in a channel, derive the capacity of a pipe, check the performance of an area-velocity flow meter, and has many more applications.

**How do you approximate an integral?**

1: The midpoint rule approximates the area between the graph of f(x) and the x-axis by summing the areas of rectangles with midpoints that are points on f(x). Use the midpoint rule to estimate ∫10x2dx using four subintervals. Compare the result with the actual value of this integral.

### What is Manning’s value?

The Manning’s n is a coefficient which represents the roughness or friction applied to the flow by the channel. Manning’s n-values are often selected from tables, but can be back calculated from field measurements.