Earth's Liquid Interior

I have thought of a simple way to prove that the earth's interior must be at least partially liquid without ever seeing the lava from a volcano. Logic tells us that since the earth is rotating, centrifugal force will be produced that will pull materials toward the equator of the earth. Sure enough, we know that the earth bulges at it's equator so that the circumference around the equator is about 40 km (27 miles) longer than the circumference around the poles.

Now, the same logic should tell us that this centrifugal force caused by the earth's rotation should pull the water in the oceans toward the equator. This means that the water in the tropics around the equator should be deeper than that of the oceans at higher latitudes. But yet there is no evidence that the water in the oceans is significantly deeper at any latitude on average than it is at any other latitude.

If the earth was purely solid, the centrifugal force caused by it's rotation would certainly cause the oceans near the equator to be deeper than at higher latitudes. The continental shelves in the higher latitudes would be dry land and the coastal lowlands in the tropics would be under water. The reason that this is not the case can be easily explained by the fact that the interior of the earth is also liquid and bulges at the equator by centrifugal force in the same way that water does.

This is why the earth's circumference at the equator is greater than at the poles but we see no significant difference in the depth of the world's oceans by latitude. Yet, we can also see that this liquid interior of the earth is much more viscous, resistant to flow, than is water because the gravity of the moon and sun change the ocean depth by tides but have no similar effect on the earth's land surface.