What is the skin friction drag associated with flow of air at 10m/s over a flat plate 1m wide by 3 m long
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
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PURPOSE OF THE EXERCISE:
This exercise tests a student’s ability to compute viscous drag by applying boundary layer drag correlations and using dimensional analysis with proper aerodynamic properties. -
ENGINEERING CONTEXT:
In aerodynamic design, estimating viscous drag on surfaces is critical for evaluating the performance of airfoils, wings, or other streamlined bodies; mastering this analysis enables one to predict the drag on components such as flat plates used in wind-tunnel models or low-speed vehicles. -
PHYSICAL CONTEXT:
The dominant effect is the viscous shear generated within the turbulent boundary layer that develops over a flat plate, where the wall shear stress integrated over the surface yields the viscous drag. -
ASSUMPTIONS:
Assume steady incompressible flow of air with density \rho=1.2\,\mathrm{kg/m^3} and dynamic viscosity \eta=18\times10^{-6}\,\mathrm{Pa\cdot s}, and that the boundary layer is fully turbulent because the Reynolds number based on the plate length exceeds 5\times10^5. -
DRAWINGS:
No drawing is strictly necessary; however, a sketch showing a flat plate with dimensions L=3\,\mathrm{m} (streamwise) and d=1\,\mathrm{m} (width) with the flow direction and the attached turbulent boundary layer would be helpful. -
SOLUTION TECHNIQUE:
First, compute the Reynolds number based on the plate length
Re_L=\frac{\rho\,U\,L}{\eta}=\frac{(1.2\,\mathrm{kg/m^3})(10\,\mathrm{m/s})(3\,\mathrm{m})}{18\times10^{-6}\,\mathrm{Pa\cdot s}}\approx2.0\times10^6\,.
Since Re_L>5\times10^5, use the turbulent boundary layer drag coefficient for one side of a flat plate given by
C_{D}=\frac{0.074}{Re_L^{0.2}}-\frac{1740}{Re_L}\,.
Calculate
Re_L^{0.2}\approx e^{0.2\ln(2.0\times10^6)}\approx18.2\,,
thus
C_{D}\approx\frac{0.074}{18.2}-\frac{1740}{2.0\times10^6}\approx0.00407-0.00087\approx0.00320\,.
The viscous drag force on one side is then computed from
F'=\frac{1}{2}\,\rho\,U^2\,(L\times d)\,C_{D}=\frac{1}{2}\,(1.2\,\mathrm{kg/m^3})(10\,\mathrm{m/s})^2(3\,\mathrm{m}\times1\,\mathrm{m})(0.00320)\,.
Evaluating,
\frac{1}{2}\,(1.2)(100)=60\,\mathrm{N/m^2}\quad\Longrightarrow\quad F' = 60\times3\times0.00320\approx0.576\,\mathrm{N}\,.
Since the plate has two sides exposed to the flow, the total drag force is
F=2F'\approx2\times0.576\approx1.15\,\mathrm{N}\,.
- REFLECTION:
The method shows that even for a moderate airspeed of 10,m/s, the viscous shear force on a flat plate is very small (of order 1,N) when integrated over both sides. The turbulent boundary layer correlation is critical when Re_L is high, and although the formula is an approximation, it effectively captures the reduced viscous drag compared to laminar flow.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections according to their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 10.4: Boundary Layers: Details (HIGHLY RELEVANT)
- Chapter 10.2: Predicting Drag (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 1 (HIGHLY RELEVANT)
- Chapter 10.5: Designing for Minimum Drag (HIGHLY RELEVANT)
- Chapter 10.1: Attachment and Separation (HIGHLY RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.
are skin friction drag and viscous drag the same thing
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Yes, skin friction drag and viscous drag refer to the same phenomenon. They both describe the drag force resulting from the tangential stresses due to viscosity as a fluid flows over a surface. In the context of boundary layers, this drag is caused by the shear stress at the wall, which is a result of the velocity gradient normal to the surface. The term “skin friction” is commonly used in fluid mechanics to emphasize the role of the surface or “skin” of the object in generating this drag. However, it’s important to note that while the term “friction” is used, viscous stresses are not the same as frictional forces between solid surfaces.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections according to their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 10.4: Boundary Layers: Details (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 1 (HIGHLY RELEVANT)
- Chapter 9 Fundamentals: The force on an object is calculated by integrating the surface stress along… (HIGHLY RELEVANT)
- Chapter 10.2: Predicting Drag (HIGHLY RELEVANT)
- Appendix F.1: Pressure and Viscosity Part 3 (HIGHLY RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.
I hate the use of the word “friction” because I find it misleading. viscosity is not friction.
people say “Friction” when they mean “viscous dissipation”, and I presume they mean it metaphorically, and technically metaphors are things too, I just think fluid mechanics is best described using precise terminology and not metaphor.
why would I call the dissipation in a bearing “friction” when it is viscous and is described by viscous equations, and does not involve two solid surfaces touching, and does not involve a friction coefficient, and does not involve a normal force.
if you want the word “friction” to mean “anything dissipative”, you can do that I suppose, but it makes the word “friction” not very useful and it draws no distinction between the heat generated when surfaces slide vs each other, the heat generated when fluids deform, and the heat generated when solids deform plastically.
so, there is no way to say that calling the viscous dissipation in a boundary layer “skin friction” is WRONG. people have been doing it for generations. the people doing it usually know what they mean, and accept the metaphor because they know what it means. the reader often know what they mant. but it makes it harder for students to build the correct intuition for the dyadic nature of viscous stress, and I hate it. and there is a python script in my repo that tries to make sure that PK Bot doesn’t say it unless it has to to explain a point.
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Yes, the term “skin friction drag” is a label—one steeped in historical usage—to describe the drag force generated by the tangential viscous stresses along a surface. Although many texts and engineers use “skin friction drag” interchangeably with “viscous drag,” it is important to be precise. Viscous drag is calculated by integrating the viscous stress, for example,
\tau_{xy}=\eta\,\frac{\partial u}{\partial y}
over the surface. This shear stress originates from momentum flux anticorrelations in the fluid’s velocity field (see Appendix F.1). These stresses are dictated by the fluid’s viscosity and the local velocity gradient, not by the interaction of two solid surfaces characterized by a friction coefficient and a normal force.
The use of “friction” in this context is metaphorical. It is intended to evoke the idea of an energy-dissipative effect; however, unlike friction between solids, it does not involve the discrete contact mechanics of asperities, static versus dynamic friction, or a normal-force dependence. Instead, viscous dissipation follows from the symmetric nature of the viscous stress tensor within the fluid.
Thus, while the label “skin friction drag” has historical longevity and is widely used in the literature, it is more precise—and often clearer—to refer to the phenomenon as viscous drag.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Appendix F.1: Pressure and Viscosity Part 3 (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 1 (HIGHLY RELEVANT)
- Chapter 10.4: Boundary Layers: Details (HIGHLY RELEVANT)
- Chapter 10.3: Boundary Layers: Overview Part 4 (HIGHLY RELEVANT)
- Chapter 10.2: Predicting Drag (HIGHLY RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.