Answer to Question #175069 in Mechanical Engineering for asd ali

Question

A cylinder of diameter d and length L is required to float in a liquid. How much L for the cylinder to float when its longitudinal axis being vertical? (specific gravity for cylinder and liquid are 0.7 & 0.9 respectively)

Answer 1

Let the length of cylinder (H) is submerged in the liquid when it is kept in the liquid such that it's longitudinal axis is vertical.

Therefore in stable equilibrium condition,

The weight of liquid displaced=weight of cylinder

If: d=diameter of cylinder

L=length of cylinder

S_c= specific gravity of the cylinder

S_L= specific gravity of liquid

Therefore,

Weight of liquid displaced=Weight of cylinder

$S_L× \frac{π}{4}×d^2×H= S_c × \frac{π}{4}×d^2×L$

Hence,

$H= \frac{S_c}{S_L}×L=\frac{0.7}{0.9}×L=\frac{7}{9}×L$

Therefore length of cylinder submerged in the liquid is,

H=$\frac{7}{9}×L$

Therefore the length of cylinder which is floating outside the liquid.

=L- H=$\frac{2}{9}×L=0.222×L$