Answered: 3. Viscous fluid occupies the region 0…

Engineering

Mechanical Engineering

3. Viscous fluid occupies the region 0 < z

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.86P: Determine the volume of the concrete arch dam.

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Question

3. Viscous fluid occupies the region 0 <z<h between two rigid boundaries z = 0 and z = h.
The lower boundary is at rest, the upper boundary rotates with constant angular velocity
N about the z-axis. Show that a steady solution of the full Navier-Stokes equations with
flow only in the 0-direction of the form
u = ug(r, z)eo
is not possible (i.e., show any rotary motion ue(r,z) in this system must be accompanied
by a secondary flow where u; or uz # 0).

Expert Solution

Step 1

In fluid mechanics, the Navier-Stokes equation is a partial differential equation that describes the flow of incompressible fluids. The equation is a generalisation of a formula created in the 18th century by Swiss mathematician Leonhard Euler to explain the flow of incompressible and frictionless fluids.

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