Continuity equation expression:

One-dimensional steady flow in which a fluid with constant density passes through the cross-sectional area A and changes with the spatial coordinate s [that is, A=A(s)] [That is, the flow rate U(s) does not change with time t for a certain s value] The continuity equation is the simplest:

AU=constant,

where U is the flow rate. For example, the flow velocity of "passage air" is large because the cross-sectional area of ??the intervening passage is small.

The continuity equation of one-dimensional steady flow with significant change in density ρ is:

AρU=constant,

For one-dimensional constant flow with significant change in density ρ Steady flow, considering two cross-sections not far apart, the fluid flowing into the first cross-section has more mass than the fluid flowing out of the second cross-section, which accumulates between the two cross-sections, thus causing two The growth of fluid density ρ between two cross sections with time. The continuity equation is the specific expression of the law of conservation of mass (see mass) in fluid mechanics. Its premise is to adopt a continuous medium model for fluids. Velocity and density are continuous and differentiable functions of spatial coordinates and time. In physics, the continuity equation is a partial differential equation that describes the transmission behavior of conserved quantities. Since mass, energy, momentum, charge, etc. are all conserved quantities under their respective appropriate conditions, many types of transport behaviors can be described by continuity equations.

The continuity equation is a local conservation law equation. Compared with the global conservation law, this conservation law is a stronger version. All examples of continuity equations in this article express the same idea - the total amount of a conserved quantity in any region changes by the amount entering or leaving the boundary; a conserved quantity cannot increase or decrease, It can only be moved from one location to another.