Contents
What is Boussinesq model?
In fluid dynamics, the Boussinesq approximation (pronounced [businɛsk], named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity.
What is Boussinesq equation used for?
Boussinesq (1842 – 1929) evolved equations that can be used to determine stresses at any point P at a depth z as a result of a surface point load.
Why is Boussinesq important?
The Boussinesq theory for the distribution of stresses in a half-space resulting from surface loads is largely used in road engineering. An important discrepancy is also observed in horizontal stress for the case of homogeneous and multilayered soil when plasticity is considered.
What is Boussinesq parameter?
Boussinesq Parameters contains inputs related to the Boussinesq model. This option appears only if Energy (in the Energy dialog box) and Gravity are enabled. This option appears only when Gravity is enabled. Specified Operating Density enables the specification of operating density.
What is Westergaard theory?
Westergaard formalized the compound material with the following assumptions: 1) The stiff layers are spaced very closely such that the compound material has the characteristics of an isotropic homogeneous material. 2) The thickness of the stiff layers are negligible compared to that of the soft materials.
How do you use Newmark’s chart?
Verify the depth below the soil where the stress increase should reach to. Plot a plan of the uniformly loaded soil area with a scale where any given point (z) is equal to the unit length between the concentric circles on Newmark’s chart. Add the points (z) to a copy of Newmark’s chart with a pencil.
What are the assumptions of Boussinesq equation?
Boussinesq’s theory formula is based on following assumptions. The soil mass is semi-infinite, homogeneous and isotropic. The soil has a linear stress-strain relationship, The soil is weightless.
What is oberbeck Boussinesq approximation?
Unlike the Boundary Layer Approximation, the Oberbeck–Boussinesq approximation is more in keeping with a perturbation of the governing equation by identifying a small non-dimensional parameter and retaining terms of like order.
What is Westergaard equation?
For vertical stress computation, he had proposed a formula in 1938. The formula is presented below. Westergaard’s Equation for Point Loads. If Q is the point load and σz is the vertical stress due to the point load, σz=Q2πz2×√(1−2μ)/(2−2μ)[(1−2μ)/(2−μ)+(r/z)2)]3/2=Qz2Iw.
Why do engineers prefer Boussinesq over Westergaard theory?
In general, sedimentary soils such as natural clay strata highlight the non-isotropic nature of soil media. As a result, the Westergaard equations better model real problems. In practice, many geotechnical engineers often prefer the Boussinesq approach primarily because it gives more conservative results.
What is Newmark’s chart used for?
Newmark’s Influence Chart is an illustration used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil of any shape.
Which is the basis of the Boussinesq approximation?
The basis of this approximation is that there are flows in which the temperature varies little, and therefore the density varies little, yet in which the buoyancy drives the motion. Thus the variation in density is neglected everywhere except in the buoyancy term.
When to neglect density variation in the Boussinesq approximation?
The Boussinesq approximation states that the density variation is only important in the buoyancy term, , and can be neglected in the rest of the equation. where the temperature and pressure-dependent density, , have been replaced by a constant density, , except in the body force term representing the buoyancy force.
Why is the Boussinesq approximation of Navier Stokes not valid?
A larger computational cost difference between the full Navier-Stokes equations and the Boussinesq approximation may indicate that the Boussinesq approximation is not valid. The Navier-Stokes equations govern the motion of fluids. In the general case of a compressible fluid, this yields
What do PA and T0 represent in Boussinesq?
Here, pA and T0 represent the reference temperature and pressure. The air viscosity is set to the constant : Finally, when using the Boussinesq approximation, we need to set the buoyancy force to : As with Approach 2, we also evaluate the reference density and viscosity from the material properties.