VOLUMETRIC FLOW: CALCULATION AND WHAT AFFECTS IT - PHYSICAL - 2024

The volume flow determines the volume of fluid flowing through a section of the conduit and provides a measure of the speed with which the fluid travels by it. Therefore, its measurement is especially interesting in areas as diverse as industry, medicine, construction and research, among others.

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

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

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

Calculation

The volumetric flow rate is represented by the letter Q. For the 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 m ² and the velocity in m / s, the flow is measured in m ³ / s.

For the cases in which the velocity of the fluid displacement creates an angle θ with the direction perpendicular to the surface section A, the expression to determine the flow rate 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, consequently, cos θ = 1.

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

Q = ∫∫ _s vd 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 duct surface and dS is a surface differential element.

Continuity equation

A characteristic of incompressible fluids is that the mass of the fluid is conserved by means of two sections. For this reason, the continuity equation is satisfied, 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 the cases of regimes in permanent flux, in which the density is constant and, therefore, it is satisfied that ρ ₁ = ρ ₂, it is reduced to the following expression:

A ₁ V ₁ = A ₂ V ₂

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

Q ₁ = Q ₂.

From the observation of the above, it follows 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 playing with the speed of movement 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, the Bernoulli 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.

The Bernoulli equation takes into account the energy of a fluid at any moment, an energy consisting of three components.

- A kinetic component 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.

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

In this case, Bernoulli's 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 friction losses occur in the fluid displacement and it is necessary to resort to a more complex equation.

What affects the volumetric flow?

The volumetric flow will be affected if there is a blockage in the duct.

In addition, the volumetric flow rate can also change due to variations in temperature and pressure in the real fluid that moves through a conduit, especially if this is a gas, since the volume that a gas occupies varies as a function of the temperature and pressure at which it is.

Simple method of measuring volumetric flow

A really simple method of measuring volumetric flow is to let a fluid flow into a metering 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 into a metering tank for a period of time, the accumulated volume is measured and the result obtained is divided by the elapsed time.

References

1. Flow (Fluid) (nd). On Wikipedia. Retrieved on April 15, 2018, from es.wikipedia.org.
2. Volumetric flow rate (nd). On Wikipedia. Retrieved on April 15, 2018, from en.wikipedia.org.
3. Engineers Edge, LLC. "Fluid Volumetric Flow Rate Equation". Engineers Edge
4. Mott, Robert (1996). "one". Applied fluid mechanics (4th edition). Mexico: Pearson Education.
5. Batchelor, GK (1967). An Introduction to Fluid Dynamics. Cambridge University Press.
6. Landau, LD; Lifshitz, EM (1987). Fluid Mechanics. Course of Theoretical Physics (2nd ed.). Pergamon Press.