$7\mathrm{.}24$ A liquid flows with a velocity $V$ through a hole in the side of a large tank. Assume that

$V=f(h,g,,)$

where $h$ is the depth of fluid above the hole, $g$ is the acceleration of gravity, $$ the fluid density, and $$ the surface tension.

Ans:

$\frac{V}{\sqrt[\phantom{2}]{gh}}=(\frac{g{h}^2}{})$

To check relationship by plotting:

To check relationship by plotting:

The following data were obtained by changing $h$ and measuring $V,$ with a fluid having a density $={10}^{3}k\frac{g}{m^3}$ and surface tension $=0\mathrm{.}074\frac{N}{m}.$

$\backslash$table$[[V(\frac{m}{s}),3\mathrm{.}13,4\mathrm{.}43,5\mathrm{.}42,6\mathrm{.}25,7\mathrm{.}00],[h(m),0\mathrm{.}50,1\mathrm{.}00,1\mathrm{.}50,2\mathrm{.}00,2\mathrm{.}50]]$

Plot these data by using appropriate dimensionless variables. Could any of the original variables have been omitted?