Question: The following variables describe mixing in a tank
f (P, N, D, ρ, μ) = 0
P id power, work/time - [ML2/t3]
N is rotational speed of impeller - [1/t]
D is a diameter of the tank - [L]
ρ is density of the fluid - [M/L3]
μ is viscosity of the fluid - [M/Lt]
a. Show the functional relationship among the variable is
F( P , D2Nr) = 0
( rN3D5 m )
b. To scale a liquid mixing tank the power input per unit volume is kept constant. If it is desired to construct a prototype of an existing mixer by a 2:1 ratio, by what ratio must the tank diameter, D, and impeller speed, N, be changed?