# Horizontal force across a partition

• Parsifal1
In summary, the question asks for the net force on a partition caused by the difference in pressure on each side.f

## Homework Statement

Find the horizontal force across the partition in a water tank with two compartments, one filled with water to x height and the other with water to y height. I've worked out the thrust acting on the partition as a result of density, height, gravity and average depth, so I have two horizontal vectors, with which to find the total horizontal force.

F=PaA
P=pgh
F=pgha

## The Attempt at a Solution

(sum) Fx=(Force from oil) - (Force from water). Problem is I don't know which force is in which direction relative to the partition. The only solution I can see, which would make sense is adding the two forces together. Is this correct?

I'm confused.
You write,
(sum) Fx=(Force from oil) - (Force from water).
... but "oil" is not mentioned in the problem statement, which says:
... two compartments, one filled with water to x height and the other with water to y height.
... just water on each side of the partition.

Looking at those heights:
Lets say y>x, then what else is in the tank at height h: y-x<h<y? What about when h>y?

Problem is I don't know which force is in which direction relative to the partition.
... but your problem statement says:
Find the horizontal force across the partition
... which direction is "horizontal"?

The question says there is a tank which has a vertical partition across the width. There are two compartments in the tank, one contains water the other oil. I have worked out the hydrostatic force each liquid exerts on the partition. Now I have to find the 'horizontal force on the partition', Do I add the two forces together?

I'm confused.
You write, ... but "oil" is not mentioned in the problem statement, which says: ... just water on each side of the partition.

Looking at those heights:
Lets say y>x, then what else is in the tank at height h: y-x<h<y? What about when h>y?

... but your problem statement says: ... which direction is "horizontal"?

Horizontal parallel to the base of the tank, normal to the vertical partition, I assume.

Does the horizontal resultant force equal the difference between the two opposing forces?

The resultant force is the vector sum of all the forces ... the horizontal resultant force is the horizontal component of the resultant force.
In your case - where do the forces come from? Where do the forces act?

I am making some assumptions about what the question is really asking ... technically the net horizontal force on the partition must be zero since it is not accelerating. I am guessing the question wants the net force due to the difference in pressure on each side.

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