Question

Derivation of momentum equation in cylindrical coordinates

Answer 1

Answer:

Explanation:

Vector Notation & derivation in Cylindrical Coordinates - Navier-Stokes equation

Using, vector notation to write Navier-Stokes and continuity equations for incompressible flow

we have four unknown quantities, u, v, w and p ,

we also have four equations, - equations of motion in three directions and the continuity equation.

In principle, these equations are solvable but to date generalized solution is not available due to the complex nature of the set of these equations.

The highest order terms, which come from the viscous forces, are linear and of second order

The first order convective terms are non-linear and hence, the set is termed as quasi-linear.

Navier-Stokes equations in cylindrical coordinate (Fig. 24.2) are useful in solving many problems. If , and $ V_{z}$ denote the velocity components along the radial, cross-radial and axial directions respectively, then for the case of incompressible flow, Eqs (24.21) and (24.22) lead to the following system of equations:

FIG 24.2 Cylindrical polar coordinate and the velocity components...