先进材料疑固实验室 Momentum transfer Laboratory of Advanced Materials Solidification The fluid is treated as a continuous distribution of matter.The study of momentum transfer,or fluid mechanics can be divided into two branches:fluid statics(fluids at rest),and fluid dynamics(fluids in motion). Wanced Materia 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Momentum transfer The fluid is treated as a continuous distribution of matter. The study of momentum transfer, or fluid mechanics can be divided into two branches: fluid statics (fluids at rest), and fluid dynamics (fluids in motion)
先进材料疑固实验室 Momentum transfer Laboratory of Advanced Materials Solidification When a fluid is flowing in the x direction parallel to a solid surface, the fluid has x-directed momentum,and its concentration is vp.By random diffusion of molecules there is an exchange of molecules in the z direction.Hence the x-directed momentum has been transferred in the =-direction from the faster-to the slower-moving layer. 1 V(y) V(y) 上游文通大学 SHANGHAI JIAO TONG UNIVERSITY
Momentum transfer When a fluid is flowing in the x direction parallel to a solid surface, the fluid has x-directed momentum, and its concentration is υxρ. By random diffusion of molecules there is an exchange of molecules in the z direction. Hence the x-directed momentum has been transferred in the z-direction from the faster- to the slower-moving layer. v V(y) v V(y)
先进材料疑固实验室 Momentum transfer Laboratory of Advanced Materials Solidification The equation for momentum transport is Newton's Law of Viscosity written as follows: dpvx 【=-V02 where is the flux of x-directed momentum in the z direction,v is kinematic viscosity,np,the momentum diffusivity,z is the distance of transport or diffusion,p is the density,and n is the viscosity. Newton's Law is the simplest relationship between the flux of momentum and the velocity gradient. 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Momentum transfer The equation for momentum transport is Newton's Law of Viscosity written as follows: where τzx is the flux of x-directed momentum in the z direction, ν is kinematic viscosity, η/ρ, the momentum diffusivity, z is the distance of transport or diffusion, ρ is the density, and η is the viscosity. Newton’s Law is the simplest relationship between the flux of momentum and the velocity gradient
先进材料疑固实验室 Momentum tansfer Laboratory of Advanced Materials Solidification Continuity equation in one dimension Pu dA=PudA P,P2---the average density at cross p2,u,,dA section A and cross section A2 pu,dA u,42---the average density at cross section A and cross section A2 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY
Momentum tansfer Continuity equation in one dimension ρ1, ρ2 --- the average density at cross section A1 and cross section A2 u1, u2 --- the average density at cross section A1 and cross section A2