Difference between partical shear stress and boundary shear stress

In summary, Boneh3ad explains that the boundary layer is a layer of water that separates the fluid (water) from the solid (sand, gravel, etc). The boundary layer exists because water obeys the no slip boundary condition. The shear stress (traction) exerted on the solid by the fluid is greater than a critical shear stress determined by the particle's size and density. The critical shear is the shear stress at which the flow rate increases so much that the tractive shear exceeds the shear imposed by the particle. The appropriate values for shear are built into the semi-empirical Shields equation.
  • #1
db725
35
0
Hi all,

I am currently studying civil hydraulics in my civil engineering course and we are going through estimating critical shear stresses for sediments. I am confused about the difference between boundary shear stress and particle shear stress. In terms of estimating critical shear stress, is there a difference between using particle shear stress and using boundary shear stress?

How would our results differ by choosing boundary/particle shear stress to begin with?

Thanks everyone in advance!
 
Engineering news on Phys.org
  • #2
I assume you are studying open channel flow, which is generally turbulent, except in the boundary layer.
This is reflected in an additional term in the viscosity - shear relationship
The total transport in any fluid is given by the sum of the molecular transport and the turbulent trnasport.

Measuring y from the bottom up with y' the thickness of the boundary layer


For turbulent flow the general equations are

momentum transfer


[tex]{\tau _{xy}} = \rho (\upsilon + \varepsilon )\frac{{\partial \overline v }}{{\partial y}}[/tex]


mass transfer


[tex]w = - \left( {D + {E_m}} \right)\frac{{\partial \overline c }}{{\partial y}}[/tex]


Heat transfer


[tex]q = - \rho {C_p}\left( {\alpha + {E_h}} \right)\frac{{\partial \overline \theta }}{{\partial y}}[/tex]


leading to


[tex]{\tau _{xy}} = \rho \varepsilon \frac{{\partial \overline v }}{{\partial y}}\;for\;y \ge y'[/tex]

Where epsilon is the turbulent factor

From this you can develop the various open channel flow formulae.

See Von Karman and Prandtl in particular.
 
  • #3
I am not a sediment transport expert but I know that in order for a sedimentary particle to be moved by a fluid, the shear stress exerted on it by the fluid must be greater than a critical shear stress determined by the particle's size and density. The boundary shear stress is the shear stress between the fluid and the particle at the boundary between the two. I am not really familiar with the particle shear stress terminology.
 
  • #4
Thanks Studiot for your very detailed explanation, however we haven't been doing much on the quantitative side so I found it a bit hard to follow the formulas you have mentioned above as I don't have much background in it. Would there be a more qualitative way of going about this question. Would you be able to explain the particle shear stress terminology as I have not been able to find anything on it anywhere..

Boneh3ad, thanks for the explanation about the boundary shear stress. I have been researching particle shear stress and haven't been successful in finding anything.
 
  • #5
OK, let's take a step back.

Do you understand what the boundary layer is? and importantly why there has to be one?
 
  • #6
From my understanding the boundary layer determines the amount of bed shear stress? so it helps us with calculations. But I am not too sure why there needs to be one.
 
  • #7
OK I am sorry I thought you were looking to develop a more theoretical approach.

The whole subject of hydraulics and in particular rough erodible channel hydraulics is semi-empirical.

It is known that water flow in such channels exerts a traction parallel to the channel sides and bed. Thus this is a shear.

The common semiempirical Shields equation is


[tex]{\tau _{critical}} = c\left( {{\rho _{solid}} - {\rho _{water}}} \right)gd[/tex]

Where c is an empirical constant around 0.05

This describes the critical shear to drive an exposed aprticle of diameter d along a horizontal bed.
This is reduced on sloping side walls by a function of the angle of repose.

In order to find a value for The shear imposed by a given flow we again employ semi-empirical methods and formulae associated wth Darcy, Chezy or Manning, Muller, Einstein or Meyer
These provide the tractive force or shear exerted on the boundary bed and walls by a given flow velocity or discharge rate (which amounts to the same thing knowing the cross sectional area).

Thus we can estimate the flow rate at which the tractive shear will first exceed the critical shear.

The appropriate values are built into these equations. which are deduced on dimensional arguments and then brought into line with reality by measured constants. That is what is meant by semi-empirical.

There is no one value for shear in the boundary layer. The boundary layer exists because water obeys the no slip boundary condition. That is the water touching the container boundary is at rest relative to it and the viscous shear increases rapidly from zero to the constant value in the bulk fluid.

To estimate this one has to consider momentum transport across a section of the boundary layer parallel to the flow and integrate perpendicular to the flow. I will post a derivation if you like.
 

1. What is the difference between particle shear stress and boundary shear stress?

Particle shear stress refers to the force per unit area acting on the surface of a particle due to the movement of fluid or other particles. Boundary shear stress, on the other hand, refers to the force per unit area acting on the boundary between two fluids with different velocities.

2. How are particle shear stress and boundary shear stress related?

Both particle shear stress and boundary shear stress are types of shear stress that occur in fluid dynamics. However, they differ in the mechanism by which they are generated and the surfaces on which they act.

3. What factors influence the magnitude of particle shear stress and boundary shear stress?

The magnitude of particle shear stress is affected by factors such as particle size, shape, and density, as well as fluid viscosity and velocity. Boundary shear stress, on the other hand, is influenced by the velocity gradient and fluid properties at the boundary.

4. Can particle shear stress and boundary shear stress be measured?

Yes, both particle shear stress and boundary shear stress can be measured using instruments such as viscometers, rheometers, and shear stress sensors. These measurements are important in understanding the behavior of fluids and particles in various environments.

5. How do particle shear stress and boundary shear stress impact sediment transport in rivers and oceans?

Particle shear stress and boundary shear stress play a crucial role in the movement of sediment in rivers and oceans. They determine the stability of sediments on the bed and the rate of sediment transport, which in turn affects the shape and morphology of river channels and coastlines.

Similar threads

  • Mechanical Engineering
Replies
1
Views
961
  • Engineering and Comp Sci Homework Help
Replies
1
Views
734
Replies
14
Views
2K
  • STEM Educators and Teaching
Replies
15
Views
3K
  • General Engineering
Replies
4
Views
3K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Replies
2
Views
1K
  • General Engineering
Replies
3
Views
10K
  • Engineering and Comp Sci Homework Help
Replies
12
Views
2K
Back
Top