By Richard H. Pletcher

This finished textual content offers uncomplicated basics of computational idea and computational tools. The booklet is split into components. the 1st half covers fabric basic to the knowledge and alertness of finite-difference tools. the second one half illustrates using such equipment in fixing kinds of advanced difficulties encountered in fluid mechanics and warmth move. The ebook is replete with labored examples and difficulties supplied on the finish of every bankruptcy.

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Example text

Gravity) applied at the centre of mass of the control volume. 3), Vj is the velocity component in the /-direction, F^^i is the resultant of the volume forces (per unit volume) and (Tij is the stress tensor (see notes below). g. x, y). g. gravity force F^^i = —grad (gz)). Further, for a Newtonian fluid the stress forces are (1) the pressure forces and (2) the resultant of the viscous forces on the control volume. 8) where P is the pressure and F^^^c is the resultant of the viscous forces (per unit volume) on the control volume.

No momentum accumulation). 13a) where ZF^ is the resultant of all the forces in the ^--direction, the subscripts 1 and 2 refer to the upstream and downstream cross-sections, respectively, and (F^/)/=i,2 is the velocity component in the ^-direction. 13b) In simple terms, the momentum equation states that the change in momentum flux is equal to the sum of all forces (volume and surface forces) acting on the control volume. Note For a steady incompressibleflow,the momentum flux equals (pQV). Application: hydraulic jump In open channels, the transition from a rapid flow to a slow flow is called a hydraulic jump (Fig.

4). 2. In practical engineering applications, N can range from 4 (for shallow waters in wide rough channels) up to 12 (smooth narrow channel). A value TV = 6 is reasonably representative of open channelflowsin smooth-concrete channels. However, it must be remembered that A/^ is a fimction of theflowresistance. 3. For a wide rectangular channel, the relationship between the mean flow velocity Fand the free surface velocity F^ax derives from the continuity equation: q = Vd= \ \ dy = — ^ F ^ a x ^ 4.

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