📂Fluid Mechanics

Flow Rate and the Continuity Equation

정의 ¹

The volume of a fluid flowing per unit time is called the volume flow rate or, more simply, the flow rate; it is usually denoted by $Q$ and its unit is $\left[ \mathrm{m}^{3} / s \right]$. If an incompressible fluid passes through the $k$-th section of a pipe, and if the cross-sectional area is $A_{k}$ and the average velocity is $U_{k}$, then the flow rate $Q$ satisfies $$ Q = A_{1} U_{1} = A_{2} U_{2} $$ In fluid mechanics this is called the equation of continuity.

설명

In the continuity equation it is hard to imagine $A$ increasing, but it is very easy to encounter it decreasing in everyday life, so it is intuitively easy to understand. For example, when you spray water through a rubber hose, if you pinch the hose with your hand and narrow it, you have likely experienced the water spraying out faster. This can be explained by the outlet cross-sectional area $A_{2}$ of the hose becoming smaller while the flow rate $Q$ supplied from the water main remains constant, so the average velocity $U_{2}$ becomes larger.

Meanwhile, flow rate is not necessarily only about volume: the mass of fluid flowing per unit time is called the mass flow rate, and it can typically be expressed in terms of the density $\rho$ as $Q_{m} = \rho Q$. Since the unit of density is $\left[ \mathrm{kg} / \mathrm{m}^{3} \right]$, the unit of mass flow rate becomes $\left[ \mathrm{kg} / \mathrm{s} \right]$. If the density $\rho$ is constant, the fluid is incompressible, and in that case it is said to obey the mass conservation law.