# How is a two-dimensional irrotational flow expressed in cylindrical coordinates?

## How is a two-dimensional irrotational flow expressed in cylindrical coordinates?

Two-Dimensional Irrotational Flow in Cylindrical Coordinates In a two-dimensional flow pattern, we can automatically satisfy the incompressibility constraint, , by expressing the pattern in terms of a stream function. Suppose, however, that, in addition to being incompressible, the flow pattern is also irrotational.

## Is the irrotational flow pattern also incompressible?

Suppose, however, that, in addition to being incompressible, the flow pattern is also irrotational. In this case, Equation ( 5.10) yields Let us search for a separable solution of Equation ( 5.61) of the form

How is the velocity potential of an irrotational flow defined?

It is to be noted, however, that the velocity potential can be defined for a general three-dimensional flow, whereas the stream function is restricted to two-dimensional flows. For an incompressible flow we know from the conservation of mass: ∇⋅=V0 and therefore for incompressible, irrotational flow, it follows that ∇2φ=0

### What is the continuity equation for incompressible flow?

where q is the volumetric flow rate per unit width between streamlines ψ1 and ψ2 . If ( ψ2 – ψ1 ) is positive, the flow is from left to right; whereas if ( ψ2 – ψ1 ) is negative, the flow is in the opposite direction (from right to left). For incompressible flow in the two-dimensional cylindrical coordinate system, the continuity equation is

### Why are cylindrical coordinates used for axisymmetric flow?

Axisymmetric flow Cylindrical coordinates are chosen to take advantage of symmetry, so that a velocity component can disappear. A very common case is axisymmetric flow with the assumption of no tangential velocity ((u_{theta}=0)), and the remaining quantities are independent of (theta).