Wall Shear Rate In Rectangular Channel Correction Factpr

1. Wall Shear Rate In Rectangular Channel Correction Factpr Form
2. Wall Shear Rate In Rectangular Channel Correction Factpr Texas

Shear rate is the rate at which a progressive shearing deformation is applied to some material.

Simple shear[edit]

Experimental results are presented concerning the boundary shear stress distribution in a rectangular compound section channel comprising rectangular main channel and two symmetrically disposed floodplains. Di erent dimensionless ratios of shear stress distributions are obtained and related to relevant parameters.

The shear rate for a fluid flowing between two parallel plates, one moving at a constant speed and the other one stationary (Couette flow), is defined by

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1. Wall and bed shear force in rectangular open channels. Mulate shear force distribution between walls and bed of a rectangular channel. Deriving this formulation is straightforward using the integral form of these conser. Shear stress on the channel bed and walls.
2. Instantaneous wall shear rate and local mass transfer were measured at an impinging wall using platinum electrodes with a diameter of 0.5 mm flush mounted into a platinum disc electrode with a diameter of 49.5 mm.

${\displaystyle \dot{\gamma }=\frac{v}{h},}$

where:

• is the shear rate, measured in reciprocal seconds;
• v is the velocity of the moving plate, measured in meters per second;
• h is the distance between the two parallel plates, measured in meters.

Or:

${\displaystyle {\dot{\gamma }}_{ij}=\frac{\mathrm{\partial }{v}_i}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }{v}_j}{\mathrm{\partial }{x}_i}.}$

Wall Shear Rate In Rectangular Channel Correction Factpr Form

For the simple shear case, it is just a gradient of velocity in a flowing material. The SI unit of measurement for shear rate is s⁻¹, expressed as 'reciprocal seconds' or 'inverse seconds'.^[1]

The shear rate at the inner wall of a Newtonian fluid flowing within a pipe^[2] is

Wall Shear Rate In Rectangular Channel Correction Factpr Texas

${\displaystyle \dot{\gamma }=\frac{8v}{d},}$

where:

• is the shear rate, measured in reciprocal seconds;
• v is the linear fluid velocity;
• d is the inside diameter of the pipe.

The linear fluid velocity v is related to the volumetric flow rate Q by

${\displaystyle v=\frac{Q}{A},}$

where A is the cross-sectional area of the pipe, which for an inside pipe radius of r is given by

${\displaystyle A=\pi r^2,}$

thus producing

${\displaystyle v=\frac{Q}{\pi r^2}.}$

Substituting the above into the earlier equation for the shear rate of a Newtonian fluid flowing within a pipe, and noting (in the denominator) that d = 2r:

${\displaystyle \dot{\gamma }=\frac{8v}{d}=\frac{8\left(\frac{Q}{\pi r^2}\right)}{2r},}$

which simplifies to the following equivalent form for wall shear rate in terms of volumetric flow rate Q and inner pipe radius r:

${\displaystyle \dot{\gamma }=\frac{4Q}{\pi r^3}.}$

For a Newtonian fluid wall, shear stress (τ_w) can be related to shear rate by τ_w = _xμ, where μ is the dynamic viscosity of the fluid. For non-Newtonian fluids, there are different constitutive laws depending on the fluid, which relates the stress tensor to the shear rate tensor.

References[edit]

1. ^'Brookfield Engineering - Glossary section on Viscosity Terms'. Archived from the original on 2007-06-09. Retrieved 2007-06-10.
2. ^Darby, Ron (2001). Chemical Engineering Fluid Mechanics (2nd ed.). CRC Press. p. 64.