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Chapter 7: Problem 9

What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows?

Short Answer

Expert verified
Answer: Surface roughness has a minor effect on the friction drag coefficient in laminar flows, but a more significant effect in turbulent flows due to increased turbulence and pressure fluctuations near the surface.

Step by step solution

01

Define laminar and turbulent flows

Laminar flow is a smooth, steady flow of fluid, with its particles moving in parallel layers or lamina. In contrast, turbulent flow is characterized by chaotic and rapidly fluctuating flow, with its particles moving haphazardly and crossing each other across different layers.
02

Explain the concept of the friction drag coefficient

The friction drag coefficient (often denoted as \(C_f\)) is a dimensionless quantity used to measure the resistance a fluid flowing over a solid surface experiences due to viscous effects. It is associated with the shear stress between the fluid and the solid surface.
03

Discuss the effect of surface roughness on friction drag coefficient in laminar flow

In a laminar flow, the friction drag coefficient is primarily determined by fluid viscosity and the size of the flow region. Surface roughness has a minor effect on the friction drag coefficient in laminar flows because the smoothness of the flow keeps particles relatively far away from the surface, and the effect of roughness is limited to a thin boundary layer near the surface. Hence, any increase in surface roughness may lead to a small increase in the friction drag coefficient.
04

Discuss the effect of surface roughness on friction drag coefficient in turbulent flow

In turbulent flows, the effect of surface roughness is more significant in determining the friction drag coefficient. The increased roughness creates additional turbulence and higher pressure fluctuations near the surface. This further increases the shear stress between the fluid and the surface, leading to a higher friction drag coefficient. However, the effect of roughness on turbulent flow is complex and may depend on several factors, including the scale of roughness compared to the flow region and the size of the turbulence eddies. To summarize, surface roughness has a minor effect on the friction drag coefficient in laminar flows but a more significant effect in turbulent flows.

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Most popular questions from this chapter

Engine oil at \(105^{\circ} \mathrm{C}\) flows over the surface of a flat plate whose temperature is \(15^{\circ} \mathrm{C}\) with a velocity of $1.5 \mathrm{~m} / \mathrm{s}\(. The local drag force per unit surface area \)0.8 \mathrm{~m}$ from the leading edge of the plate is (a) \(21.8 \mathrm{~N} / \mathrm{m}^{2}\) (b) \(14.3 \mathrm{~N} / \mathrm{m}^{2}\) (c) \(10.9 \mathrm{~N} / \mathrm{m}^{2}\) (d) \(8.5 \mathrm{~N} / \mathrm{m}^{2}\) (e) \(5.5 \mathrm{~N} / \mathrm{m}^{2}\) (For oil, use $\nu=8.565 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}, \rho=864 \mathrm{~kg} / \mathrm{m}^{3}$ )

In flow over blunt bodies such as a cylinder, how does the pressure drag differ from the friction drag?

Hydrogen gas at \(1 \mathrm{~atm}\) is flowing in parallel over the upper and lower surfaces of a 3 -m-long flat plate at a velocity of $2.5 \mathrm{~m} / \mathrm{s}\(. The gas temperature is \)120^{\circ} \mathrm{C}$, and the surface temperature of the plate is maintained at \(30^{\circ} \mathrm{C}\). Using appropriate software, investigate the local convection heat transfer coefficient and the local total convection heat flux along the plate. By varying the location along the plate for \(0.2 \leq x \leq 3 \mathrm{~m}\), plot the local convection heat transfer coefficient and the local total convection heat flux as functions of \(x\). Assume flow is laminar, but make sure to verify this assumption.

Combustion air in a manufacturing facility is to be preheated before entering a furnace by hot water at \(90^{\circ} \mathrm{C}\) flowing through the tubes of a tube bank located in a duct. Air enters the duct at \(15^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with a mean velocity of \(4.5 \mathrm{~m} / \mathrm{s}\), and it flows over the tubes in the normal direction. The outer diameter of the tubes is \(2.2 \mathrm{~cm}\), and the tubes are arranged in-line with longitudinal and transverse pitches of \(S_{L}=S_{T}=5 \mathrm{~cm}\). There are eight rows in the flow direction with eight tubes in each row. Determine the rate of heat transfer per unit length of the tubes and the pressure drop across the tube bank. Evaluate the air properties at an assumed mean temperature of \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Is this a good assumption?

Air at \(20^{\circ} \mathrm{C}\) flows over a 4-m-long and 3 -m-wide surface of a plate whose temperature is \(80^{\circ} \mathrm{C}\) with a velocity of $5 \mathrm{~m} / \mathrm{s}$. The rate of heat transfer from the surface is (a) \(7383 \mathrm{~W}\) (b) \(8985 \mathrm{~W}\) (c) \(11,231 \mathrm{~W}\) (d) 14,672 W (e) 20,402 W (For air, use $k=0.02735 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \operatorname{Pr}=0.7228, \nu=1.798 \times\( \)\left.10^{-5} \mathrm{~m}^{2} / \mathrm{s}\right)$
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