We explain what volumetric flow is, how to calculate it and the factors that affect it

**What is volumetric flow?**

He **volumetric flow** It allows determining the volume of fluid that passes through a section of the conduit and offers a measure of the speed with which the fluid moves through it. Therefore, its measurement is especially interesting in fields as diverse as industry, medicine, construction and research, among others.

However, measuring the speed of a fluid (whether it is a liquid, a gas or a mixture of both) is not as simple as it can be to measure the speed of movement of a solid body. Therefore, it happens that to know the speed of a fluid it is necessary to know its flow.

This and many other issues related to fluids are dealt with by the branch of physics known as fluid mechanics. The flow is defined as how much fluid passes through a section of a conduit, whether it is a pipe, an oil pipeline, a river, a canal, a blood conduit, etc., taking into consideration a unit of time.

Usually the volume that crosses a certain area in a unit of time is calculated, also called volumetric flow. Mass or mass flow through a given area at a specific time is also defined, although it is used less frequently than volumetric flow.

**How is volumetric flow calculated?**

The volumetric flow is represented by the letter Q. For cases in which the flow moves perpendicular to the conductor section, it is determined with the following formula:

Q=A=V/t

In this formula, A is the section of the conductor (it is the average speed of the fluid), V is the volume and t is the time. Since in the international system the area or section of the conductor is measured in m2 and the velocity in m/s, the flow is measured in m3/s.

For the cases in which the velocity of the displacement of the fluid creates an angle θ with the direction perpendicular to the surface section A, the expression to determine the flow is the following:

Q = A cos θ

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

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

Q = ∫∫svd S

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

dS = ndS

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

**Continuity equation**

A characteristic of incompressible fluids is that the mass of the fluid is conserved by means of two sections. Therefore, the continuity equation is fulfilled, which establishes the following relationship:

ρ1 A1 V1 = ρ2 A2 V2

In this equation ρ is the density of the fluid.

For the cases of regimes in permanent flow, in which the density is constant and, therefore, it is fulfilled that ρ1 = ρ2, it is reduced to the following expression:

A1 V1 = A2 V2

This is equivalent to affirming that the flow is conserved and, therefore:

Q1=Q2.

From the observation of the above, it can be deduced that fluids accelerate when they reach a narrower section of a conduit, while they slow down when they reach a wider section of a conduit. This fact has interesting practical applications, since it allows us to play with the displacement velocity of a fluid.

**Bernoulli’s principle**

Bernoulli’s principle determines that for an ideal fluid (that is, a fluid that has neither viscosity nor friction) that moves in circulation through a closed conduit, its energy remains constant throughout its entire displacement.

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

h + v2 / 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 moment, energy that consists of three components.

A component of a kinetic nature that includes energy, due to the speed with which the fluid moves.

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

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

In this case, Bernoulli’s equation is expressed as follows:

h ρ g + (v2 ρ)/2 + P = constant

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

**What affects volumetric flow?**

Volumetric flow will be affected if there is an obstruction in the duct.

In addition, the volumetric flow can also change due to the effect of temperature and pressure variations in the actual fluid moving through a conduit, especially if it is a gas, since the volume that a gas occupies varies depending on the temperature and pressure at which it is found.

**Simple method of measuring volumetric flow**

A really simple method of measuring volumetric flow is to let a fluid flow inside a measuring tank for a set 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 rate of a fluid.

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

**References**** **

Flow (Fluid) (nd). On Wikipedia. Retrieved from es.wikipedia.org.

Volumetric flow rate (nd). On Wikipedia. Retrieved from en.wikipedia.org.

Engineers Edge, LLC. “Fluid Volumetric Flow Rate Equation”. Engineers Edge

Mott, Robert (1996). «1». Applied Fluid Mechanics (4th Edition). Mexico: Pearson Education.

Batchelor, GK (1967). An Introduction to Fluid Dynamics. Cambridge University Press.

Landau, L.D.; Lifshitz, E. M. (1987). Fluid Mechanics. Course of Theoretical Physics (2nd ed.). Pergamon Press.