## I4 Fluid Mechanics

In industrial processes we deal with materials that can be made to flow in a conduit of some sort. The laws that govern the flow of materials form the science that is called fluid mechanics. The behavior of the flowing fluid controls pressure drop (pumping power), mixing efficiency, and in some cases the efficiency of heat transfer. So it is an integral portion of an energy conservation program.

### I.4.1 Fluid Dynamics

When a fluid is caused to flow, certain governing laws must be used. For example, mass flows in and out of control volumes must always be balanced. In other words, conservation of mass must be satisfied.

In its most basic form the continuity equation (conservation of mass) is

Fig. I.11 Radiation shape factor for perpendicular rectangles with a common edge.

That is, the mass flow rate m is constant and is equal to the product of the fluid density p^, the duct cross section Ac, and the average fluid velocity u.

If the fluid is compressible and the flow is steady, one gets pmj = constant = (üAc) [üAc) 2

where 1 and 2 refer to different points in a variable area duct.

I.4.2 First Law—Fluid Dynamics

The first law of thermodynamics can be directly applied to fluid dynamical systems, such as duct flows. If there is no heat transfer or chemical reaction and if the internal energy of the fluid stream remains unchanged, the first law is

V2 _ Ve zi - ze Pi - pe / ^ V e + g eg + i p e + \wv - Wf) = 0 2gc gc p y p f> (I.s)

Fig. I.13 Radiation shape factor for concentric cylinders of finite length.

where the subscripts i and e refer to inlet and exit conditions and Wp and w^are pump work and work required to overcome friction in the duct. Figure I.15 shows schematically a system illustrating this equation.

Any term in equation I.8 can be converted to a rate expression by simply multiplying by , the mass flow rate. Take, for example, the pump horsepower, w mwS mas*veneiy]

Fig. I.14 Radiation shape factor for parallel, directly opposed rectangles.

Elevation reference

Fig. I.15 The first law applied to adiabatic flow system.

In the English system, horsepower is hp = m lb,

' 1 hp - sec 1 |

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