# Vortex Flow (Kinematics and Dynamics of Flow Part-4)

### Free Vortex Flow

##### Example:Flow in a circular pipe or A whirlpool in river.

First of all, let’s take a general case where the fluid is rotating about some axis and we will find an expression for the pressure at some point.

Let us consider a small element of fluid element rotating at uniform velocity in horizontal plane about an axis perpendicular to out of plane.

##### If it is positive then pressure increases with radiaus and if it is negative pressure decreseas with radius

But we already know that pressure variation in vertical plane is given by hydrostatic law, as

#### ∂P/∂h = ρg

Hence, it can be said that pressure at any point is function of h and r

### Equation of forced vortex flow

##### Putting we get,

The pressure difference between two points can be calculated with the help of the integrating function.

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