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1. #VOLUME OF TRAPEZOIDAL PRISM HOW TO#
2. #VOLUME OF TRAPEZOIDAL PRISM FULL#
3. #VOLUME OF TRAPEZOIDAL PRISM SOFTWARE#
4. #VOLUME OF TRAPEZOIDAL PRISM PLUS#

For our tank problem we have the required data pairs - they represent the bottom and top y values for the interval for which a volume result is needed, and two x widths corresponding to the y values.įrom a technical standpoint, equation (5) first "normalizes" the range of x values - that is, it makes them fall between zero and one. Now that we have computers to help us, we can use a combined equation that eliminates the need to separately compute m and b:įor equation (5), instead of computing m and b, we directly use the two data pairs ( xa,ya and xb,yb) shown in Figure 2. In that time it was desirable to break the calculation into as many individual steps as possible to avoid errors and make the process more manageable.

#VOLUME OF TRAPEZOIDAL PRISM HOW TO#

Having gotten a value for m, here is how to compute b:Įquations (2) through (4) show the classical form of linear interpolation that predates the computer era, a time when these results were likely to be acquired through hand calculation. Two new variables appear in equation (2): m and b. In this context, "linear" means a graphical representation will produce a straight line passing through two defined data points as in Figure 2. If given an x argument, equation (2) creates a y result that has been shifted and scaled to agree with any desired linear transformation. Here is the classical way to express this idea: The desired intermediate y values are computed using a method called "linear interpolation," a way to translate one numerical range to another ("interpolation" means computing intermediate values between defined points). Given these two defined points, we can compute intermediate y values for provided x arguments.

This very useful method requires two defined data pairs ( xa,ya and xb,yb) as shown in Figure 2.

#VOLUME OF TRAPEZOIDAL PRISM FULL#

It should be obvious that each intermediate height of a trapezoidal tank is computed the same way that the full tank is, but it's not obvious what the intermediate x widths should be for each height in the y dimension - that will be our next task.įigure 2: Linear Interpolation Graph Linear Interpolation That's fine for a full volume result, but it would be useful to obtain intermediate volume results - a volume for each content height in the tank as measured by a level sensor, for example. Computing the full volume for this tank type is then very easy: As shown in Figure 1, let:įigure 1 shows that the x dimension of the tank is different at the bottom than at the top, so we'll use the name xb to refer to the x dimension's bottom width and xt to refer to the x dimension's top width. If there’s no Encasement, then no adjustment is made.The full volume for a first-order trapezoidal tank is quite easy to compute, but first let's adopt a variable naming convention to be used through this entire exercise.

#VOLUME OF TRAPEZOIDAL PRISM SOFTWARE#

When No Headers has been chosen and a Stone Encasement has been selected, the software will still add an amount to each end of the Barrel equal to the (Encasement Width – Chamber Span)/2.

#VOLUME OF TRAPEZOIDAL PRISM PLUS#

This will tend to increase the total encasement depth at the downstream end (Depth as inputted plus L x Slope) and resulting storage. Instead, the software assumes the encasement is level on top but sloped on the bottom. It should be noted that the top of the stone encasement is not subject to an inputted barrel slope. When the pipe slope equals zero, Volume = L x A1 Stone Encasements M = cross-sectional area of depth at midsection Volume of a generic chamber pipe only is computed by:Ī1 = cross-sectional area of depth at downstream endĪ2 = cross-sectional area of depth at upstream end Z = side slope, (Z:1) (horizontal to 1-vertical) Generic Underground Chambers Trapezoidal shaped ponds are computed by: The Conic method uses this equation:ĭ = change in elevation between points 1 and 2Ī2 = surface area at elevation 2 Trapezoid Hydrology Studio uses either the average-end-area method applied vertically or the Conic method. Stage Storage calculations use the procedures below based on the storage type selected.