$7\mathrm{.}7\mathrm{.}3($C$)$ WD$)$ The pressure drop across a short hollowed plug placed in a circular tube through which a liquid is flowing $($see Fig. P$7\mathrm{.}7\mathrm{.}3)$ can be expressed as

$p=f(,V,D,d)$

where $$ is the fluid density, and $V$ is the mean velocity in the tube. Some experimental data obtained with $D=0\mathrm{.}2ft,=2\mathrm{.}0$ slugs $\frac{?}{f{t}^3},$ and $V=2f\frac{t}{s}$ are given in the following table:

$\backslash$table$[[d(ft),0\mathrm{.}06,0\mathrm{.}08,0\mathrm{.}10,0\mathrm{.}15],[p(l\frac{b}{f}{t}^2),493\mathrm{.}8,156\mathrm{.}2,64\mathrm{.}0,12\mathrm{.}6]]$

Plot the results of these tests, using suitable dimensionless parameters, on a log$-$log scale. Use a standard curve$-$fitting technique to determine a general equation for $p.$ What are the limits of applicability of the equation?

FIGURE P $7\mathrm{.}7\mathrm{.}3$