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Chapter 6: Problem 36

What is turbulent viscosity? What is it caused by?

Short Answer

Expert verified
Answer: Turbulent viscosity is a property of fluids that represents the diffusion of momentum within a turbulent flow, describing the increase in the apparent viscosity of a fluid due to the presence of turbulent fluctuations. It is caused by the transport and mixing of momentum in a turbulent flow, due to the random, chaotic motion of fluid particles. This occurs when a fluid flows at a high velocity or over an obstacle, causing a laminar flow to become unstable and transition into a turbulent flow—resulting in increased mixing of fluid particles and an increased apparent viscosity.

Step by step solution

01

Definition of Turbulent Viscosity

Turbulent viscosity is a property of fluids that represents the diffusion of momentum within a turbulent flow, which means it describes the increase in the apparent viscosity of a fluid due to the presence of turbulent fluctuations.
02

Cause of Turbulent Viscosity

Turbulent viscosity is caused by the transport and mixing of momentum in a turbulent flow, due to the random, chaotic motion of fluid particles. When a fluid flows at a high velocity or over an obstacle, a laminar flow (organized and layered flow) can become unstable and transition into a turbulent flow. The chaotic motion in turbulent flows creates eddies or swirls, which results in the increased mixing of fluid particles and therefore increases the apparent viscosity of the fluid.

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Most popular questions from this chapter

When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid?

An airfoil with a characteristic length of \(0.2 \mathrm{ft}\) is placed in airflow at \(1 \mathrm{~atm}\) and \(60^{\circ} \mathrm{F}\) with free stream velocity of \(150 \mathrm{ft} / \mathrm{s}\) and convection heat transfer coefficient of \(21 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot{ }^{\circ} \mathrm{F}\). If a second airfoil with a characteristic length of \(0.4 \mathrm{ft}\) is placed in the airflow at \(1 \mathrm{~atm}\) and \(60^{\circ} \mathrm{F}\) with free stream velocity of \(75 \mathrm{ft} / \mathrm{s}\), determine the heat flux from the second airfoil. Both airfoils are maintained at a constant surface temperature of \(180^{\circ} \mathrm{F}\).

A 6-cm-diameter shaft rotates at \(3000 \mathrm{rpm}\) in a 20 -cm-long bearing with a uniform clearance of \(0.2 \mathrm{~mm}\). At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at \(50^{\circ} \mathrm{C}\), and the viscosity and thermal conductivity of lubricating oil are \(0.05 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\) and \(0.17 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). By simplifying and solving the continuity, momentum, and energy equations, determine \((a)\) the maximum temperature of oil, \((b)\) the rates of heat transfer to the bearing and the shaft, and \((c)\) the mechanical power wasted by the viscous dissipation in the oil.

What is external forced convection? How does it differ from internal forced convection? Can a heat transfer system involve both internal and external convection at the same time? Give an example.

Air flowing over a \(1-\mathrm{m}\)-long flat plate at a velocity of \(7 \mathrm{~m} / \mathrm{s}\) has a friction coefficient given as \(C_{f}=0.664(V x / \nu)^{-0.5}\), where \(x\) is the location along the plate. Determine the wall shear stress and the air velocity gradient on the plate surface at mid-length of the plate. Evaluate the air properties at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
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