Determination of free surface and gravitational flow of liquid in triangular groove

The problem of determination of friction factor (or average fluid velocity) for a steady gravitational flow of fluid in an inclined open triangular gr oove is addressed. It is assumed that the angle of slope of the groove is k nown and the gravity is the only driving force of flow. The solution comprises of two parts. First, for a given groove's basal angl e, liquid-solid contact angle, and the Bond number, the shape of free surfa ce is determined starting from the Young-Laplace equation. The optimization technique as developed formerly is applied. Then, having determined the sh ape of the free surface and slope of the groove, the distribution of fluid flow is determined. The boundary value problem is solved using boundary col location method in least square sense. Given the distribution of fluid velo city the friction factor as a function of the other parameters of the model is analyzed.