# External Flow

External flow is one where fluid is made to flow over or around an object, rather than through it. The two forces that are predominately associated with external flow are lift (a force that causes bodies to raise vertically) and drag (the friction force that acts against bodies moving through fluids). This article discusses the forces associated with external flow and how to calculate them.

## Contents

Cengel and Cimbala, Fluid Mechanics: Fundamentals and Applications, (2nd ed, Singapore, McGraw Hill Education, 2010), pp. 538 - 621 (Chapter 11).

## Lift and Drag Coefficients

Formally, drag is the component of the force created by external flow on a body that acts parallel to the direction of motion, while lift is the component of the force acting normal to the flow direction. Since both vary with many variables such as area, fluid density, surface roughness, velocity etc. it is convenient to work with dimensionless numbers when calculating these forces. These dimensionless numbers are the drag and lift coefficients, given by:  Where:

CD = Drag Coefficient
CF = Lift Coefficient
A = Frontal Area. That is the area projected on a plane normal to the direction of flow.

Hence, if the coefficients are known, then the respective forces can be calculated by simple rearrangement of the above equations. Often the coefficients are known from experimental results or data tables.

### Corollary to the Drag Coefficient

Drag can actually occur due to both pressure differences and due to to frictional forces. hence drag is the sum of both of these effects. The issue is that often decreasing one of these components increases the other and hence the actual target should be to reduce their sum, not the individual components.

Another issue is that of flow separation, which is when, at high velocities, fluid stops attaching itself to the body and separates off it. When this happens, the separated fluid creates a low pressure area and recirculation, which can further increase pressure drag.

## Induced Drag

At wing tips, fluids create vortices which can induce extra drag on the body being lifted. To reduce these effects, its common to add wing tips to stop vortices from being created.