Mechanics

# Conservation of mass in flow

The volumes of the liquids in the shaded area are equal

In our studies we have already defined that a fluid does not have its own shape and adapts to the shape of the container in which it is contained. We also saw that when analyzing the movement of any fluid, we must separate its characteristics, such as: density, pressure, temperature, velocity, etc.

Therefore, when we have a liquid coming out of a pipe system (pipe), we see that the flow of such fluid through the pipe is the same, that is, the flow is constant throughout the pipe. However, when the fluid leaves a thicker pipe into a thinner pipe, we will notice that the speed at which the fluid flows changes so that the amount of mass or volume of the fluid remains the same. Therefore, we can conclude, given the above, that the amount of fluid that enters one part of the pipe must be the same amount of fluid that leaves the other part.

Let’s see the figure above, it represents a liquid that passes through a thick pipe and finally leaves through a thin pipe, that is, the volume of liquid that passes through area A during a certain time interval is given by volume A:

The volume that passes through area B, based on the same time interval, is given by:

B = A B .   x B

As the flows (flows) must be equal, you must have that:

Simplifying the time interval on both sides of the equality, we have:

A .v A =A B .v B

In the above equation, A and B are the liquid velocities at each point in the pipe. According to the equation we can see that depending on the area of ​​the pipe there is a variation in the flow velocity.

Therefore, we can conclude that when a fluid passes from a thick pipe to a thinner one, its flow velocity must increase.