Regarding Skin Friction coefficient (C_f), I have gaon through several papers. Almost all papers calculate C_f*Re instead of C_f. Is this correct? I mean C_f*Re gives skin friction coefficient? Also C_f involves Tao_w, shear stress. Some papers use negative velocity and some papers use positive velocity gradients. i.e, Tao=-mu(patial u/partial y) or Tao= mu(patial u/partial y). Which one of this is correct? Please give your suggestions.
According to certain authors the velocity gradients indicate the shear stress level both in the laminar as well as turbulent flow, although there are different method to estimate the same for respective flow conditions.
Reynold no. measure the dominance of inertial forces over the viscous forces. Hence, it is an important parameter at different scales of the flow measurement studies.
Coefficient of friction is non-dimensional quantity or it can also viewed as constant of proportionality. The actual relations are often normalized or expressed in a non-dimension form.
Hence, as far as it appears from the relation the Reynold no. is multiplied to the skin friction coefficient either to amplify or reduce effect of skin friction. To fit the value to scale of interest.
Well, as an answer to your original question, c_f is the skin friction coefficient and Reynolds no. is being multiplied to obtain the corresponding value in the region of study.
while the sign remains just the matter of convention it depends on whether the gradient is positive or negative in your intended direction of study.
I think the reason to use C_f Re instead of C_f might be that you have a laminar boundary layer. If the boundary layer is laminar the shear stress will grow proportionally to speed. The definition of C_f includes the velocity squared while the fenomenon depends only on velocity. A problem of how C_f is defined. My opinion is that a correlation and the definition of the parameters used form a package! So you have to use the correlation of C_f with the parameters as defined in the context of that correlation.
Dear Prof. Abdul, I am investigating fully developed flow in a channel and hence it is one dimensional. Also, Tau_w is negative or positive?
Hi Nicolas, Thanks for your suggestion. My doubt is the skin friction is used as either C_f*Re or its just (Pa U)/(Pa Y). Does this quantity (Pa U)/(Pa Y) can be called as skin friction coefficient?
According to certain authors the velocity gradients indicate the shear stress level both in the laminar as well as turbulent flow, although there are different method to estimate the same for respective flow conditions.
Reynold no. measure the dominance of inertial forces over the viscous forces. Hence, it is an important parameter at different scales of the flow measurement studies.
Coefficient of friction is non-dimensional quantity or it can also viewed as constant of proportionality. The actual relations are often normalized or expressed in a non-dimension form.
Hence, as far as it appears from the relation the Reynold no. is multiplied to the skin friction coefficient either to amplify or reduce effect of skin friction. To fit the value to scale of interest.
Well, as an answer to your original question, c_f is the skin friction coefficient and Reynolds no. is being multiplied to obtain the corresponding value in the region of study.
while the sign remains just the matter of convention it depends on whether the gradient is positive or negative in your intended direction of study.
Dear Abdul and Aditya, Thanks for your explanation. It was indeed good one and my doubt is completely cleared.
Regards,
Sankar
In lubrication flow, we use friction coefficient, which is defined as tauw/(mu U / h) instead of tauw/ (rho U^2). The conversion between these two will be the Reynolds number. tauw/(rho U^2) is normally used in aerodynamics
The skin friction coefficient C_f can be defined as the resultant of \sqrt( ( wall- x-shear stress (\tau_x^2) + wall-y-shear stress ( \tau_y^2))/(0.5*rho*U^2)), hence the C_f must be positive. However, the positive or negative sign of \tau-x or \tau-y, refers to the direction of the flow velocity.
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