GATE 2026 AG – Question 59
Meteorologically similar catchments M and N have $(L,L_{ca},A)$ equal to $(36\,\mathrm{km},18\,\mathrm{km},250\,\mathrm{km^2})$ and $(50,30,400)$ respectively. M’s six-hour unit hydrograph peaks at 50 m³/s,12 hours after rainfall excess begins. Using Snyder’s method, find the peak of N’s six-hour unit hydrograph in m³/s, to two decimals.
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Correct answer: 64.20 to 64.80
Explanation
M’s adjusted lag from the rainfall centroid is $t_{L6,M}=12-6/2=9$ h. Snyder’s standard duration is $t_r=t_L/5.5$ and adjusted lag $t_{L6}=t_L+.25(6-t_L/5.5)$. Thus $t_{L,M}=(9-1.5)/(1-.25/5.5)=7.85714$ h. Similarity gives $t_{L,N}=7.85714[(50\cdot30)/(36\cdot18)]^{.3}=10.10694$ h. Readjust to six-hour duration:$t_{L6,N}=10.10694+.25(6-10.10694/5.5)=11.14753$ h. With common peaking coefficient,$Q_N/Q_M=(A_N/A_M)(t_{L6,M}/t_{L6,N})$. Therefore $Q_N=50(400/250)(9/11.14753)=\mathbf{64.59}$ m³/s.