Question

The gauge pressure at the bottom of a cylinder of liquid is 0.30atm. The liquid is poured into another cylinder with twice the radius of the first cylinder. what is the gauge pressure at the bottom of the second cylinder?

Answer 1

Answer:

$P_g' = 0.075 atm$

Explanation:

Gauge pressure at the bottom of the cylinder depends on the height of water in the cylinder

So here we can say that

$P_g = \rho g h$

now when liquid is filled to height "h" in base area "A" then gauge pressure of the liquid at the bottom is given as

$P_g = 0.30 atm$

now we put the whole liquid into another cylinder with twice radius of the first cylinder

So area becomes 4 times

now by volume conservation we can say that if area is increased by 4 times then height of liquid will decrease by 4 times

so we have

$h' = \frac{h}{4}$

so gauge pressure is given as

$P_g' = \frac{0.30}{4} = 0.075 atm$