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Instability
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In a flow competes the inertia, which causes the masses to move without the effect of the surrounding masses, and the viscosity, which causes the masses to drag the surrounding masses.
If the viscosity is large, the correlation between the masses and the conformation of a laminar flow dominates. If the viscosity is low, the inertia dominates and the masses move without coordinating with the surrounding areas leading to areas that even form units that can rotate and move independently corresponding to the whirlpools.
ID:(878, 0)
Different viscosities
Description
Viscosity has a profound effect on the behavior of a fluid, as can be seen in the following three examples:
ID:(7068, 0)
Turbulence generated by a Cigarette
Description
A cigarette has a glowing tip that heats the air in its surroundings. Additionally, the expelled smoke allows us to visualize the movement of the air. The heating leads to an expansion of the air, resulting in a decrease in density and, consequently, generates a lift force. As a result, the smoke starts to rise in a laminar fashion, forming the typical lines that are seen.
During this process, the gas begins to cool down, losing lift force, and certain regions start ascending more slowly, obstructing the upward movement of the air. This obstruction creates turbulence, and the same regions that ascend slower begin to rotate, forming part of the vortices observed in that area.
ID:(1654, 0)
Instability
Description
In a flow competes the inertia, which causes the masses to move without the effect of the surrounding masses, and the viscosity, which causes the masses to drag the surrounding masses. If the viscosity is large, the correlation between the masses and the conformation of a laminar flow dominates. If the viscosity is low, the inertia dominates and the masses move without coordinating with the surrounding areas leading to areas that even form units that can rotate and move independently corresponding to the whirlpools.
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Examples
Viscosity has a profound effect on the behavior of a fluid, as can be seen in the following three examples:
(ID 7068)
The mixing ratio of water vapor with air is defined as the ratio of the masses of each component present in a volume:
$\displaystyle\frac{M_v}{M_a}=\displaystyle\frac{n_vM_{mol,v}}{n_aM_{mol,a}}=\displaystyle\frac{p_v}{p_a}\displaystyle\frac{M_{mol,v}}{M_{mol,a}}\sim 0.01$
Where $M_v$ and $M_a$ are the masses of water vapor and air respectively, $n_v$ and $n_a$ are the moles of water vapor and air, $M_{mol,v}$ and $M_{mol,a}$ are the molar masses of water vapor and air, $p_v$ and $p_a$ are the relative pressures of water vapor and air, and $r$ is the mixing ratio. Therefore, we have
| $ r =\displaystyle\frac{ M_v }{ M_a }$ |
In the specific case of water vapor in air, the mixing ratio is proportional to the relative pressures, which can be quantified using the vapor pressure of water $p_v\sim 1500 Pa$ and the air pressure $p_a\sim 10^5 Pa$. By applying the ideal gas equation and the definition of molar mass, it can be determined that the mixing ratio is approximately $0.01$. This means that the amount of water vapor compared to air is low under normal conditions.
(ID 7069)
The key criterion for determining whether a medium is laminar or turbulent is the Reynolds number, which compares the energy associated with inertia to that associated with viscosity. The former depends on the density ($\rho$), the mean Speed of Fluid ($v$), and the typical Dimension of the System ($R$), while the latter depends on the viscosity ($\eta$), defining it as:
| $ Re =\displaystyle\frac{ \rho R v }{ \eta }$ |
(ID 3177)
A cigarette has a glowing tip that heats the air in its surroundings. Additionally, the expelled smoke allows us to visualize the movement of the air. The heating leads to an expansion of the air, resulting in a decrease in density and, consequently, generates a lift force. As a result, the smoke starts to rise in a laminar fashion, forming the typical lines that are seen.
During this process, the gas begins to cool down, losing lift force, and certain regions start ascending more slowly, obstructing the upward movement of the air. This obstruction creates turbulence, and the same regions that ascend slower begin to rotate, forming part of the vortices observed in that area.
(ID 1654)
ID:(878, 0)