Find Oil Density in Open Tank with Horizontal Bottom

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adoza
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An open tank has a horizontal bottom. It is divided into two parts by a vertical gate. The gate
is rectangular, 3m high and it is hinged at its top. Water of density p,=1000kg/m3 in one part
of the tank is acting on one side of the gate, and oil of density p, in the other part of the tank
is acting on the other side of the gate. The gate is in equilibrium in vertical position. The
water depth is 1.50m and the oil depth is 1.65m. Find the oil density p,.
 

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i have tried working out the pressures of each liquid hence the horizontall pressure they apply to the gate but have always come up with the wrong answer. do i need to find the horizontall pressure to find the density of the oil?
 
adoza said:
i have tried working out the pressures of each liquid hence the horizontall pressure they apply to the gate but have always come up with the wrong answer. do i need to find the horizontall pressure to find the density of the oil?

pressure acts in all directions, so saying horizontal pressure is redundant. but yes.

remember at eqbm, the moment at the hinge of the gate is 0.
a moment is a force times an area
a force is a pressure times an area
pressure in a fluid varies with height

i did the hard part, your turn - it should be all numbers from here on out