The problem asks for the peak discharge of direct runoff from a watershed given its area, the shape and base of its unit hydrograph, and the amount of rainfall-excess.
Calculate Runoff Volume for Unit Hydrograph
The volume under a unit hydrograph represents the direct runoff from a unit depth of rainfall-excess. The unit depth is typically 1 cm.
- Watershed Area, $A = 360 \text{ km}^2 = 360 \times (1000 \text{ m})^2 = 360 \times 10^6 \text{ m}^2$.
- Unit Depth = $1 \text{ cm} = 0.01 \text{ m}$.
- Volume under UH, $V_{UH} = A \times \text{Unit Depth} = (360 \times 10^6 \text{ m}^2) \times (0.01 \text{ m}) = 3.6 \times 10^6 \text{ m}^3$.
Calculate Peak Discharge of Unit Hydrograph
The unit hydrograph is triangular with a base ($B_{UH}$) of $50$ hours.
- Convert base to seconds: $B_{UH} = 50 \text{ hours} \times 3600 \text{ s/hour} = 180000 \text{ s}$.
- The area of a triangle is $0.5 \times \text{Base} \times \text{Height}$. Here, Height is the peak discharge ($Q_{peak, UH}$).
- $V_{UH} = 0.5 \times B_{UH} \times Q_{peak, UH}$
- $3.6 \times 10^6 \text{ m}^3 = 0.5 \times (180000 \text{ s}) \times Q_{peak, UH}$
- $Q_{peak, UH} = \frac{3.6 \times 10^6 \text{ m}^3}{0.5 \times 180000 \text{ s}} = \frac{3.6 \times 10^6}{90000} \text{ m}^3 \text{ s}^{-1} = 40 \text{ m}^3 \text{ s}^{-1}$.
Calculate Peak Discharge for Given Rainfall-Excess
The peak discharge is directly proportional to the amount of rainfall-excess.
- Rainfall-excess, $R_{ex} = 3 \text{ cm}$.
- Peak discharge of the direct runoff hydrograph, $Q_{peak} = Q_{peak, UH} \times R_{ex}$ (where $R_{ex}$ is in units relative to the UH definition, e.g., cm).
- $Q_{peak} = (40 \text{ m}^3 \text{ s}^{-1}) \times 3 = 120 \text{ m}^3 \text{ s}^{-1}$.
The peak discharge of the direct runoff hydrograph is $120.00 \text{ m}^3 \text{ s}^{-1}$.
Important Questions from Unit Hydrograph Theory
- Two catchments M and N are meteorologically similar. The basin length (L), length to the centroid (Lca), and the drainage area (A) of catchment M are $36\text{ km}$, $18\text{ km}$, and $250\text{ km}^2$, respectively. The L, Lca and A for catchment N are $50\text{ km}$, $30\text{ km}$, and $400\text{ km}^2$, respectively.
For 6-h unit hydrograph in catchment M, the peak discharge of $50\text{ m}^3\text{.s}^{-1}$ occurs at $12\text{ h}$ from the beginning of the rainfall excess. Using Snyder’s method, the peak of the 6-h unit hydrograph for catchment N (in $\text{m}^3\text{.s}^{-1}$) is ________. (Rounded off to two decimal places) - 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 $\phi$-index of $0.25 \, cm \, h^{-1}$ and runoff coefficient of 0.6, the peak ordinate of the 6-h unit hydrograph in $m^3 \, s^{-1}$ will be ________.
- The ordinates of a 6-hour S-hydrograph of a catchment are given in Table below.
The catchment has phi-index of $0.25 \text{ cm h}^{-1}$ and baseflow of $10.5 \text{ m}^3 \text{ s}^{-1}$. The peak of the flood hydrograph generated from this catchment due to a storm of 45 mm received during the first 6 h in $\text{m}^3 \text{ s}^{-1}$ isTime (h) 0 6 12 18 24 30 36 42 48 Ordinate ($\text{m}^3 \text{ s}^{-1}$) 0 30 90 180 252 306 342 360 360 - The 6-hour unit hydrograph of a watershed is represented by an isosceles triangle with the peak of 180 $m^3$ $s^{-1}$ and time to peak of 18 hours. The phi-index ($\emptyset$) of this watershed is 3.0 mm $h^{-1}$ and the constant baseflow is 20 $m^3$ $s^{-1}$. The accumulated rainfall received in this watershed at 6 h and 12 h from the start of the storm are 38 mm and 106 mm, respectively. The resulting peak of the flood hydrograph due to this storm event is ________ $m^3$ $s^{-1}$.
The peak of a flood hydrograph due to a 5-hour storm is 670 $m^3$ $s^{-1}$. The total depth of rainfall is 9 cm. Assuming an average infiltration loss of 0.2 cm $h^{-1}$ and a constant baseflow of 30 $m^3$ $s^{-1}$, the peak discharge of the 5-hour unit hydrograph for this catchment in $m^3$ $s^{-1}$ is ________________.
