# Inviscid flow

(Difference between revisions)
 Revision as of 09:21, 12 September 2005 (view source)Praveen (Talk | contribs)← Older edit Revision as of 09:54, 12 September 2005 (view source)Praveen (Talk | contribs) Newer edit → Line 2: Line 2: ==Governing Equations== ==Governing Equations== - The governing equations for inviscid flow are obtained by discarding the viscous terms from the Navier-Stokes equations + The governing equations for inviscid flow, also known as ''Euler equations'', are obtained by discarding the viscous terms from the Navier-Stokes equations *Continuity equation *Continuity equation Line 11: Line 11: *Momentum equation *Momentum equation + + $+ \frac{\partial}{\partial t}(\rho u_i) + \frac{\partial}{\partial x_j}(\rho u_i u_j + p \delta_{ij}) = 0 +$ *Energy equation *Energy equation + + $+ \frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial x_j}[(\rho E + p)u_j] = 0 +$ + + where + + * $\rho$ is the density + * $u_i$ is the fluid velocity + * $p$ is the pressure + * $E$ is the total energy per unit mass of fluid

## Revision as of 09:54, 12 September 2005

A flow in which viscous effects can be neglected is known as inviscid flow. At high Reynolds numbers, flow past slender bodies involve thin boundary layers. Viscous effects are important only inside the boundary layer and the flow outside it is nearly inviscid. If the boundary layer is not separated then the inviscid flow model can be used to predict the pressure distribution with reasonable accuracy.

## Governing Equations

The governing equations for inviscid flow, also known as Euler equations, are obtained by discarding the viscous terms from the Navier-Stokes equations

• Continuity equation

$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}(\rho u_j)= 0$

• Momentum equation

$\frac{\partial}{\partial t}(\rho u_i) + \frac{\partial}{\partial x_j}(\rho u_i u_j + p \delta_{ij}) = 0$

• Energy equation

$\frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial x_j}[(\rho E + p)u_j] = 0$

where

• $\rho$ is the density
• $u_i$ is the fluid velocity
• $p$ is the pressure
• $E$ is the total energy per unit mass of fluid