Question

The pressure at the bottom of a full barrel of water is Poriginal. Determine what happens to the pressure when the radius or height of the barrel is changed and water is added to make the barrel full again. What happens to the pressure at the bottom of the barrel if the radius is increased by a factor of 3 and more water is added to fill the barrel to the top again?

Pressure does not change
A) Pnew = Poriginal/3
B) Pnew=Poriginal ×9
C) Pnew=Poriginal/9
D) Pnew = Poriginal x3

Answer 1

C) Pnew=Poriginal/9

Step-by-step explanation:

From the given conditions:

Original area,
`A_o=\pi.r_o\,^2`

New area of the barrel bottom panel after increasing by a factor of 3:

`r_(new)=3r_o`

On increasing the radius the area now becomes:

`A_(new)=\pi.(3r_o)^2`

`A_(new)=9\pi.(r_o)^2=9A_o`

As we know that there will be no increase in the down-force since the height remains constant.

Pressure is given as:

`P_(original)=(Force)/(A_o)`

∴New pressure:

`P_(new)=(Force)/(9A)`

`\Rightarrow P_(new)=(P_(original))/(9)`