Question

A stadia measurement was undertaken with a theodolite having an internal focusing

telescope and stadia interval factor of 98.8. When a backsight was taken on a turning

point whose elevation is 205.62 m, the rod interval observed was 1.94 m; and with the

horizontal hairs set at 1.50 m on the rod, the vertical angle reading was +13045’. For a

foresight to a control point, the rod intercept was 1.17 m; and with the horizontal hair

reading of 1.60 m on the rod, the vertical angle observed was -7018’. Determine the

elevation of the line of sight at the instrument point and the elevation of the point on

which the foresight was taken.

Answer 1

For no spilling of water, rise above the original water level is equal to fall below the original water level

Height of paraboloid of revolution, 

where, 

ω = Angular velocity

R = Radius of cylinder

Calculations:

Given Data:

Diameter = 2 m

Height of Tank = 4 m

Depth of water = 1.5 m

So, Radius, R = 1 m

Rise above the original water level for no spilling = 4 - 1.5 = 2.5 m

As, Rise above level = Fall below level

So, Fall = 2.5 m

So, the total height of paraboloid = Rise + Fall = 2.5 + 2.5 = 5 m

Putting all that data in above equation, we get,

$5 = ω ^2 × 1 ^2 /2 × 9.81$

ω = 9.9 rad/sec