Current Attempt in Progress

An incompressible fluid oscillates harmonically $(V=V_0$ sin $t,$ where $V$ is the velocity$)$ with a frequency of $8ra\frac{d}{s}$ in a $3-$in$--$diameter pipe. A $\frac{1}{3}$ scale model is to be used to determine the pressure difference per unit length, $p_1($at any instant$)$ along the pipe. Assume that

$p_l=f(D,V_0,,t,,)$

where $D$ is the pipe diameter, $$ the frequency, $t$ the time, the $$ fluid viscosity, and $$ the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate?

${}_m=$

$ra\frac{d}{s}$