Answer to Question #151311 in Classical Mechanics for Dan

Question

A steel pipeline conveying gas has an internal diameter of 1.2m and an external diameter of 1.25m. It is laid across the bed of a river, completely immersed in water and is anchored at intervals of 3m along its length. Determine the buoyancy force in newtons per metre run and the upward force in newtons on each anchorage. Density of steel = 7900 kg/m¬3, density of water is 1000 kg/m3.

Answer 1

Answer

Buoyancy force per meter

=$V\rho_{water} g\\$

$=9810\times \frac{\pi}{4}\times1.25^2\times1\\=12039N/m$

Buoyancy force for 3 meter

$F=12039\times3=36117N$

Weight of steel pipe

$W=3\times7900\times9.81\times\frac{\pi}{4}\times(1.25^2-1.20^2) \\W=22369N$

Total upward force

$=F-W\\=36117-22369\\=13748N$