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Chapter 8: Problem 9

How does surface roughness affect the pressure drop in a tube if the flow is turbulent? What would your response be if the flow were laminar?

Short Answer

Expert verified
Short Answer: Surface roughness has a significant impact on pressure drop in turbulent flow by increasing drag force, creating additional velocity fluctuations and turbulent eddies. In laminar flow, the impact of surface roughness on pressure drop is generally negligible due to the orderly flow pattern, although it can trigger transitional flows to become turbulent, subsequently causing an increase in pressure drop.

Step by step solution

01

Understand the difference between turbulent and laminar flows

In fluid dynamics, there are two main types of internal flows: laminar and turbulent. Laminar flow occurs when the fluid moves smoothly and orderly in parallel layers (also known as streamlines). Turbulent flow, on the other hand, is characterized by chaotic and disorderly flow patterns, with the fluid moving in random directions and eddies present within the fluid. In general, as the flow velocity, pipe diameter, or fluid density increases, the likelihood of turbulent flow also increases. This is often quantified using the dimensionless Reynolds number, with turbulent flow occurring above a certain Reynolds number value.
02

Understand the impact of surface roughness on turbulent flow

In turbulent flow, the presence of surface roughness significantly influences both the fluid flow patterns and the pressure drop within the tube. Rough surfaces increase the drag force exerted by the fluid on the pipe walls, and this drag, in turn, leads to a higher pressure drop across the pipe. The reason for this is that roughness elements, such as rough protrusions and irregularities, create additional velocity fluctuations and turbulent eddies, increasing the energy dissipation within the flow. The effect of surface roughness is typically quantified using the relative roughness (a non-dimensional parameter), which is given by the ratio of the pipe's roughness height to its inner diameter.
03

Understand the impact of surface roughness on laminar flow

In laminar flow, the fluid typically flows in parallel layers, and any disturbance or velocity fluctuation tends to dampen out quickly. As a result, the presence of surface roughness has a much lower impact on pressure drop in laminar flow compared to turbulent flow. In fact, at very low Reynolds numbers, the influence of surface roughness on pressure drop is almost negligible. However, when the flow is transitional (i.e., close to the boundary between laminar and turbulent flow), surface roughness can act as a trigger, causing the flow to become turbulent, which increases the pressure drop.
04

Conclusion: Discussion of surface roughness impact on pressure drop in turbulent and laminar flows

To summarize, surface roughness significantly affects the pressure drop in a tube when the flow is turbulent because it increases the drag force, creating additional velocity fluctuations and turbulent eddies. Conversely, the impact of surface roughness on pressure drop in laminar flow is often negligible due to the orderly nature of the flow. However, surface roughness can act as a trigger causing transitional flows to become turbulent, subsequently increasing the pressure drop.

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Most popular questions from this chapter

Air at \(10^{\circ} \mathrm{C}\) enters an \(18-\mathrm{m}\)-long rectangular duct of cross section \(0.15 \mathrm{~m} \times 0.20 \mathrm{~m}\) at a velocity of \(4.5 \mathrm{~m} / \mathrm{s}\). The duct is subjected to uniform radiation heating throughout the surface at a rate of \(400 \mathrm{~W} / \mathrm{m}^{3}\). The wall temperature at the exit of the duct is (a) \(58.8^{\circ} \mathrm{C}\) (b) \(61.9^{\circ} \mathrm{C}\) (c) \(64.6^{\circ} \mathrm{C}\) (d) \(69.1^{\circ} \mathrm{C}\) (e) \(75.5^{\circ} \mathrm{C}\) (For air, use \(k=0.02551 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.7296, v=1.562 \times\) \(10^{-5} \mathrm{~m}^{2} / \mathrm{s}, c_{p}=1007 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, \rho=1.184 \mathrm{~kg} / \mathrm{m}^{3}\).)

Consider fully developed laminar flow in a circular pipe. If the viscosity of the fluid is reduced by half by heating while the flow rate is held constant, how will the pressure drop change?

An engineer is to design an experimental apparatus that consists of a \(25-\mathrm{mm}\)-diameter smooth tube, where different fluids at \(100^{\circ} \mathrm{C}\) are to flow through in fully developed laminar flow conditions. For hydrodynamically and thermally fully developed laminar flow of water, engine oil, and liquid mercury, determine \((a)\) the minimum tube length and \((b)\) the required pumping power to overcome the pressure loss in the tube at largest allowable flow rate.

The velocity profile in fully developed laminar flow of water at \(40^{\circ} \mathrm{F}\) in a 140 -ft-long horizontal circular pipe, in \(\mathrm{ft} / \mathrm{s}\), is given by \(u(r)=0.8\left(1-625 r^{2}\right)\) where \(r\) is the radial distance from the centerline of the pipe in \(\mathrm{ft}\). Determine \((a)\) the volume flow rate of water through the pipe, \((b)\) the pressure drop across the pipe, and \((c)\) the useful pumping power required to overcome this pressure drop.

Consider turbulent forced convection in a circular tube. Will the heat flux be higher near the inlet of the tube or near the exit? Why?
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