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Chapter 6: Problem 40

What is turbulent viscosity? What is it caused by?

Short Answer

Expert verified
Answer: Turbulent viscosity, also known as eddy viscosity, is an artificial term in fluid mechanics used to describe the apparent increase in overall fluid viscosity due to the presence of turbulence. This concept is crucial for modeling the transfer of momentum in turbulent flows. Turbulent viscosity is caused by turbulence, the chaotic and random motion of fluid particles that leads to increased energy dissipation and momentum transport. Factors causing turbulence include high fluid velocity, sudden changes in fluid properties, external disturbances, and instabilities.

Step by step solution

01

Definition of Turbulent Viscosity

Turbulent viscosity, also called eddy viscosity, is an artificial term used in fluid mechanics to describe the apparent increase in the overall viscosity of a fluid due to the presence of turbulence. It is used to model the transfer of momentum in turbulent flows. Turbulent viscosity plays a significant role in determining the overall behavior of fluid and helps in solving complex flow problems.
02

Causes of Turbulent Viscosity

Turbulent viscosity is caused by turbulence, which is the chaotic and random motion of fluid particles that leads to increased energy dissipation and transport of momentum within the fluid. Turbulence is caused by multiple factors such as: 1. High fluid velocity: As the fluid velocity increases, the chances of turbulence occurring also increase. 2. Changes in fluid properties: Sudden changes in fluid properties, such as density or temperature, can lead to the generation of turbulence. 3. External disturbances: Interactions with solid boundaries, sudden pressure gradients, or external forces can create disturbances that lead to turbulence. 4. Instabilities: Changes in fluid flow and shear forces can create instabilities, which ultimately result in turbulence. Understanding turbulent viscosity and its causes is crucial in fluid mechanics, as it helps in analyzing and predicting the behavior of complex fluid flows in various applications.

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Most popular questions from this chapter

A long steel strip is being conveyed through a 3 -m-long furnace to be heat treated at a speed of \(0.01 \mathrm{~m} / \mathrm{s}\). The steel strip $\left(k=21 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \rho=8000 \mathrm{~kg} / \mathrm{m}^{3}\right.\(, and \)\left.c_{p}=570 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\( has a thickness of \)5 \mathrm{~mm}$, and it enters the furnace at an initial temperature of \(20^{\circ} \mathrm{C}\). Inside the furnace, the air temperature is maintained at \(900^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of $80 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Using appropriate software, determine the surface temperature gradient of the steel strip as a function of location inside the furnace. By varying the location in the furnace for \(0 \leq x \leq 3 \mathrm{~m}\) with increments of \(0.2 \mathrm{~m}\), plot the surface temperature gradient of the strip as a function of furnace location. Hint: Use the lumped system analysis to calculate the plate surface temperature. Make sure to verify the application of this method to this problem.

What is the physical significance of the Reynolds number? How is it defined for external flow over a plate of length \(L\) ?

Consider fluid flowing with a free stream velocity of $1 \mathrm{ft} / \mathrm{s}\( over a flat plate, where the critical Reynolds number is \)5 \times 10^{5}$. Determine the distance from the leading edge at which the transition from laminar to turbulent flow occurs for air (at 1 atm), liquid water, isobutane, and engine oil, and mercury. Evaluate all properties at $50^{\circ} \mathrm{F}$.

Atmospheric air with a velocity of \(10 \mathrm{~m} / \mathrm{s}\) and a temperature of \(20^{\circ} \mathrm{C}\) is in parallel flow over a flat heater surface which is maintained at \(80^{\circ} \mathrm{C}\). The surface area of the heater is \(0.30 \mathrm{~m}^{2}\). The drag force induced by the airflow on the heater is measured to be \(0.2 \mathrm{~N}\). Using the momentum-heat transfer analogy, determine the electrical power needed to maintain the prescribed heater surface temperature of \(80^{\circ} \mathrm{C}\). Evaluate the air properties at \(50^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Consider a flat plate positioned inside a wind tunnel, and air at 1 atm and \(20^{\circ} \mathrm{C}\) is flowing with a free stream velocity of $60 \mathrm{~m} / \mathrm{s}$. What is the minimum length of the plate necessary for the Reynolds number to reach \(2 \times 10^{7}\) ? If the critical Reynolds number is \(5 \times 10^{5}\), what type of flow regime would the airflow experience at \(0.2 \mathrm{~m}\) from the leading edge?
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