Continuity equation

Continuity Equation
To understand the continuity equation it helps to consider the flow rate f first : f=Av the flow rate describes the volume of fluid that passes a particular point per unit time (like how many liters of water per minute are coming out of a pipe). A is the cross-sectional area of the pipe at any point, v is the average speed of the flow at that point.

Continuity Equation

A pipe, with a fluid (e.g. air) in it is considered, where one part is wider than the other : V1/t = V2/t since v= s/t (s is the distance from each point of the cross-section part): A1*s1/t = A2*s2/t A1 is the area of the cross section of the pipe's wider part, A2 the cross-section area of the pipe's narrow part ; v1 and v2 show the velocity of the fluid passing through A1 and A2. The fluid in the pipe has a laminar flow  (no troubles in it, steady) and is incompressible, which means the density is constant → in the same time intervalls the same volumina of the fluid will pass through each cross section of the pipe. According to the continuity equation, a fluid willl pass more rapid through the narrow part of the pipe. The flow speed is higher in the constricted part of the pipe. The wider the pipe is, the slower is the flow speed, if the pipe narrows, the flow speed will increase. The conclusion of it is, that the flow speed is inversely proportional to the cross-sectional area of the pipe.