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 = 13 m. The canal has a width D = 50 m , a water depth H = 15 m, and a uniform water-flow speed vi = 2.0 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 = 0.70 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.

Explanation / Answer

given,

Initial velocity, Vi = 2 m/s

Width of the canal, D = 50 m

Water depth, H = 15 m

so, Cross- sectional area of canal, Ai = H*D = 50 * 15 = 750 m2

a)

At point, a , Cross sectional area, Aa = (H - h)* D - (b-h)*d

= (15 - 0.7)*50 - (13 - 0.7)* 32 = 321.4 m2

Apply continuity equation,

Ai * Vi = Aa * Va

so, Va = Ai * Vi / Aa = 750 * 2 / 321.4 = 4.667 m/s

b)

At point, b , Cross sectional area, Ab  = H * D - b*d

= 15 *50 - 13 * 32 = 334 m2

Apply continuity equation,

Ai * Vi = Ab * Vb

so, Vb = Ai * Vi / Ab = 750 * 2 / 334 = 4.491 m/s

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