# Volume flow

Physical size
Surname Volume flow (flow rate)
Formula symbol ${\ displaystyle Q}$
Size and
unit system
unit dimension
SI m 3 · s -1 L 3 · T −1

The volume flow (or imprecise flow rate and flow rate ) is a physical quantity from fluid mechanics . It indicates how much volume of a medium is transported through a specified cross-section over a period of time . The medium is usually a fluid ( liquid or gas ). The SI unit of the volume flow is m³ / s, depending on the magnitude of the volume flow, many other units are also in use. For example ml / min (200 ml / min blood flow through the inner carotid artery of humans ) or m³ / h (on average 1 million m³ / h natural gas flows through the Nord Stream pipeline ). The volume flow is measured using flow meters.

${\ displaystyle Q = {\ dot {V}} = {\ frac {\ mathrm {d} V} {\ mathrm {d} t}}}$

With

${\ displaystyle Q}$: Volume flow
${\ displaystyle V}$: Volume
${\ displaystyle t}$: Time

## Relationship with flow velocity

The volume flow is related to the mean flow velocity through the cross-sectional area via the relationship: ${\ displaystyle Q}$ ${\ displaystyle v_ {A}}$${\ displaystyle A}$

Sketch to explain a flow profile . In a pipeline, the flow velocity of individual streams is not constant over the cross section. At the pipe wall the flow velocity is zero and in the case of undisturbed flows it is maximum in the middle. The shape of the flow profile depends on the Reynolds number .
${\ displaystyle Q = v_ {A} \ cdot A}$

With this formula , if the cross-sectional area ( pipes , channels ) is known, the volume flow can be calculated if the flow velocity at the cross-section through which the flow passes is known.

The flow velocity in a cross-section is generally not constant over the cross-section (see illustration); for laminar flow , the mean flow velocity generally results in

${\ displaystyle v_ {A} = {\ frac {1} {A}} \ cdot \ int _ {A} v (y, z) \, \ cdot \ mathrm {d} A}$

With

${\ displaystyle v (y, z)}$: Speed ​​at the point of the cross-section, with flow in - direction.${\ displaystyle (y, z)}$${\ displaystyle x}$

## Law of continuity

Sketch to explain the maintenance of the volume flow of an incompressible fluid when changing the cross-section through which it flows.

If the cross-section changes, the law of continuity applies to flows of incompressible fluids :

${\ displaystyle Q = A_ {1} \ cdot v_ {1} = A_ {2} \ cdot v_ {2}}$

Here is the cross section through which the fluid flows at an average speed . If you change the cross-section to , the mean flow velocity changes to . In other words: For incompressible fluids, the volume flow is a maintenance variable when the cross-section of the flow changes. ${\ displaystyle A_ {1}}$${\ displaystyle v_ {1}}$${\ displaystyle A_ {2}}$${\ displaystyle v_ {2}}$

Liquids are incompressible as a first approximation, i. H. their density does not change if the flow cross-section is widened or constricted at a constant volume flow (and thus the pressure changes). This does not apply to gases, however, since they are compressible.

## Connection with mass flow

The mass flow hangs over ${\ displaystyle q_ {m}}$

${\ displaystyle q_ {m} = {\ dot {m}} = {\ frac {\ mathrm {d} m} {\ mathrm {d} t}} = \ rho \ cdot {\ dot {V}} = \ rho \ cdot Q}$

together with the volume flow , if the density is constant over the cross-section. Otherwise this product must be integrated across the cross-section. ${\ displaystyle Q}$ ${\ displaystyle \ rho}$

## Standard volume flow

The volume of a given amount of gas depends on pressure and temperature . Since both parameters are not constant in pipeline networks or industrial processes, the volume flow of gases is often given as the standard volume flow . For this purpose, the volume measured in a certain period of time ( operating volume ) is converted to a standard volume with a specified pressure and temperature. It applies

${\ displaystyle Q _ {\ mathrm {N}} = Q \ cdot {\ frac {p \ cdot T _ {\ mathrm {N}}} {p _ {\ mathrm {N}} \ cdot T}}}$ ,

there are and actually prevailing pressure and temperature during the operating volume measurement and and pressure and temperature of the standard conditions (for example and , the standard conditions vary worldwide and also include other conditions such as air humidity ). Here and must be understood as an absolute temperature . This is related to the Celsius temperature as follows: . ${\ displaystyle p}$${\ displaystyle T}$${\ displaystyle p _ {\ mathrm {N}}}$${\ displaystyle T _ {\ mathrm {N}}}$${\ displaystyle p _ {\ mathrm {N}} = 1 {,} 01325 \, \ mathrm {bar}}$${\ displaystyle T _ {\ mathrm {N}} = 273 {,} 15 \, \ mathrm {K}}$${\ displaystyle T}$${\ displaystyle T _ {\ mathrm {N}}}$${\ displaystyle t}$${\ displaystyle T / \ mathrm {K} = t / ^ {\ circ} \ mathrm {C} +273 {,} 15}$

## Designations

In some areas of science and technology, volume flows are briefly referred to as -flow , e.g. B. the discharge in hydrology , cf. Flow (physics) . In technology and business, a fuel can throughput , a conveyance amount , a feed power or the pumping capacity of a pump be given as volume flow. In medicine one speaks analogously of cardiac output or synonymously of cardiac output with the unit l / min.

## Individual evidence

1. John P. Woodcock: Theory and Practice of Blood Flow Measurement . Butterworth-Heinemann, 2013, ISBN 978-1-4831-8273-5 , pp. 197 .
2. Focus / dpa: Baltic Sea pipeline to Western Europe opened. Focus, November 8, 2011, accessed on March 28, 2015 (German).
3. Horst-Walter Grollius: Fundamentals of Pneumatics . Carl Hanser Verlag GmbH Co KG, 2012, ISBN 978-3-446-43398-4 , p. 47 .