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>Model

ID:(2070, 0)

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ID:(15713, 0)

Concept

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The definition of the volume flow ($J_V$) is the volume element ($\Delta V$) over the time elapsed ($\Delta t$):

which, in the limit of an infinitesimal time interval, corresponds to the derivative of the volume ($V$) with respect to the time ($t$):

ID:(15718, 0)

Concept

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The volume ($V$) for a tube with constant the section Tube ($S$) and a position ($s$) is

If the section Tube ($S$) is constant, the temporal derivative will be

$\displaystyle\frac{dV}{dt} = S\displaystyle\frac{ds}{dt}$

thus, with the volume flow ($J_V$) defined by

and with the flux density ($j_s$) associated with the position ($s$) via

it is concluded that

ID:(15717, 0)

Concept

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In the case that the flux density ($j_s$) is constant, the volume flow ($J_V$) can be calculated using the section or Area ($S$) according to:

If the flux density ($j_s$) varies, sufficiently small sectional elements $dS$ can be considered so that the equation remains valid in the sense that the contribution to flow is:

$dJ_V = j_s dS$

Integrating this expression over the entire section results in

ID:(15719, 0)

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Parameters

$V$

V

Volumen

m^3

Variables

$j_s$

j_s

Flux density

m/s

$s$

s

Position

m

$S_d$

S_d

Section presenting the planet

m^2

$S$

S

Section Tube

m^2

$t$

t

Time

s

$V$

V

Volume

m^3

$J_V$

J_V

Volume flow

m^3/s

Calculations

• Alternative method
• Traditional method
• Strategy
• 2D
• 3D

Equation

Number

First, select the equation: to , then, select the variable: to

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Calculations

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable Given Calculate Target : Equation To be used

Equations

ID:(15714, 0)

Equation

>Top, >Model

The volume flow ($J_V$) corresponds to the quantity volume ($V$) that flows through the channel during a time ($t$). Therefore, we have:

$J_V =\displaystyle\frac{ dV }{ dt }$

Conditions

Variables

$t$

Time

$s$

10148

$V$

Volume

$m^3$

9847

$J_V$

Volume flow

$m^3/s$

5448

Relation

Development

The definition of the volume flow ($J_V$) is the volume element ($\Delta V$) over the time elapsed ($\Delta t$):

$J_V =\displaystyle\frac{ \Delta V }{ \Delta t }$

which, in the limit of an infinitesimal time interval, corresponds to the derivative of the volume ($V$) with respect to the time ($t$):

$J_V =\displaystyle\frac{ dV }{ dt }$

ID:(12713, 0)

Equation

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The volume ($V$) is calculated by multiplying the section Tube ($S$) with the position ($s$) along the tube:

$V = s S$

$V = h S$

Conditions

Variables

$h$

$s$

Position

$m$

9849

$S$

Section presenting the planet

$m^2$

6700

$V$

Volumen

$m^3$

6699

Relation

ID:(4876, 0)

Equation

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The flux density ($j_s$) is related to the position ($s$), which is the fluid position at the time ($t$), through the following equation:

$j_s =\displaystyle\frac{ ds }{ dt }$

Conditions

Variables

$j_s$

Flux density

$m/s$

7220

$s$

Position

$m$

9849

$t$

Time

$s$

10148

Relation

ID:(12714, 0)

Equation

>Top, >Model

A flux density ($j_s$) can be expressed in terms of the volume flow ($J_V$) using the section or Area ($S$) through the following formula:

$J_V = S j_s$

Conditions

Variables

$j_s$

Flux density

$m/s$

7220

$S$

Section Tube

$m^2$

6267

$J_V$

Volume flow

$m^3/s$

5448

Relation

Development

The volume ($V$) for a tube with constant the section Tube ($S$) and a position ($s$) is

$V = s S$

If the section Tube ($S$) is constant, the temporal derivative will be

$\displaystyle\frac{dV}{dt} = S\displaystyle\frac{ds}{dt}$

thus, with the volume flow ($J_V$) defined by

$J_V =\displaystyle\frac{ dV }{ dt }$

and with the flux density ($j_s$) associated with the position ($s$) via

$j_s =\displaystyle\frac{ ds }{ dt }$

it is concluded that

$J_V = S j_s$

ID:(15716, 0)

Equation

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If the flux density ($j_s$) is not constant and varies across the flow tube section the volume flow ($J_V$), it is calculated as the integral over that section:

$J_V =\displaystyle\int j_s dS$

Conditions

Variables

$j_s$

Flux density

$m/s$

7220

$J_V$

Volume flow

$m^3/s$

5448

Relation

Development

In the case that the flux density ($j_s$) is constant, the volume flow ($J_V$) can be calculated using the section or Area ($S$) according to:

$J_V = S j_s$

If the flux density ($j_s$) varies, sufficiently small sectional elements $dS$ can be considered so that the equation remains valid in the sense that the contribution to flow is:

$dJ_V = j_s dS$

Integrating this expression over the entire section results in

$J_V =\displaystyle\int j_s dS$

ID:(15712, 0)