Question

A straight ditch is 100m long and has the cross-section of a semi-circle of radius 1m. The ditch is full of water (density 103kg/m3 ) and we wish to calculate how much work is required to empty the ditch by pumping all the water to the top of the ditch where it can flow out through an overflow pipe. You should take the acceleration due to gravity to be g = 9.8m/s2 .

(a) Draw a sketch of the ditch showing your choice of the x-axis. Show on your sketch a typical slice of water that can be used to set up the work calculation.

(b) Calculate the work required to move this typical slice of water to the top of the ditch.

(c) Use the result of (b) to write down an expression for the total work required to empty the ditch as a limit of a sum, and write this expression as a definite integral.

(d) Evaluate the definite integral obtained in (c) to determine the total work required to empty the ditch

Answer 1

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