Question 11.6: A rectangular channel 3.0 m in width has two reaches, A and ......
A rectangular channel 3.0 m in width has two reaches, A and B in series. The bed slope of reach A is 0.001 and that of the reach B is 0.01. Find the type of water surface profiles which occur in the channel for a discharge of 3.3 m³/s. Assume, Manning n = 0.012 for both the reaches.
The unit discharge q = 3.3/3.0 = 1.1 m²/s
The critical depth, y_{c}={\sqrt[3]{\frac{q^{2}}{g}}}={\sqrt[3]{\frac{1.1^{2}}{9.61}}}\approx0.5\,{\mathrm{m}}
The critical velocity =\;\frac{q}{y_{c}}=\frac{1.1}{0.5}=2.20\;\mathrm{m/s};
Hydraulic radius R = A/P = (3.0 × 0.5)/(3.0 + 2 × 0.5) = 0.375 m
From Manning equation, the critical slope S_{c}=n^{2}\;v^{2}/{ R}^{4/3}.
Substituting the values of n, v and R, S_{c}=\frac{0.012^{2}\times2.2^{2}}{0.375^{4/3}}=2.576\times10^{-3}=0.00257
For reach A, the bed slope is less than the critical slope. In contrast, the slope of reach B is greater than the critical slope. Hence a M_2 profile in A will be followed by a S_2 profile in B as shown in Fig. 11.19. The flow depth in reach B will finally attain a super critical depth y_{n2}.
