![]() U freestream = (10^7 * 1.8 * 10^-5 kg/ms) / (1.2 kg/m^3 * 10 m)įirst of all workout if the initially laminar side changes (transitions) to turbulent at some point along the length of the plate. #Skin friction coefficient freeReL at the end of the plate where x = L is given as 10^7įrom here free stream velocity can be found as: Where mu = dynamic Viscosity = 1.8 * 10^-5 Trailing edge is the end of the plate where length is measured to Note: Leading edge is the start of the plate where we measure length from L = length of plate from leading to trailing edge. Where ReL = Reynolds Number at the trailing edge of the plate = 10^7 ReL = (Rho * U freestream * L) / mu = 10^7 We need to find the free stream velocity using the equation for the Reynolds Number at the trailing edge of the plate : at the end of the plate), $Re = 10^7$ which is higher then critical $Re$ at which conversion occurs: $Re_$$ It is clear because it is stated that at the trailing edge (i.e. It is clear from the statement of your problem, that at some point the boundary layer of your flow converts from laminar to turbulent. How to deal with it, if we have only formulas for entire laminar and entire turbulent boundary layers? There is one way (not very difficult) of dealing with it, about which one may read in the Nunn's book, for instance. And then it is turbulent to the end of the plate. It was revealed that in most cases of flows over a plate, boundary layer can start as laminar and then at some length of the plate become turbulent. There are two formulas for friction drag coefficient: one if the ENTIRE boundary layer (over the entire length of the plate) is laminar the other one is if the ENTIRE boundary layer is turbulent. And revealed that drag force can very conveniently be calculated using "skin friction coefficient" $c_f$ in general and "friction drag coefficient" $C_f$ (or $C_D$ sometimes) in particular. That is why in order to find drag force which fluid exerts on the plate, one should consider only narrow layer of the flow adjacent to the plate, i.e. It was found that when a fluid flows over a flat plate, almost all flow velocity reduction happens in a narrow layer adjacent to the plate. In the 1989 edition (probably the first edition of the book) I would refer you to the paragraph 13.5 "Flat plate boundary layer flows" on p.255. Nunn "Intermediate fluid mechanics" text book. Regarding your question - where to start at - I would recommend Robert H. #Skin friction coefficient how toOtherwise, it will be difficult to understand how to solve the problem since the books are not very clear on the subject. What is important to remember when dealing with this problem is that it is crucial to attend the lecture at which the subject was covered. Therefore, I would be reluctant to provide the solution. In the case of a steady-state flow, the friction factor also characterizes the energy losses due to friction it should not be confused with the "coefficient of resistance," which includes not only energy losses due to friction, but also energy losses of a different nature.The problem you cite in the question is a pretty standard homework problem in a graduate fluid mechanics course (it might be also an undergraduate course but less likely). A distinction is made between the "instantaneous local friction factor," the "average instantaneous friction factor over the surface," the "time-average local friction factor," and the "time- and surface-average friction factor."Ģ. Where σ w is the shear stress at the surface of the body (wall) ρ is the density of the fluid w 0 is the characteristic velocity of the flow (in the case of flow in pipes, it is the average value over the cross section in the case of external flow past a body, it is the value in the external flow).Ĭomments. Skin-friction coefficientĪ dimensionless number characterizing the frictional force at the boundary between fluid and a wall it is defined by the identity:ī) in the case of external flow past a body ![]()
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