Mass Flow Rate and Volume Flow Rate

The integral:

m = JJn. V pdS (3.27 )

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over a selected part of a control surface of area A through which fluid passes often is referred to as the mass flow rate, m, across that surface area. If English units are used, the velocity is in [ft/sec], the compatible unit of density is [slug/ft3], and the area is in [ft2]. Then, the mass flow rate has units of mass units per unit time, or [slug/sec]. A common practice in thermodynamics is to express the flow rate in [lbm/sec], but this is not a truly compatible unit (see Examples 2.1 and 2.2). It is more correctly
called the weight flow rate because an factor of g was applied. The usual cautions of mixing force and mass units apply. In metric units, the flow rate often is expressed in [kg/sec].

When the density is constant, as in an incompressible flow, mass flow rate still can be used as defined. In some problems, there is no dependence on the density; therefore, the rate of flow can be described in terms of the volume flow rate:

Q =j] n-V dS. (3.28)

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Typical units for volume-flow rate are [ft3/sec] and [m3/sec]. The following examples show how these measures of the rate of fluid flow enter problems naturally.