Question: A liquid of density p and viscosity flows down an open channel of width W on a channel slope sin . The mean speed

A liquid of density p and viscosity μ flows down an open channel of width W on a channel slope sin θ. The mean speed V is believed to depend on, among other things, the depth (d), the gravitational acceleration (g), and the roughness height (ε). Find the dimensionless parameters that may affect the coefficient k in the formula V = k √dg sin θ.

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Based on the problem statement V f d g or fV d g 0 with n 6 m 3 is dimensionless and n m 3 dimensionless groups and thus 1 2 3 0 Taking d g and as the repeating variables we have 1 d a g b c V d 2 d e g f h i 3 d j g k s t Based on Newtons 2nd Law F ma the dimension ... View full answer

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