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Calculate velocity gradient and shear stress
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- This relationship can be exploited to measure the wall shear stress. If a sensor could directly measure the gradient of the velocity profile at the wall, then multiplying by the dynamic viscosity would yield the shear stress. Such a sensor was demonstrated by A.
- The full bed shear stress , calculated with b=1 mm above the canopy top, compared with estimating u * as (a) , the turbulent Reynolds stress from the acoustic Doppler velocimeter at 5 cmab extrapolated to the bed, (b) u *c, the friction velocity estimated from a log law fit (equation 20) to Vectrino mean velocity data, and (c) u *A from the acoustic Doppler current
- The velocity profile for a thin film of a Newtonian fluid that is confined between a plate and a fixed surface is defined by u = \left ( 10y - 0.25y^{2} \right ) mm/s , where y is in mm. Determine the shear stress that the fluid exerts on the plate and on the fixed surface.
- To find the velocity distribution, we need to introduce a relationship between the shear stress and the velocity gradient. Recall the Newtonian constitutive model . z rz dv dr τµ= where . µ is the dynamic viscosity of the fluid. Use of this constitutive model in the result for the shear stress leads to . 2 dv z P r dr Lµ ∆ ==−. r z R τ (r)
- Young's modulus is the ratio of stress and strain. Evaluate stress / strain to get the answer. Example. Question: A wire of length 2 m and cross-sectional area 10-4 m 2 is streched by a load of 102 kg. The wire is streched by 0.1 cm. Calculate longitudinal stress, longitudinal strain and Young's Modulus of the material wire? Solution: Given that,