Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
A catchment of 720 ha area has 25-year mean rainfall intensity of 100 mm h⁻¹ occurring for a duration equal to its time of concentration. During a storm event, the catchment received a total of 7.5 cm design rainfall for 6 hours. Assuming ϕ-index of 0.25 cm h⁻¹ and runoff coefficient of 0.6, the peak ordinate of the 6-h unit hydrograph in m³ s⁻¹ will be _____.
Official Answer Key:
20
Step-by-Step Solution & Explanation
Step 1 – Peak discharge of the actual storm event, using the Rational formula with the given design (peak) rainfall intensity, runoff coefficient and catchment area (Q in m³/s, i in mm/h, A in ha):
Q_peak = C×i×A/360 = 0.6×100×720/360 = 120 m³/s.
Step 2 – Total direct-runoff (excess rainfall) depth for the 6-h storm, using the ϕ-index method:
Excess rainfall = Total rainfall − (ϕ-index × duration) = 7.5 − (0.25×6) = 7.5 − 1.5 = 6 cm.
Step 3 – Peak ordinate of the 6-h unit hydrograph (normalised to 1 cm of excess rainfall) is obtained by linearly scaling the actual storm's peak discharge by its excess-rainfall depth:
UH peak ordinate = Q_peak/Excess depth = 120/6 = 20 m³/s. Matches the official key exactly.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.