Tetrachloroethylene $($TCE$)$ at $20C$ flows into a large tank at a rate of $3\mathrm{.}93k\frac{g}{s}.$ The dense liquid has a density of $1620k\frac{g}{m^3}.$ A $2\mathrm{.}1cm-$diameter hole at the bottom of the tank allows TCE to escape at a velocity $U$ that follows the Bernoulli equation from a stagnant $($zero velocity$)$ point on the surface of the water in the tank. Pressure at the TCE surface is atmospheric; and the prespure of the TCE just below the drain hole is also atmospheric.

$7\frac{m}{s}($a$)$ Determine the steady outlet velocity. This is the point at which the flow out of the tank equals the flow into the tank $-$ the mass flow out through the drain is therefore $3\mathrm{.}93k\frac{g}{s}.$

$($b$)$ Determine the Bernoulli unit of pressure, corresponding to the outlet velocity.

$2\mathrm{.}5m$

$($c$)$ Determine the steady height of TCE in the tank.