This is the same as having a square plate of sides 6.0 cm submerged in mercury.

Finding force due to liquid pressure by integration

 

This is a very basic example where the width of the plate does not change as we move down the plate.

It is always `x = 6`.

Also, the depth of the top of the plate is 0, so `a = 0`.

To apply the formula, we have:

`x = 0.06\ "m"`

`y` is the variable of integration

`w = 133\ "kN m"^-3= 133,000\ "N m"^-3`

`a = 0`

`b = 0.06`

So we have:

`"Force"=w int_a^b xy\ dy`

`=133000 int_0^0.06 0.06y\ dy`

`=7980 int_0^0.06\ y\ dy`

`=7980[(y^2)/(2)]_0^0.06`

`=14.4\ text[N]`

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