A sewer is laid from a manhole A to a manhole B, 250 m apart along a downward grade of 1 in 125. If the R.L. of the invert at A is 205.75 m and the length of boning rod is 3 m, then R.L. of the sight rail at B is
206.75 m
Understanding Sewer Gradients and Levels
This problem involves calculating the Reduced Level (R.L.) of a sight rail at manhole B, given the distance between two manholes, the downward grade of the sewer, the R.L. of the invert at the starting manhole (A), and the length of a boning rod.
Calculating the Sewer Invert Drop
First, we need to determine the total vertical drop of the sewer invert between manhole A and manhole B.
- Distance between A and B = 250 m
- Grade = 1 in 125 (downward)
The grade of 1 in 125 means that for every 125 meters horizontally, the sewer drops 1 meter vertically.
To find the total drop over 250 m, we can use the following calculation:
Total Drop = \(\frac{\text{Distance}}{\text{Grade denominator}}\)
Total Drop = \(\frac{250 \text{ m}}{125}\)
Total Drop = \(2 \text{ m}\)
Calculating the R.L. of the Invert at B
We know the R.L. of the invert at manhole A and the total drop between A and B. The R.L. of the invert at B is calculated by subtracting the total drop from the R.L. of the invert at A.
- R.L. of invert at A = 205.75 m
- Total Drop = 2 m
R.L. of invert at B = R.L. of invert at A - Total Drop
R.L. of invert at B = \(205.75 \text{ m} - 2 \text{ m}\)
R.L. of invert at B = \(203.75 \text{ m}\)
Determining the R.L. of the Sight Rail at B
Sight rails are used to establish the correct gradient line for setting out levels. The boning rod is used in conjunction with the sight rails. A common practice is to set the sight rail at a specific, consistent height above the invert level at each manhole. The length of the boning rod often represents this height difference.
In this case, the boning rod length is given as 3 m. We assume the sight rail at manhole B is set 3 meters above the invert at manhole B.
- R.L. of invert at B = 203.75 m
- Height difference (Boning Rod Length) = 3 m
R.L. of sight rail at B = R.L. of invert at B + Height difference
R.L. of sight rail at B = \(203.75 \text{ m} + 3 \text{ m}\)
R.L. of sight rail at B = \(206.75 \text{ m}\)
Conclusion
Based on the calculations, the R.L. of the sight rail at manhole B is 206.75 m. This aligns with the principle of maintaining a consistent offset from the invert level using the provided boning rod length.
Important Questions from Levelling
Calculate the true reduced level (m) of a point A after correcting the refraction and curvature. The staff reading at the point taken from an instrument set at a distance of 2 km from the point A is 2.56 m. The staff reading from the same station on a bench mark of reduced level is 100 m is 1.34 m.
The dumpy level is most suitable for levelling survey:
Levelling in which staff and readings and the distance between the points is required is called:
In permanent adjustment of levels, two peg test is done to correct:
In a levelling work, seven readings were taken with a level as - 1.42, 1.57, 0.765, 1.11, 1.95, 2.9, and 1.825 m. If the instrument was shifted after the third and fifth readings, the readings recorded under the fore sight column will be:
