Canal effect. The figure shows an anchored barge that extends across a canal by

Question

Canal effect. The figure shows an anchored barge that extends across a canal by distance d = 32 m and into the water by distance b-10 m. The canal has a wdth D = 58 m , a water depth H = 12 m, and a uniform water-flow speed v 1.4 m/s. Assume that the flow around the barge is uniform. As the water passes the bow, the water level undergoes a dramatic dip known as the canal effect. If the dip has depth h = 0.65 m, what is the water speed alongside the boat through the vertical cross sections at (a) point a and (b) point b? The erosion due to the speed increase is a common concern to hydraulic engineers. de Units (a) Number (b) Number Units

Explanation / Answer

a) Area at point a

A = (H - h)D

A = (b-h)d

Total area =  (H - h)D - (b-h)d

Put the values, we get

A = (12 - 0.65)58 - (10 - 0.65)32

A = 658.3 - 299.2

A = 359.1

Now, use contunuity equation, we get

12*58*1.4 = 359.1*va

va = 2.7135 m/s

b) At point b,

A = HD - bd

A = 376

vb = 974.4 / 376

vb = 2.5915 m/s

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