Problem $3$: $(30$pts$.)$ The siphon spillway depicted below is operating at capacity with $H=10\mathrm{.}5m.$ The $50-m-$long siphon has a diameter of $1m,$ a friction factor of $0\mathrm{.}02,$ an inlet loss coefficient of $0\mathrm{.}5,$ and an exit loss coefficient of $1\mathrm{.}0.$ The crown of the siphon is $1\mathrm{.}2m$ below the reservoir level and $10m$ of pipe length from the reservoir.

$(1)$ Determine the velocity head and flow rate in the pipe $(15\text{'}).$

$(2)$ Determine the pressure at the siphon crown in $k\frac{N}{m^2}.(10\text{'}).$ Does this pressure cause cavitation, why? $(5\text{'})$