5. An existing sewer at P is to be continued to Q and R on a falling gradient of 1 in 150 for plan distances of 27.12 m and 54.11 m consecutively, where the positions of \( \mathrm{P}, \mathrm{Q} \) and R are defined by wooden uprights. Given the following level observations, calculate the difference in level between the top of each upright and the position at which the top edge of each sight rail must be set at \( \mathrm{P}, \mathrm{Q} \) and R if a 2.5 m traveller is to be used. Level reading to staff on TBM on wall (RL 89.52 m\( ) 0.39 \mathrm{~m} \) Level reading to staff on top of upright at P 0.16 m Level reading to staff on top of upright at Q 0.35 m Level reading to staff on top of upright at R 1.17 m Level reading to staff on invert of existing sewer at P 2.84 m . All readings were taken from the same instrument position.

To calculate the difference in level between the top of each upright and where the top edge of the sight rail must be set, you first need to determine the reduced levels (RLs) for each position. For this, you can subtract the level readings from the RL of the TBM at P, which is 89.52 m. For example, at upright P: RL at P = 89.52 m - 0.16 m (staff reading) = 89.36 m. Similarly, do this computation for Q and R using their respective readings. Now, regarding the settings for the sight rail at each upright, we must account for the designed gradient. Since the sewer has a gradient of 1 in 150, calculate the necessary fall from P to Q and P to R. For instance, the fall from P to Q over a distance of 27.12 m at a 1 in 150 gradient gives a total fall of approximately 0.18 m, which alters the RL at Q. Don't forget to take the 2.5 m traveler height into account when calibrating where to set the sight rail! By accurately calculating these factors, you'll ensure precise leveling for the sewer continuation and avoid any future complications!