Uhannel section the ratio of the bed width to oent tapezoida

Uhannel section the ratio of the bed width to oent tapezoidar depth is (a) 0.50 (c) 0.866 (b) 0.707 (d) 1.155 13. The most efficient channel has the shape of (a) Semi Circular (c) Triangular (b) Parabolic (d) Ellipse 14. For a uniform flow with a depth of 0.6 m and Froude number of 2.0 in a rectangular channel, the specific energy will be (a) 2.4 m (c) 2.6 m (b) 0.8 m (d) 1.8 m 15. The characteristics of the critical state of flow through the channel sections are

Solution

(13) From Manning\'s equation,

Discharge through a channel, Q = A R^2/3 S^0.5 / n in SI units

where A = area of cross-section of channel

R = Hydraulic radius = A/P

P = Wetted perimeter of channel

S = Slope of channel

n = Manning\'s coefficient

So, Q = A^5/3 S^0.5 / (n P^2/3)

For a given A, S and n, discharge will be maximum when P will be minimum. The corresponding cross-section of channel will be the most efficient section. Both circular and semi-circular cross-section has the least perimeter for a given area of any geometric shape. If open channel flow is considered, the semi-circular cross-section has the most efficient section.

(14) Depth, y = 0.6 m

Let velocity of flow is V.

Froude Number, F_R = V/(gy)^0.5

=> 2 = V / (g x 0.6)^0.5

=> 4 = V² / (0.6 g)  

=> V²/g = 0.6 x 4 = 2.4

Specific Energy = y + V²/2g = 0.6 + (2.4/2) = 0.6 + 1.2 = 1.8 m