Documentation:CHBE Exam Wiki/Midterm Exam 1 2016W/MT1 Question 2/Solution Q2 D

Left hand side - units
$F_{C}[=]N=kg\cdot {\frac {m}{s^{2}}}$

Right hand side - units
${\frac {4}{3}}\cdot \pi \cdot \rho _{p}\cdot {r_{p}}^{3}\cdot {u_{t}}^{2}[=]{\frac {kg}{m^{3}}}\cdot m^{3}\cdot {\frac {m^{2}}{s^{2}}}=kg\cdot {\frac {m^{2}}{s^{2}}}$

The equation is not dimensionally consistent. We need another term with [1/m] on the right hand side, or [m] on left hand side.