Applications-
- Equation (26.8) is commonly used in the measurement of viscosity with the help of capillary tube viscometers . Such a viscometer consists of a constant head tank to supply liquid to a capillary tube (Fig. 26.4).
FIG 26.4 Schematic diagram of the experimental facility for determination of viscosity
- Pressure drop readings across a specified length in the developed region of the flow are taken with the help of a manometer. The developed flow region is ensured by providing the necessary and sufficient entry length.
- From Eq. (26.8), the expression for viscosity can be written as
- The volumetric flow rates (Q) are measured by collecting the liquid in a measuring cylinder. The diameter (D) of the capillary tube is known beforehand. Now the viscosity of a flowing fluid can easily be evaluated.
- Shear stress profile across the cross-section can also be determined from this information. Shear stress at any point of the pipe flow is given by
| |
From Eq. (26.5)
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or
| (26.9a) |
which means
| (26.9b) |
This also indicates that varies linearly with the radial distance from the axis.
- At the wall, assumes the maximum value.
Again, over a pipe length of l , the total shear force is
or
or
[Pressure drop between the specified length] | |
as it should be. Negative sign indicates that the force is acting in opposite to the flow direction.
- However, from Eq. (26.6b), we can write
| (26.9c) |
or | (26.10)
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