A horizontal thin tube of length 2L completely filled with a liquid of density `delta` rotates about a vertical axis passing through one of its end and along the diameter of its side face with an constant angular velocity `omega`. Two vertical thin long tubes are fitted with the horizontal tube to measure the pressure difference between points A and B which are at same horizontal level as shown. Neglect viscous forces and surfaces tension of liquid.

The graph of the pressure gradient `((dP)/(dx))` with the distance x meaured from the axis of rotation is :