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The mean depth is calculated by ________ the depths of two consecutive sections.
adding
averaging
subtract
multiplying
averaging
In surveying for earthwork calculations, the mean depth of two consecutive sections is determined by calculating the arithmetic mean of their individual depths. This approach assumes that the cross-sectional area changes linearly between the two given stations.
In surveying for earthwork calculations, the mean depth of two consecutive sections is determined by calculating the arithmetic mean of their individual depths. This approach assumes that the cross-sectional area changes linearly between the two given stations.
dmтАЛ=2d1тАЛ+d2тАЛтАЛ тАФ formula for mean depth of two sections
V=AmтАЛ├ЧL тАФ formula for volume calculation using mean area
The mean depth method (also known as the average depth method) is applied to estimate the volume of earthwork between two sections. If d1тАЛ and d2тАЛ are the depths at two consecutive sections separated by a length L, the mean depth dmтАЛ is given by dmтАЛ=2d1тАЛ+d2тАЛтАЛ. This simplifies the computation of volumes for embankments or cuttings, although it is an approximation compared to the prismoidal formula.
Mean depth method is the simplest approach for earthwork estimation.
It assumes a linear variation of cross-sectional area between stations.
It is typically used for preliminary estimates rather than high-precision projects.
Simple and quick calculation
Requires minimal data points
Less accurate than the prismoidal formula
May overestimate volume if the ground profile is significantly non-linear
Preliminary road construction planning
Estimation of volume for minor earthwork projects
The prismoidal formula provides more accurate results for curved surfaces by incorporating the mid-section area.
Option A (adding) is incorrect as it would provide the sum, not the average.
Option C (subtract) is incorrect as it relates to the difference between stations.
Option D (multiplying) is incorrect as it does not represent the geometric mean of depth.
B is correct тАФ the mean depth is calculated by averaging the depths of two consecutive sections to estimate the average cross-sectional profile.
Always remember that for high-precision earthwork calculations in competitive exams, the prismoidal formula V=6LтАЛ(A1тАЛ+4AmтАЛ+A2тАЛ) is preferred over the mean area or mean depth methods.
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