Flat plates friction coefficient

Momentum boundary layer calculations are useful to estimate the skin friction on a number of objects, such as on a ship hull, airplane fuselage and wings, a water surface, and a terrestrial surface. Once we know the boundary layer thickness, occurring where the velocity is 99% of the free-stream velocity, skin friction coefficient and the skin friction drag on the solid surface can be calculated. Estimate the laminar boundary layer thickness of a 1-m-long, thin flat plate moving through a calm atmosphere at 20 m/s. 

Equation (5-56), called the Reynolds-Colburn analogy, expresses the relation between fluid friction and heat transfer for laminar flow on a flat plate. The heat-transfer coefficient thus could be determined by making measurements of the frictional drag on a plate under conditions in which no heat transfer is involved. 

Schlichting [1] has surveyed experimental measurements of friction coefficients for turbulent flow on flat plates. We present the results of that survey so that they may be employed in the calculation of turbulent heat transfer with the fluid-friction-heat-transfer analogy. The local skin-friction coefficient is given by... 

The average-friction coefficient for a flat plate with a laminar boundary layer up to Recrii and turbulent thereafter can be calculated from... 

Nitrogen at 1 atm and 20°C is blown across a 130-cm-square flat plate at a velocity of 3.0 m/s. The plate is maintained at a constant temperature of lOO C. Calculate the average-friction coefficient and the heat transfer from the plate. 

The idea of utilizing a coefficient of friction is not new, having been proposed and tested for the cleaning of flat plates with air at least two decades ago by Zimon.f l Similar ideas have been proposed for the cleaning of wafers/discs by spinning them.t If the particles that... 

Friction Coefficient 400 Heat Transfer Coefficient 401 Flat Plate with Unhealed Starting I engih 403 Uniform Heat Flux 403... 

We start this chapter with a general physical description of the convection mechanism. We then discuss (he velocity and thermal botmdary layers, and laminar and turbitlent flows. Wc continue with the discussion of the dimensionless Reynolds, Prandtl, and Nusselt nuinbers, and their physical significance. Next we derive the convection equations on the basis of mass, momentiim, and energy conservation, and obtain solutions for flow over a flat plate. We then nondimeiisionalizc Ihc convection equations, and obtain functional foiinis of friction and convection coefficients. Finally, we present analogies between momentum and heat transfer. 

The friction coefficient and Nusselt number for a flat plate were determined in Section 6-8 to be... 

For flat plates, the drag force is equivalent to friction force. The average friction coefficient Qcan be determined from Eq. 6-11,... 

C What does the friction coefficient represent in flow over a flat plate How is it related to the drag force acting on the plate ... 

B Develop an intuitive understanding of friction drag and pressure drag, and evaluate the average drag and convection coefficients in external flow, a Evaluate the drag and heat transfer associated with flow over a flat plate for both laminar and turbulent flow,... 

For parallel flow over a flat plate, the pressure drag is zero, and thus the drag coefficient is equal to the friction coefficient and the drag force is equal to the friction force. 

Note that /i, is proportional to Re and thus to. v- - for laminar flow. Therefore, is infinite at the leading edge (jc = 0) and decreases by a factor of.r in the flow direction. The variation of the boundary layer thickness 5 and the friction and heat transfer coefficients along an isothermal flat plate are shown in Fig. 7-9. The local friction and heat transfer coefficients are higher in... 

The variation of the local friction and heat transfer coefficients for flow over a flat plate. 

The local coefficient of friction. In the case of two-sided flow past a flat plate, the local coefficient of friction Cf = Cf(X) is expressed via other hydrodynamic parameters as... 

For the turbulent boundary layer on a flat plate, von Karman s friction law with modified numerical coefficients [212,289],... 

More detailed information about the structure of turbulent flows on a flat plate, as well as various relations for determining the average velocity profile and the local coefficient of friction, can be found in the references [135, 138, 268, 276, 289, 427], which contain extensive literature surveys. 

Consider a flat plate steadily oscillating with velocity V0 sin cat on top of another flat plate (Fig. 3P-4). The pressure and dry friction coefficient between the plate are p and pc, respectively. Find the steady periodic temperature fluctuations in the system. 

Figure 6.4 Friction coefficient for smooth flat plate (from Rohsenow Choi [14]),...

Equation 6.17 indicates that on a flat plate the average skin friction coefficient is equal to twice the local skin friction coefficient at the trailing edge. 

FIGURE 6.10 Local laminar boundary layer skin friction coefficient on a flat plate at uniform temperature, Pr = 0.725 and 0o = 3 [5]. 

The quantity cy in Eqs. 6.219 and 6.221 is found from the equations given in the section on uniform free-stream conditions. For example, at moderate Reynolds numbers on a flat plate, the skin friction coefficient is given by... 

Similar behavior is observed in a turbulent boundary layer over a rough flat plate, where Prandtl and Schlichting [128] showed that the important parameter is kslx. The local skin friction coefficient is shown in Fig. 6.45 as a function of Re with x/ks as a parameter. 

FIGURE 6.45 Variation of local skin friction coefficient along a sand-roughened flat plate [65]. 

Local drag coefficient for a flat plate. Experimental data are compared with Blasius solution (Eq, 11.16) and with Prandtl s equation (Eq. 11.36). [From H. W. Liepmann and S. Dahwan, Direct measurements of local skin friction in low-speed and high-speed flow, Proc. First U.S. Natl. Congr. AppL Mech, ASME, New York, 1952, p. 873. Reproduced with the permission of the publisher,] I... 

Obtain expressions for the local and mean values of the wall shear stress and friction factor (or drag coefficient) for the laminar boundary layer flow of an incompressible power-law fluid over a flat plate Compare these results with the predictions presented in Table 7.1 for different values of the power-law index. 

Equation (7.3-13) has been shown to be quite useful in correlating momentum, heat, and mass transfer data. It permits the prediction of an unknown transfer coefficient when one of the other coefficients is known. In momentum transfer the friction factor is obtained for the total drag or friction loss, which includes form drag or momentum losses due to blunt objects and also skin friction. For flow past a flat plate or in a pipe where no form drag is present, //2 = J = Jp- When form drag is present, such as in flow in packed beds or past other blunt objects,772 is greater thanJ, otJ andJ s Jg. 

A reciprocating motion set-up involves the back-and-forth motion between a ball or a pin and a flat plate. The friction coefficient is obtained from the measurement of the normal and the tangential forces. This type of set-up can be easily adapted to the study of tribocorrosion behavior in electrolyte solutions. For this, the contact is immersed in the electrolyte that is contained in a cell equipped with a reference electrode and a counter electrode. The rubbing metal surface is branched as the working electrode in a potentiostatic circuit, which permits to perform rubbing experiments under potential control. The friction coefficient shown in Figure 10.11 was determined in this way by scanning the potential of the stainless steel in the positive direction. 

This type of dependence is a characteristic of dry friction, that is, corresponds to Coulomb s dry friction law, Ff, = pF, . Plastic behavior can be modeled by a friction element, that is, two flat plates with a friction coefficient, p, with respect to each other and compressed with a normal force Fn in such a way that the applied tangential force F would correspond to the yield stress of a given material (Figure 3.7). 

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