Square character degree graphs yield direct products

If $G$ is a solvable group, we take $\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\Delta (G)$ is a square, then $G$ must be a direct product

Effects of Laminar Boundary Layer on a Model Broad-Crested Weir

This report describes an approximate method for the analysis of flow with a laminar boundary layer over a model hroad-crested weir. The method has been used to demonstrate the effects of the laminar boundary layer and the results have shown that these effects are significant. If the energy is calculated from depth and discharge measurements, large energy losses appear to occur at low flow rates in laboratory experiments. Losses real and apparent, are explained and the methods presented may be used to estimate the correct energy values