Question

A cylindrical container with a cross-sectional area of 68.2cm2 holds a fluid of density 826kg/m3 . At the bottom of the container the pressure is 119kPa . Assume Pat = 101 kPa and h = 2.22m

Find the pressure at the bottom of the container after an additional 2.55×10−3m3 of this fluid is added to the container. Assume that no fluid spills out of the container.

Answer 1

I used the equation h=V/CSA to find out the height that was added to the fluid:
\[h = \frac{ 2.55*10^{-3}m ^{3} }{ 0.682m ^{2} } = 0.0037m\]
Then, I added it to the height and used proportionality:
\[P = \frac{ \left( 2.22m+0.0037m \right)119kPa}{ 2.22m } = 119198Pa\]
I was told it is wrong, but idk what im doing wrong.

Answer 2

Looking at the question, the cylinder seems to be open from the top. Hence you must take into account atmospheric pressure when you write the total pressure at the bottom:

\[P(at) + \rho gh = P(bottom) \]

Hence, your proportionality equation is incorrect.

Use the above equation to find the answer.

Answer 3

I used the equation that you gave:
\[P(bottom) = 101kPa + (826kg/m ^{3})(9.81m/s^{2})(2.2237m) = 281*10^{3} Pa\]
The answer is wrong. It's supposed to be 1.22×105 Pa

Answer 4

1.22*10^5 Pa

Answer 5

Check your calculations. I am getting the right answer.