Concept explainers
Calculate the nine components of the viscous stress tensor in cylindrical coordinates (see Chap. 9) for the velocity field of Prob 10-107. Discuss your results.
The nine component of the viscous stress tensor in cylindrical coordinates.
Answer to Problem 108P
The nine component of the viscous stress tensor in cylindrical coordinates is
Explanation of Solution
Given information:
The radial velocity component is
Write the expression for all the nine component of viscous stress tensor in cylindrical coordinates.
Here, viscous stress tensor in
Write the expression for viscous stress tensor in
Here, dynamic viscosity is
Write the expression for viscous stress tensor in
Here, velocity in angular direction is
Write the expression for viscous stress tensor in
Here, velocity in z-direction is
Write the expression for viscous stress tensor in
Write the expression for viscous stress tensor in
Write the expression for viscous stress tensor in
Write the expression for viscous stress tensor in
Write the expression for viscous stress tensor in
Write the expression for viscous stress tensor in
Substitute
Substitute
Here, all component of viscous stress tensor is zero, so flow is inviscid and no viscous stress is present in flow field.
Conclusion:
The nine component of the viscous stress tensor in cylindrical coordinates is
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Chapter 10 Solutions
Fluid Mechanics: Fundamentals and Applications
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