GATE 2022 AG – Question 58
Inflow ordinates at hours 0–9 are0,23,57,119,98,71,57,28,11,0 m³/s. Muskingum Δt=1 h, X=.2,K=.7 h. Find outflow at hour2 in m³/s, to two decimals.
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Correct answer: 33.60 to 33.70
Explanation
Use $O_{t+1}=C_0I_{t+1}+C_1I_t+C_2O_t$, with denominator $K(1-X)+\Delta t/2=1.06$. Coefficients are C₀=.36/1.06,C₁=.64/1.06,C₂=.06/1.06. Initially O₀=0 gives O₁=7.81132. Then $O_2=(.36(57)+.64(23)+.06(7.81132))/1.06=\mathbf{33.69}$ m³/s.