(Solved): (a) The wall shear stress W in a boundary layer depends upon the stream velocity U, boundary layer ...

(a) The wall shear stress ?W in a boundary layer depends upon the stream velocity U, boundary layer thickness ?, local turbulence velocity u?, density ?, and local pressure gradient dp/dx. Find an expression using ?, U, ? as repeating variables of a dimensionless function. (15 marks) (b) The Froude and Weber numbers for a specific fluid-flow problem are experimentally studied by using a 1:20 scale model. Assuming the model and prototype operate in the same gravitational field, and with the density scale of 1, what is the required surface tension scale for the experiment setup?

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(a) The wall shear stress Tw in a boundary layer depends upon the stream velocity U, boundary layer thickness \( \delta \), local turbulence velocity \( u^{\prime} \), density \( \rho \), and local pressure gradient \( \mathrm{dp} / \mathrm{dx} \). Find an expression using \( \rho, U, \delta \) as repeating variables of a dimensionless function. (15 marks) (b) The Froude and Weber numbers for a specific fluid-flow problem are experimentally studied by using a 1:20 scale model. Assuming the model and prototype operate in the same gravitational field, and with the density scale of 1 , what is the required surface tension scale for the experiment setup?