A fluid in a tank that rotates at a constant angular velocity about an axis (in this case about the

axis), rotates with the tank as a rigid body. The pressure gradient is written in cylindrical coordinates:

,

,

,

.

For this type of rigid body rotation, pressure is a function of

and

:

,

.

Integrating the last equation yields the pressure distribution:

,

.

Along an isobaric surface (surface of constant pressure)

, so:

,

,

integrating both sides yields the equation for surfaces at constant pressure:

,

since

, the equation is simplified to:

,

where

is the pressure in the fluid (Pa),

is the radial distance from the center (m),

is distance from the tank bottom (m),

is fluid density (

),

is angular velocity (rad/s),

is specific weight (

),

is acceleration due to gravity,

is a constant estimated as

(

), where

is fluid height (m).

[1] B. R. Munson, T. H. Okiishi, and W. W. Huebsch,

*Fundamentals of Fluid Mechanics*, 6th ed., Hoboken, NJ: John Wiley & Sons, 2010.