Lecture no4 Application Linear Momentum （讲座4号应用线性动量）.pdfVIP

Principle of Linear Momentum Application Henryk Kudela Contents 1 Introduction 1 2 Application of the linear momentum equation 2 3 Elementary facts from Vector Calculus 5 3.1 Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 The flux of vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Gauss’ theorem (the divergence theorem) . . . . . . . . . . . . . . . . . . . . . 7 4 Problems 7 1 Introduction Let as recall the material from the lecture n3 equation of motion. Equation of motions is build on the basis of the balance of momentum principle. In particle mechanics a particle P that has mass m and move with the velocity v is said to posses (linear) momentum mv and the general statement of Newton ’s second law is d (mv) =F. (1) dt The term F encompass the ”sum of the forces acting on the mass ”. To generalize this law to continuum mechanics we define the linear momentum at time t possed by material of density x ρ ( ,t ) that occupies a region Ω(t) as x v ρ ( ,t) dυ . Ω(t ) This region Ω(t) is moved with the fluid and boundary