The Navier-Stokes equation is the fundamental equation of fluid dynamics. In one of its many forms (incompressible and viscous flow) the equation is p dt + (V. V)V) = -Vp + µ(V · V)V. In the notation, V =< u, v, w > is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and u is the constant viscosity. (i) Take the dot product of V and the nabla V operator, then apply the result to u to show that du du (V.V)u = du + w + v + w- u = u + v dz he (ii) Assume u = ry 23 and find (V V)u at (1, 1, 1) where V =< 1,x, 1 >. (iii) Write out the 1st component equation of the Navier-Stokes vector equation.

The Navier-Stokes equation is the fundamental equation of fluid dynamics. In one of its many forms (incompressible and viscous flow) the equation is p dt + (V. V)V) = -Vp + µ(V · V)V. In the notation, V =< u, v, w > is the three-dimensional velocity field, p is the (scalar) pressure, p is the constant density of the fluid, and u is the constant viscosity. (i) Take the dot product of V and the nabla V operator, then apply the result to u to show that du du (V.V)u = du + w + v + w- u = u + v dz he (ii) Assume u = ry 23 and find (V V)u at (1, 1, 1) where V =< 1,x, 1 >. (iii) Write out the 1st component equation of the Navier-Stokes vector equation.

Name: The Navier-Stokes equation is the fundamental equation of fluid dynam
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Description: The Navier-Stokes equation is the fundamental equation of fluid dynamics. In one of its many forms(incompressible and viscous flow) the equation is pƏt + (V. V)V= -Vp + µ(V V)V. In thenotation, V = is the three-dimensional velocity field,

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter14: Fluid Mechanics

Section: Chapter Questions

Problem 89P: A container of water has a cross-sectional area of A=0.1m2 . A piston sits top of the water (see be...

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