# Continuity equation

The continuity equation relates the area available for a fluid to flow and its velocity.

**the continuity equation**.

This equation relates the flow velocity of a fluid and the area available for such flow. From the image below, notice that the path made by the fluid has two different areas: A _{1} > A _{2.} Imagine, therefore, that, in a time interval (Δt), a volume (ΔV) of the fluid enters through area A _{1} . Adopting the fluid as incompressible, we must assume that the same volume (ΔV) must leave the edge of area A _{2} .

During the time interval considered, the space covered by the fluid can be given, from the average velocity equation , by Δs = v.Δt, where **v** is the flow velocity. Taking the gray markings on the figure as the volumes occupied by the moving fluid and knowing that they are equal, we have:

_{1}= V

_{2}

A _{1.} Δs = A _{2.} Δs

A _{1.} v _{1} .Δt = A _{2.} v _{2} .Δt

A _{1 . }v _{1} = A _{2.} v _{2}

Thus, we can see that the smaller the flow area available for a fluid, the greater its velocity and vice versa. As a final example, we can imagine the “thread” of water formed by a half-open faucet. Note that the lower you look, the thinner the water stream will be, because, with the action of gravity acceleration , the fluid’s velocity increases, decreasing its flow area.