Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow at rate 0.3 m/s.

Correct result:

V =  19824.012 m3

Solution:

c=19.7 m a=28.5 m x=ac=28.519.7=445=8.8 m  A=67+30/60=1352=67.5 B=61+15/60=2454=61.25 C=180(A+B)=180(67.5+61.25)=2054=51.25  S1=x2 sinA sinB/(2 sinC)=x2 sin67.5  sin67.5 /(2 sin67.5 )=8.82 sin67.5  sin67.5 /(2 sin67.5 )=8.82 0.92388 0.92388/(2 0.92388)=40.21469  h=2 S1/x=2 40.2147/8.89.1397 m S2=c h=19.7 9.1397180.0521 m2 S=S1+S2=40.2147+180.0521220.2668 m2 l=5 60 0.3=90 m  V=l S=90 220.2668=19824.012 m3

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