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Physics · 术语表

什么是 Mass flow rate and volume flow rate？

Definition 2.7 University Physics — Year 2 · 第 2 章 — Fluid Kinematics

The mass flow rate through an oriented surface SS is the mass crossing it per unit time, Dm=∑ρ v→⋅n→  ⁣dSD_m = \sum\rho\,\vect v\cdot\vect n\,\dd S — the flux of the mass current density j→=ρv→\vect j = \rho\vect v (unit kg m−2 s−1\mathrm{kg}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}); the volume flow rate is DV=∑v→⋅n→  ⁣dSD_V = \sum\vect v \cdot\vect n\,\dd S (m3/s\mathrm{m}^{3}/\mathrm{s}). For a uniform velocity normal to a plane section of area SS, Dm=ρvSD_m = \rho vS and DV=vSD_V = vS.

Left: the mass balance of a fixed box — the net outflow through its six faces, per unit volume, is the divergence of v. Right: in a steady flow the mass flow rate is the same through every section of a stream tube.
Left: the mass balance of a fixed box — the net outflow through its six faces, per unit volume, is the divergence of ρv→\rho\vect v. Right: in a steady flow the mass flow rate is the same through every section of a stream tube.

示例

Example 2.11 (Blood)

The aorta (section 2.5 cm22.5\,\mathrm{cm}^{2}) carries 5 L/min5\,\mathrm{L}/\mathrm{min} =83 cm3/s= 83\,\mathrm{cm}^{3}/\mathrm{s}: v=33 cm/sv = 33\,\mathrm{cm}/\mathrm{s}. The same flow passes through some 101010^{10} capillaries of total section about 2500 cm22500\,\mathrm{cm}^{2}: v=0.3 mm/sv = 0.3\,\mathrm{mm}/\mathrm{s} — slow enough for exchanges through the walls, the point of the branching.

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