A centrifugal pump is used to pump a viscous fluid with a density of 800 kg/m^3 and a viscosity of 0.05 Pas. The pump impeller has a diameter of 30 cm and rotates at 1000 RPM. The fluid enters the pump at a radius of 5 cm and exits the pump at a radius of 15 cm, with a flow rate of 0.1 m^3/s. Assuming steady, axisymmetric flow and neglecting the effects of turbulence, use the Navier-Stokes equation in cylindrical coordinates to calculate the pressure distribution and velocity profile of the fluid in the pump.

Given parameters:

Fluid density = 800 kg/m^3

Fluid viscosity = 0.05 Pas

Impeller diameter = 30 cm

Impeller rotational speed = 1000 RPM

Inlet radius = 5 cm

Outlet radius = 15 cm

Flow rate = 0.1 m^3/s