For determine the density at a point, In fig. 2. 1 point C(x, y, z),s density is defined as mass per unit volume, the mean density within volume V would be given by P m/V, at point C (2-1) p=p(x,v,z, t) (2-2)
For determine the density at a point , In fig.2.1 point C(x,y,z)’s density is defined as mass per unit volume, the mean density within volume V would be given by = m/V, at point C lim (2 1) ' = − → V m V V C = (x, y,z,t) (2−2)
2-2 velocity field V=v(x,y,,t) V=ui+vi+wk Steady flow unsteady flow an(p,p, v 0 an(p,p, k ≠0 t t 2-2.1 one-two-and three-Dimensional flows
2-2 velocity field • 2-2.1 one-,two-,and three-Dimensional flows V V(x, y,z,t) = V ui vj wk ˆ ˆ ˆ = + + Steady flow unsteady flow 0 ( , , .....) = t p V 0 ( , , .....) t p V
Fig. 2.2, Example of one-dimensional flow Fig 2.3 Example of two-dimensional fiow
2-2.2 Timelines Pathlines. streaklines and Streamlines Visual representation of a flow field TL, PL STKL STML Timeline a number of adjacent fluid particles in the flow field are marked at given instant they form a line in the field Pathline: the path or trajectory traced out by moving fluid particle, the line traced out by the particle
2-2.2 Timelines, Pathlines, streaklines, and Streamlines • Visual representation of a flow field: TL; PL, STKL, STML • Timeline:a number of adjacent fluid particles in the flow field are marked at given instant, they form a line in the field • Pathline: the path or trajectory traced out by moving fluid particle, the line traced out by the particle
Sf treakline: a number of identifiable fluid particles in the low passed through one fixed location in space the line joining these fluid particles is defined as a streakline Streamline are lines drawn in the flow field so that at a given instant they are tangent to the direction of flow at every point in the flow field. No flow across a streamline
Streakline:a number of identifiable fluid particles in the flow passed through one fixed location in space , the line joining these fluid particles is defined as a streakline Streamline:are lines drawn in the flow field so that at a given instant they are tangent to the direction of flow at every point in the flow field. No flow across a streamline