Pressure at the bottom of a container containing two liquids

In summary: Consider the two volumes of liquid as objects with forces operating on them.The upper volume has the force Fa of the atmosphere pressing down on top, a normal force Fm pushing up from the lower volume, and gravity Fgu. These three forces are in balance, so Fm=Fa+Fgu.The lower volume likewise has three forces, Fb=Fm+Fgl, where Fb is the normal force from the bottom of the tube and Fgl is the force of gravity on the lower volume.Combining these we have Fb=Fa+Fgu+Fgl.So the pressures add up as you assumed.Thankss...:biggrin:
  • #1
Akash47
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5

Homework Statement


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(In the attachment)There is two layers of liquids in the container .The density of the upper layer of the container, ##ρ_1=800kg/m^3## and the density of the bottom layer of the container ,##ρ_2=13600kg/m^3## .What is the pressure at the bottom of the container?

Homework Equations


Pressure at height ##h## in a liquid from the surface, ##p=hρg##

The Attempt at a Solution


I have first calculated the pressure at the bottom of the first layer,##p_1=(3*800*9.8)=23520~pa##.Then taking the bottom of the first layer as the surface of the second layer,pressure at the bottom of the second layer,##p_2=(1*13600*9.8)~pa=133280~pa##.So the total pressure at the bottom of the container,##p=p_o+p_1+p_2=(101325+23520+133280)~pa=258125~pa.##Is my solution correct?If yes,then how can I make the solution more better(as I think it's not enough).If my solution is wrong,then tell me what's wrong and give hint for the solution.
 

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  • #2
Akash47 said:
how can I make the solution more better
Some data you are using is only to two significant figures, so you should claim no greater precision in your answer. I would round it to 258000 Pa, or maybe even 260000.
 
  • #3
I've made an assumption of adding the pressures at the bottom of different layers of liquids.I am looking for a reasonable logic for that.Is my solution overall correct?
 
  • #4
Akash47 said:
I've made an assumption of adding the pressures at the bottom of different layers of liquids.I am looking for a reasonable logic for that.Is my solution overall correct?
Yes, of course. It is a simple balance of forces. The normal force from the bottom of the container must balance the sum of the downward forces on the lower liquid: gravity and the normal force from the upper liquid. Likewise for the upper liquid.
 
  • #5
haruspex said:
Yes, of course. It is a simple balance of forces. The normal force from the bottom of the container must balance the sum of the downward forces on the lower liquid: gravity and the normal force from the upper liquid. Likewise for the upper liquid.
I haven't understand your language properly as I am not fluent in English.Please express your words more easily.
 
  • #6
Akash47 said:
I haven't understand your language properly as I am not fluent in English.Please express your words more easily.
Consider the two volumes of liquid as objects with forces operating on them.
The upper volume has the force Fa of the atmosphere pressing down on top, a normal force Fm pushing up from the lower volume, and gravity Fgu. These three forces are in balance, so Fm=Fa+Fgu.
The lower volume likewise has three forces, Fb=Fm+Fgl, where Fb is the normal force from the bottom of the tube and Fgl is the force of gravity on the lower volume.
Combining these we have Fb=Fa+Fgu+Fgl.
So the pressures add up as you assumed.
 
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Likes Akash47
  • #7
Thankss...:biggrin:
 

Related to Pressure at the bottom of a container containing two liquids

What is pressure at the bottom of a container containing two liquids?

The pressure at the bottom of a container containing two liquids is the force per unit area exerted by the weight of the liquids and any additional external forces.

How is pressure at the bottom of a container containing two liquids calculated?

The pressure at the bottom of a container containing two liquids is calculated by dividing the total force at the bottom of the container by the area of the bottom surface.

Does the density of the liquids affect the pressure at the bottom of the container?

Yes, the density of the liquids plays a crucial role in determining the pressure at the bottom of the container. The denser the liquids, the higher the pressure exerted at the bottom.

What other factors can affect the pressure at the bottom of a container containing two liquids?

The height of the liquids, the acceleration due to gravity, and the external forces acting on the surface of the liquids can also affect the pressure at the bottom of the container.

How does the pressure at the bottom of a container containing two liquids change when one liquid is more dense than the other?

If one liquid is more dense than the other, the pressure at the bottom of the container will be higher for the denser liquid and lower for the less dense liquid. This is because the denser liquid exerts a greater force on the bottom of the container.

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