A plug will be placed inside a tank and the tank will be filled with water to full height. Water will then be

slowly drained and the water level will start to drop. The height of the water level $h($see figure below$)$ at

which the plug pops up will be measured.

Given Data:

$h_1={5\mathrm{.}0}^{\text{'}\text{'}}$

$D={3\mathrm{.}5}^{\text{'}\text{'}},A=\frac{}{4}{D}^2$

$D_0=2.O^{\text{'}\text{'}},A_0=\frac{}{4}{D}_0^2$

Mass $of$ plug $=269g$

EXERCISES

Draw pressure distribution diagram for the cylindrical plug and calculate the vertical pressure forces

in terms of $A,A_0,h,h_1$ and $.$

Construct a Free Body Diagram for the cylinder by adding any other pertinent forces to the diagram

in part $1.$

Calculate the following in terms of $A,A_0,h,h_1$ and $$ :

a$.$ The expression for the equilibrium for the plug.

b$.$ The expression for the buoyant force. Show on the diagram, by shading, the portion of the

volume equivalent to the effective buoyant volume.

c$.$ The expression for the height $h$ at which the plug pops up$.$ Also, give the numerical value in

inches and compare with the experimental result.

For what value of A will the plug pop up when $h=0?$