Manometer reading doubt in the case of viscous fluid

In summary, the conversation discusses the correct way to read an open air manometer in the case of viscous fluid. The main issue is that the green and black points are not at the same height due to the fluid in B being in the manometer for a longer time. Bernoulli's equation cannot be used in this case, but there may be a way to correct for the effect of viscosity. Further research is needed to determine the precise relation between pressure at the green and black points.
  • #1
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I wonder if it is correct to read an open air manometer in the case of viscous fluid in the following (usual) way. Consider the situation showed in the picture where a viscous fluid is flowing, in fact ##z_C <z_A##.

4567890.png


The reading of the manometer would be ##p_a=\rho g z_a##, ##p_b=\rho g z_b##, ##p_c=\rho g z_c##,

The main problem is that, while the black points ##A##, ##B## and ##C## are at the same heights, the fluid in ##B## is in the manometer for an height ##d## more than the fluid in ##A## and ##C## (or equivalently, the corresponding green points are not at the same height).

In the manometer the fluid is not moving, so I have no problem in writing that ##\Delta p=\rho g h##, but inside the tube the fluid is moving and therefore the variation of pressure with height would be different.

That would not be a problem if the green points were at the same height or in the case of validity of Bernoulli equation because ##\Delta p=\rho g h## would still be valid along vertical lines (even if the fluid is in motion).

But here Bernoulli equation cannot be used, since the fluid is viscous, so my question is: can I read the manometer referring heights to the horizontal line in the middle of the tube, or is there some other way to read it.

Furthermore I would like to know if there is a precise relation between the pressure in the green points and the pressure at black points. As said before, in the case of non viscous fluid, the pressures would be equal there, but what about this case?
 
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  • #2
Soren4 said:
But here Bernoulli equation cannot be used, since the fluid is viscous, so my question is: can I read the manometer referring heights to the horizontal line in the middle of the tube, or is there some other way to read it.

the effect of viscosity may not be accounted for by just changing the base reference of measuring 'pressure' as due to constriction the velocity of the fluid must have increased.

there are some studies done for correction to Bernoulli's equation due to viscous flow ,therefore one can relate it...
you may see
<https://www.researchgate.net/publication/1773651_Bernoulli_correction_to_viscous_losses_Radial_flow_between_two_parallel_discs> [Broken]
well i do not know (as i have not worked on it in detail)
whether it can work but as some experimental data have been generated ,so it may be helpfull.
 
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  • #3
In laminar viscous flow in a horizontal pipe, the pressure varies hydrostatically in the vertical direction, and the pressure gradient in the axial direction does not depend on the vertical coordinate.
 

1. What is a manometer?

A manometer is a device used to measure the pressure of a fluid, typically a liquid or gas. It consists of a U-shaped tube filled with the fluid and a scale to read the height difference between the two sides of the tube.

2. How does a manometer work?

A manometer works by balancing the pressure of the fluid being measured with the weight of a column of the same fluid. The difference in height between the two sides of the tube indicates the pressure of the fluid.

3. What is a viscous fluid?

A viscous fluid is a type of fluid that has a high resistance to flow. This is due to its internal friction, which is caused by the fluid's molecular structure. Examples of viscous fluids include honey, syrup, and motor oil.

4. Can the reading on a manometer be affected by the viscosity of the fluid?

Yes, the reading on a manometer can be affected by the viscosity of the fluid being measured. Viscous fluids have a higher resistance to flow, so the height difference between the two sides of the tube may be greater compared to a less viscous fluid at the same pressure.

5. How can we account for the viscosity of the fluid when using a manometer?

To account for the viscosity of the fluid, we can use a correction factor in the manometer reading calculation. This factor takes into account the density and viscosity of the fluid, as well as the dimensions of the manometer tube, to provide a more accurate pressure measurement.

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