GATE AG 2022 • Q46 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Flood routing, hydrological reservoir and channel routing

Question Statement:

The ordinates of an inflow hydrograph are provided in the table below. If the routing interval (Δt) is one hour, weighting factor in Muskingham equation (X) is 0.2, and the storage-time constant (time of travel of flood wave through the channel reach) (K) is 0.7 hour, using the Muskingham method of flood routing, the ordinate of the outflow (routed) hydrograph for 2nd hour in m³ s⁻¹ is _______. [round off to two decimal places]

Official Answer Key:

33.60 to 33.70

Step-by-Step Solution & Explanation

• Muskingham coefficients: D = K(1−X)+0.5Δt = 0.7×0.8+0.5 = 1.06 • C0 = (−KX+0.5Δt)/D = 0.36/1.06 = 0.3396; C1 = (KX+0.5Δt)/D = 0.64/1.06 = 0.6038; C2 = (K−KX−0.5Δt)/D = 0.06/1.06 = 0.0566 (C0+C1+C2=1 ✓) • O1 = C0·I1+C1·I0+C2·O0 = 0.3396×23+0+0 = 7.81 m³/s (taking I0=O0=0) • O2 = C0·I2+C1·I1+C2·O1 = 0.3396×57 + 0.6038×23 + 0.0566×7.81 = 19.36+13.89+0.44 = 33.69 m³/s Computed value: 33.69 m³/s (within official range 33.60–33.70) Section 5 — Irrigation and Drainage Engineering

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