The power required to rotate a drilling string is a function of string diameter d, number of rotation of string per unit time n, viscosity of drilling fluid u, density of drilling fluid p. it is assumed that a power law may be used to describe the functional relationship between the drilling string power and these independent physical variables. 1. from a dimensional analysis, obtain a relation between the string power and the four physical variables (hint: solve in terms of the exponent of viscosity). 2. the power consumption is found experimentally to be proportional to the square of the speed of rotation n. by what factor would the power be expected to increase if the string diameter were doubled?