$(20$ points$)$ A $500m$ long channel has a trapezoidal cross section. The bottom of cross section is $50m$ wide, the depth is $15m,$ and the side slope is $3$:$1.$ The channel slope is $0\mathrm{.}002,$ and Manning's roughness is $0\mathrm{.}01.$ The design flow discharge is $2000\frac{m^3}{s}.$ The flow at the design condition is uniform flow at the downstream section.

a$).(10$ points$)$ Use HEC$-$RAS model, design a one$-$pier bridge in the middle of the channel. The lower chord is $5m$ above the bottom, and the high chord is $1m$ above the lower chord. The bridge is $10m$ wide. The pier diameter is $2m.$ No abutment is needed. No debris will be considered.

b$).(5$ points$)$ What's flow depth at the bridge section when flow is the design discharge $2000\frac{m^3}{s}.$

c$).(5$ points$)$ At flow $Q=2500\frac{m^3}{s},$ what's flow depth at the bridge section? Is choking occurring?