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Herschel-Bulkley fluid (constitutive equation)

The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a ... more

Tensile Stress Area

Bolted joints are one of the most common elements in construction and machine design. They consist of fasteners that capture and join other parts, and are ... more

Barlow's formula - sphere

In the pipeline industry it is neccecary to verify that pipe used for gathering, transmission, and distribution lines can safely withstand operating ... more

Barlow's formula - pipe

In the pipeline industry it is neccecary to verify that pipe used for gathering, transmission, and distribution lines can safely withstand operating ... more

Bingham number

ratio of yield stress to viscous stress

... more

Blood pressure ( related to the wall tension of artery or vein)

Blood pressure is related to the wall tension of the artery or vein, according to the Young–Laplace equation (assuming that the thickness of the vessel ... more

dynamic viscosity of water (as a function of temperature temperature)

The viscosity of a fluid is the measure of its resistance to gradual deformation by shear stress or tensile stress. For liquids, it corresponds to the ... more

Worksheet 316

Calculate the change in length of the upper leg bone (the femur) when a 70.0 kg man supports 62.0 kg of his mass on it, assuming the bone to be equivalent to a uniform rod that is 45.0 cm long and 2.00 cm in radius.

Strategy

The force is equal to the weight supported:

Force (Newton's second law)

and the cross-sectional area of the upper leg bone(femur) is:

Disk area

To find the change in length we use the Young’s modulus formula. The Young’s modulus reference value for a bone under compression is known to be 9×109 N/m2. Now,all quantities except ΔL are known. Thus:

Young's Modulus

Discussion

This small change in length seems reasonable, consistent with our experience that bones are rigid. In fact, even the rather large forces encountered during strenuous physical activity do not compress or bend bones by large amounts. Although bone is rigid compared with fat or muscle, several of the substances listed in Table 5.3(see reference below) have larger values of Young’s modulus Y . In other words, they are more rigid.

Reference:
This worksheet is a modified version of Example 5.4 page 188 found in :
OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Shear modulus (related to Young's modulus and Poisson's ratio)

The shear modulus is one of several quantities for measuring the stiffness of materials and describes the material’s response to shear stress (like ... more

Shear stress (acting on the bed of a channel)

For a channel that is at an angle a from horizontal, the shear component of the stress acting on the bed , which is the component acting ... more

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