Differential and Integral Approach

Differential approach aims to calculate flow at every point in a given flow field in the form P(x,y,z,t). When we determine the flow about an aerofoil using this approach we try to obtain the needed properties like $\rho, p,T$ everywhere within the region R surrounding the aerofoil as shown in Fig.3.16. From the detailed knowledge of the flow field we deduce features such as drag and lift. Aerofoil flow is complicated and we will have to solve the differential equations of motion. Obviously this is a costly approach calling for methods in computational fluid dynamics to be used.

Figure 3.16: Differential and Integral approaches to calculate flow about an Aerofoil.

 

Not every flow is as complicated as an aerofoil flow. In addition there is not necessary always to get a detailed information of the flow. One may establish a big control volume to encompass the region R and calculate the overall features like drag and lift by studying what happens at the boundary of the control volume, i.e., at the control surface.This procedure is called the Integral approach. Both these approaches are important to us. First we discuss the integral approach. When we are more familiar with the methods to analyse the flow we take up the differential approach.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney