Solve Centrifuge Problem with Calculus & Angular Velocity

[Omar.Castillo]

I have a problem with a small physics problem. It requires some knowledge of calculus which I don't yet posses I am looking here for ideas. The problem states that there is a centrifuge tube with a length 12cm that is caused to spin by a rotating arm with lengt 8 cm. The tube is filled with 10 cm of a homogenous liquid with density p. It is rotating at a full angular velocity w and its traveling fast enough to be almost horizontal.

The question requires me to show that the resultant pressure of the liquied at a distance r from the axis of rotation is delta p/ delta r= prw^2

any suggetions on how to get this result?

 

[Doc Al]

Start by writing the net force on a small slice (thickness delta r) of the liquid. Use Newton's 2nd law to find that force. The acceleration is centripetal.