Question

A uniform hollow cylinder is filled with equal mass amounts of pure water and oil such that the substances are completely separated if the pressure at the bottom of the water is 10.5 higher than it is at the top of the oil, then how high is the oil level above the bottom of the containter

Answer 1

@phi @amistre64

Answer 2

\[p_bot=p_0+p_{oil}+p_{h2o}\]

Answer 3

@phi hmmm ican't figure this out... i know that the bottom will be the pressures of all these...

Answer 4

and i know the masses are the same

Answer 5

of oil and water

Answer 6

I assume the top of the cylinder is open, and P_top is the pressure of the atmosphere
If we make the cylinder have a base area of 1 cm^2 we can fill in the numbers.
per http://www.engineeringtoolbox.com/liquids-densities-d_743.html
olive oil has a density of about 0.9 g/ cm^3
and water has a density of 1 g/ cm^3

Can you make progress with this?

Answer 7

i have 1000 kg/m^2 and 890kg/m^2

Answer 8

should i first solve m=m

Answer 9

solve m=m?

I would find the force of the water: mass* g and then the pressure
mass*g/base area of the cylinder
ditto for the oil

and you need the pressure of the atmosphere at sea level

Answer 10

per wikipedia
, a column of air one square centimeter in cross-section, measured from sea level to the top of the atmosphere, has a mass of about 1.03 kg

Answer 11

i have no mas for water... i only know that mass of both liquids are thesame

Answer 12

for force i need mass and i have no volume either

Answer 13

so the force of the water is unable to be gotten,

\[F_w=m_w*g\]

Answer 14

the mass of water however is

\[\rho V=\rho Ah\\]

Answer 15

mass is density times volume
density of water is 1000 kg/m^3
volume will be h1*1000 (assume base area is 1 m^2)
mass of the oil is 890*h2
h1+h2= h

Answer 16

\[\rho V=\rho Ah\]

Answer 17

that's correct, we don't know the height of the cylinder so i'm still not seeing the point of this

Answer 18

equal mass
h1*1000 = h2*890

Answer 19

\[i did this

Answer 20

so i got something

\[\frac{\rho_{h_2o}h_{h_2o}}{\rho_{oil}}\]

Answer 21

i left rho's by themself because i ned to symbolically solve for my class

Answer 22

actually we want the depth of the water correct

Answer 23

mass of the water is 1000*h1= 1000*0.89*h2= 890 h2
mass of the oil is 890*h2
together 2*890*h2
so we have
1780 h2 + Ptop= 10.5*Ptop

we need a number for Ptop

Answer 24

\[\frac{\rho_{oil}h_{oil}}{\rho h_{h_2o}}=h_{h_2o}\]

Answer 25

once we get any height we can solve for whatever they want...

Answer 26

yes but wy not solve for the heigt of water because that will be the height frm the bottom or the container to the oil level

Answer 27

yes but wy not solve for the heigt of water because that will be the height frm the bottom or the container to the oil level

mostly because 0.89 is nicer than 1/0.89

Answer 28

what idon't understand is when you did