By R. A. Wallis

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13) where U is the local free stream velocity and C/=2m/(i2 0 ). For two-dimensional flow, dA can be replaced by dx, as unit length is assumed in the direction normal to the flow path. 14) I n the above it will be seen t h a t the characteristic lengths have been replaced by unity, ax and Θ respectively. The non-dimensional coefficient, c/, is called the local skin friction coefficient. Assuming a smooth surface, the process of determining the total force, F, acting on a surface can be simplified.

These will naturally be a function of the non-uniformity in roughness height on a given surface. This information is not available in most cases and parameters which are a function of the equivalent roughness height, 1c, must be adopted. 53) W(TOIP) > 60 For values between 3 and 60, the skin friction is a function of both Reynolds number and roughness distribution. I n this transitional region between smooth and fully rough conditions, the equivalent roughness rule tends to be inaccurate when the individual heights of the roughness present vary by an appre­ ciable amount.

Dp/dx = 0. An­ other solution exists for fully developed flow in a pipe. In a turbulent boundary layer, the turbulent stresses which provide the turbulent mixing are much greater than the viscous stresses. I n an attempt to represent the turbulent stresses, the first equation of motion is empirically modified to include a term, e, called the " a p p a r e n t " kinematic viscosity due to turbulent shear. Hence, U du te +V du 1 dp . +{v+e) Ty=- £ . d 2u W* / 0 ox (3 3) · p Despite many attempts, no successful solution of this equation has been obtained.

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