Control surfaceS S Control volume V Finite control volume moving Finite control volume with the fluid such that the fixed in space with the same fluid particles are al ways nuid moving through it in the same control volume
Step 2. Introduction of the concept of mass flow. Let a given area A is arbitrarily oriented in a flow the figure given bellow is an edge view If A is small enough, then the velocity v over the area is uniform across a. the volume across the area a in time interval dt can be given as Volume=(ndt)a A (edge view) V dr
Step 2. Introduction of the concept of mass flow. Let a given area A is arbitrarily oriented in a flow, the figure given bellow is an edge view. If A is small enough, then the velocity V over the area is uniform across A. The volume across the area A in time interval dt can be given as Volume = (Vn dt)A
The mass inside the shaded volume is Mass= p(,dt)A The mass flow through is defined as the mass crossing A per unit second, and denoted as in m=p(,dt)A dt O厂 m=pv a
The mass inside the shaded volume is Mass = (Vn dt)A The mass flow through is defined as the mass crossing A per unit second, and denoted as m dt V dt A m n ( ) = or m = Vn A
The equation above states that mass flow through A is given by the product Area X density X component of flow velocity normal to the area mass flux is defined as the mass flow per unit area Mass flux O丿
The equation above states that mass flow through A is given by the product Area X density X component of flow velocity normal to the area mass flux is defined as the mass flow per unit area Vn A m Mass flux = =
Step 3. Physical principle Mass can be neither created nor destroyed Step 4. Description of the flow field, control volume and control surface p=p(x,,z,t),v=v(x,y,z, t) ds Directional elementary surface area on the control surface dv: Elementary volume inside the finite controlvolume
Step 3. Physical principle Mass can be neither created nor destroyed. Step 4. Description of the flow field, control volume and control surface. (x, y,z,t), V V(x, y,z,t) = = dS : Directional elementary surface area on the control surface dV : Elementary volume inside the finite control volume