# Displacement thickness

﻿
Displacement thickness

Displacement thickness is the distance by which a surface would have to be moved parallel to itself towards the reference plane in an ideal fluid stream of velocity $u_0$ to give the same mass flow as occurs between the surface and the reference plane in a real fluid.

In practical aerodynamics, the displacement thickness essentially modifies the shape of a body immersed in a fluid. It is commonly used in aerodynamics to overcome the difficulty inherent in the fact that the fluid velocity in the boundary layer approaches asymptotically to the free stream value as distance from the wall increases at any given location. The mathematical definition of the displacement thickness for incompressible flow is given by

:$\left\{delta^*\right\}= int_0^\left\{infty\right\} \left\{\left(1-\left\{uover u_0\right\}\right)dy\right\}$

and for compressible flow, by

:$\left\{delta^*\right\}= int_0^\left\{infty\right\} \left\{\left(1-\left\{ ho uover ho_0 u_0\right\}\right)dy\right\}$

where $ho_0$ and $u_0$ refer to the density and velocity outside the boundary layer.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Boundary-layer thickness — This page describes some parameters used to measure the properties of boundary layers. Consider a stationary body with a turbulent flow moving around it, like the semi infinite flat plate with air flowing over the top of the plate. At the solid… …   Wikipedia

• Momentum thickness — In aeronautics and viscous fluid theory, the boundary layer thickness ({delta}) is the distance from a fixed boundary wall where zero flow is considered to occur, and beyond {delta} the fluid is considered to move at a constant velocity. This… …   Wikipedia

• Boundary layer — For the anatomical structure, see Boundary layer of uterus. Boundary layer visualization, showing transition from laminar to turbulent condition In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of… …   Wikipedia

• Shape factor (boundary layer flow) — A shape factor is used in boundary layer flow to determine the nature of the flow.:H= frac {delta^*}{ heta}where H is the shape factor, delta^* is the displacement thickness and θ is the momentum thickness. Displacement thickness is defined as… …   Wikipedia

• Dimensionless quantity — In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a pure number, and as such always has a dimension of 1.[1] Dimensionless quantities are widely used… …   Wikipedia

• Cebeci-Smith model — The Cebeci Smith model is a 0 equation eddy viscosity model used in computational fluid dynamics analysis of turbulent boundary layer flows. The model gives eddy viscosity, mu t, as a function of the local boundary layer velocity profile. The… …   Wikipedia

• толщина вытеснения — (δ*) Расстояние по нормали к обтекаемой поверхности, которое определяет смещение линий тока вследствие вытесняющего действия пограничного слоя. Примечание Уравнение для расчета толщины вытеснения получается в результате рассмотрения баланса …   Справочник технического переводчика

• Birefringence — Displacement of light rays with perpendicular polarization through a birefringent material …   Wikipedia

• Quartz crystal microbalance — A quartz crystal microbalance (QCM) measures a mass per unit area by measuring the change in frequency of a quartz crystal resonator. The resonance is disturbed by the addition or removal of a small mass due to oxide growth/decay or film… …   Wikipedia

• Mindlin–Reissner plate theory — Deformation of a plate highlighting the displacement, the mid surface (red) and the normal to the mid surface (blue) The Mindlin Reissner theory of plates is an extension of Kirchhoff–Love plate theory that takes into account shear deformations… …   Wikipedia