Modern Physics

# Volumetric flow: calculation and what affects it?

The volumetric flow to determine the volume of fluid passing through a section of the duct and provides a speed as the fluid travels through it. Therefore, its measurement is especially interesting in fields as diverse as industry, medicine, construction and research, among others.

However, measuring the velocity of a fluid (whether it is a liquid, a gas or a mixture of both) is not as simple as measuring the velocity of displacement of a solid body. Therefore, to know the velocity of a fluid, it is necessary to know its flow.

This and many other issues related to fluids are dealt with in the branch of physics known as fluid mechanics. The flow rate is defined as the amount of fluid that flows through a section of a conduit, be it a tube, a pipe, a river, a canal, a blood conduit, etc., taking into account a temporary unit.

Typically, the volume that passes through a given area in a unit of time, also called volumetric flow, is calculated. It also defines the mass or mass flow that passes through a certain area at a specific time, although it is used less frequently than volumetric flow.

## Calculation

The volumetric flow is represented by the letter Q. In cases where the flow travels perpendicular to the conductor section, it is determined by the following formula:

Q = A = V / t

In the aforementioned formula, A is the conductor’s section (it is the average velocity that the fluid has), V is the volume and t is time. As in the international system the area or section of the conductor is measured in m 2 and the velocity in m / s, the flow is measured in m 3 / s.

In cases where the fluid displacement velocity creates an angle θ with the direction perpendicular to the surface section A, the expression to determine the flow rate is as follows:

Q = A cos θ

This is consistent with the previous equation because when the flow is perpendicular to area A, θ = 0 and therefore cos θ = 1.

The above equations are only true if the fluid velocity is uniform and the section area is flat. Otherwise, the volumetric flow is calculated using the following integral:

Q = v s v S

In this integral dS is the surface vector, determined by the following expression:

dS = n dS

There, n is the unit vector normal to the surface of the pipeline and dS is a differential element of the surface.

### continuity equation

A characteristic of incompressible fluids is that the fluid’s mass is preserved through two sections. That is why the continuity equation is fulfilled, which establishes the following relationship:

ρ 1 A 1 V 1 = ρ 2 A 2 V 2

In this equation, ρ is the density of the fluid.

For cases of permanent flow regimes, in which the density is constant and, therefore, it is true that ρ 1 = ρ 2 , it is reduced to the following expression:

1 V 1 = A 2 V 2

This is equivalent to stating that the flow is conserved and therefore:

1 = Q 2 .

From the above observation, it follows that fluids accelerate when they reach a narrower section of a pipeline, while slowing down when they reach a wider section of a pipeline. This fact has interesting practical applications, as it allows playing with the speed of movement of a fluid.

### Bernoulli’s principle

Bernoulli’s principle states that for an ideal fluid (ie, a fluid that has no viscosity or friction) traveling through a closed conduit, it is satisfied that its energy remains constant throughout its displacement.

Finally, Bernoulli’s principle is nothing more than the formulation of the Energy Conservation Law for the flow of a fluid. Thus, Bernoulli’s equation can be formulated as follows:

h + v 2 / 2g + P / ρg = constant

In this equation, h is the height and g is the acceleration due to gravity.

Bernoulli’s equation takes into account the energy of a fluid at any time, energy made up of three components.

– A component of a kinetic nature that includes energy due to the speed at which the fluid travels.

– A component generated by the gravitational potential, as a consequence of the height at which the fluid is.

– A component of flow energy, which is the energy a fluid has due to pressure.

In this case, the Bernoulli equation is expressed as follows:

h ρ g + (v 2 ρ) / 2 + P = constant

Logically, in the case of a real fluid, the expression of the Bernoulli equation is not fulfilled, since in the displacement of the fluid friction losses occur and it is necessary to resort to a more complex equation.

## What affects volumetric flow?

Volumetric flow will be affected if there is a blockage in the pipeline.

In addition, the volumetric flow rate can also change due to temperature and pressure variations in the actual fluid traveling through a conduit, especially if it is a gas, since the volume occupied by a gas varies depending on temperature. temperature and pressure at which it is found.

### Simple volumetric flow measurement method

A really simple method to measure volumetric flow is to allow a fluid to flow into a measuring tank for a certain period of time.

This method is generally not very practical, but the truth is that it is extremely simple and very illustrative to understand the meaning and importance of knowing the flow of a fluid.

In this way, fluid is allowed to flow into a measuring tank for a period of time, the accumulated volume is measured and the result obtained is divided by the elapsed time.