Question

, di un object with d mass of 200 kg at a location where g # 9.6 m/s2? A pool of volume V (in m2) is to be filled with water using a hose of diameter D (in m). If the average discharge velocity is V (in m/s) and the filling time is t (in s), obtain a relation for the volume of the pool based on considerations of quantities involved. 2.

Answer 1

a pool of volume v(in m^3) a house of diameter D(in m) velocity is v (in m/s) time is t (in s) rightarrow Lets assume v = D^a v^b + t^c constant Now the dimensions of volume v = [L^3] Diameter D = [L] velocity V = [LT^- 1] time t = [T] constant = dimension less [L^3] = [L]^a [LT^- 1]^b [T]^c rightarrow a + b = 3 - b + c = 0 rightarrow b = c in general this volume depends on the area of cross- section g house i.e alpha D^2 Therefore a = 2 rightarrow b = c c = 1 Now V = C d^2 vt