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Chapter 8: Problem 7

Consider laminar flow in a circular tube. Will the friction factor be higher near the inlet of the tube or near the exit? Why? What would your response be if the flow were turbulent?

Short Answer

Expert verified
Answer: In a laminar flow, the friction factor is constant along the length of the tube and does not depend on the position, either near the inlet or the exit of the tube. In a turbulent flow, the friction factor will be higher near the exit of the tube than near the inlet due to fully developed turbulence and eddies.

Step by step solution

01

Understand Laminar and Turbulent Flows

In laminar flow, the fluid particles move in parallel layers without any mixing or significant turbulence. The flow is characterized by a low Reynolds number (Re < 2000). The laminar flow is smooth and well ordered. On the other hand, turbulent flow occurs when the fluid experiences chaotic, unpredictable behavior and significant mixing. The flow is characterized by a high Reynolds number (Re > 4000). Turbulent flow is disorderly and full of eddies and swirls.
02

Define Friction Factor

The friction factor (f) is a dimensionless quantity representing the ratio of shear stress at the tube wall to the dynamic pressure. It indicates the resistance to flow caused by wall friction. In pipe flow, the friction factor depends on the flow regime (laminar or turbulent), and it is also a function of the Reynolds number and the roughness of the pipe wall.
03

Discuss Friction Factor in Laminar Flow

In laminar flow, the fluid layers slide over one another, and the resistance to flow is mainly due to viscous forces. The friction factor for laminar flow in a circular pipe is given by the Hagen-Poiseuille equation: f = 16 / Re where Re is the Reynolds number. Since the Reynolds number is constant along the length of the tube, we can conclude that the friction factor is also constant in laminar flow and does not depend on the position, either near the inlet or the exit of the tube.
04

Discuss Friction Factor in Turbulent Flow

In turbulent flow, the resistance to flow is primarily due to turbulence and eddies. Near the inlet of the tube, the flow may not have fully developed its turbulence, which can make the local friction factor slightly lower than in the fully developed turbulent flow region. Contrarily, near the exit, the turbulent flow will be fully developed, and the friction factor will be higher. So, the friction factor will be higher near the exit of the tube in a turbulent flow than near the inlet.
05

Conclusion

In laminar flow, the friction factor is constant along the length of the tube and does not depend on the position, either near the inlet or the exit of the tube. However, in turbulent flow, the friction factor will be higher near the exit of the tube than near the inlet, as the flow becomes fully developed and experiences greater turbulence and eddies.

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Most popular questions from this chapter

A 10 -m-long and 10 -mm-inner-diameter pipe made of commercial steel is used to heat a liquid in an industrial process. The liquid enters the pipe with \(T_{i}=25^{\circ} \mathrm{C}, V=0.8 \mathrm{~m} / \mathrm{s}\). A uniform heat flux is maintained by an electric resistance heater wrapped around the outer surface of the pipe, so that the fluid exits at \(75^{\circ} \mathrm{C}\). Assuming fully developed flow and taking the average fluid properties to be \(\rho=1000 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=\) \(4000 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, \mu=2 \times 10^{-3} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}, k=0.48 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and \(\operatorname{Pr}=10\), determine: (a) The required surface heat flux \(\dot{q}_{s}\), produced by the heater (b) The surface temperature at the exit, \(T_{s}\) (c) The pressure loss through the pipe and the minimum power required to overcome the resistance to flow.

In the effort to find the best way to cool a smooth thin-walled copper tube, an engineer decided to flow air either through the tube or across the outer tube surface. The tube has a diameter of \(5 \mathrm{~cm}\), and the surface temperature is maintained constant. Determine \((a)\) the convection heat transfer coefficient when air is flowing through its inside at \(25 \mathrm{~m} / \mathrm{s}\) with bulk mean temperature of \(50^{\circ} \mathrm{C}\) and \((b)\) the convection heat transfer coefficient when air is flowing across its outer surface at \(25 \mathrm{~m} / \mathrm{s}\) with film temperature of \(50^{\circ} \mathrm{C}\).

Liquid glycerin is flowing through a 25-mm-diameter and 10 -m-long tube. The liquid glycerin enters the tube at \(20^{\circ} \mathrm{C}\) with a mass flow rate of \(0.5 \mathrm{~kg} / \mathrm{s}\). If the outlet mean temperature is \(40^{\circ} \mathrm{C}\) and the tube surface temperature is constant, determine the surface temperature of the tube.

Air is flowing through a smooth thin-walled 4-indiameter copper tube that is submerged in water. The water maintains a constant temperature of \(60^{\circ} \mathrm{F}\) and a convection heat transfer coefficient of \(176 \mathrm{Btu} / \mathrm{h}-\mathrm{ft}^{2} \cdot \mathrm{R}\). If air (1 atm) enters the copper tube at a mean temperature of \(90^{\circ} \mathrm{F}\) with an average velocity of \(8 \mathrm{ft} / \mathrm{s}\), determine the necessary copper tube length so that the outlet mean temperature of the air is \(70^{\circ} \mathrm{F}\).

Electronic boxes such as computers are commonly cooled by a fan. Write an essay on forced air cooling of electronic boxes and on the selection of the fan for electronic devices.
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