Pressure at the bottom of a container containing two liquids

[Akash47]

Homework Statement

(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.

 

[haruspex]

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.

 

[Akash47]

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?

 

[haruspex]

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.

 

[Akash47]

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.

 

[haruspex]

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 F_a of the atmosphere pressing down on top, a normal force F_m pushing up from the lower volume, and gravity F^gu. These three forces are in balance, so F_m=F_a+F_gu.
The lower volume likewise has three forces, F_b=F_m+F_gl, where F_b is the normal force from the bottom of the tube and F_gl is the force of gravity on the lower volume.
Combining these we have F_b=F_a+F_gu+F_gl.
So the pressures add up as you assumed.

 

[Akash47]

Thankss...