A full channel width vertical undershot sluice gate, produces a downstream jet depth of $0\mathrm{.}40m$

when installed in a long rectangular channel $5\mathrm{.}0m$ wide conveying a steady discharge of $20\mathrm{.}0$

$\frac{m^3}{s}.$ Assuming that the flow depth downstream of the gate returns to the uniform flow depth of

$2\mathrm{.}5m$ after a hydraulic jump

a$)$ determine the head loss across the hydraulic jump $($ I $)$

$(1\mathrm{.}968m)$

b$)$ if $5\%$ of the total head is lost as water flows under the gate, calculate the depth upstream of

the gate $(I)$

$(5\mathrm{.}786m)$