The intensity-duration relationship for a rainfall on a rectangular plot ABCD of area 7 ha (1 ha =10⁴ m²) can be modelled by the following equation:

I = 25/(t +10)

where I is rainfall intensity (in cm/h), and t is the duration (in minutes) of rainfall. The average runoff coefficient over the area is 0.60. The time of entry (in minutes) to the outfall from the corners A, B, C, and D is 10, 20, 15 and 25, respectively. The design flowrate (in m³/h) of the storm-sewer at the outfall is________(in integer).

The correct answer is 300.

To find the design flowrate of the storm-sewer at the outfall, we use the Rational Method formula:

$$Q=C·I·A$$

where:
- $Q$ is the design flowrate (discharge),
- $C$ is the runoff coefficient,
- $I$ is the rainfall intensity, and
- $A$ is the catchment area.

Step 1: Identify the Given Data
- Catchment area, $A=7\text{ha}=7\times {10}^4{\text{m}}^2$
- Average runoff coefficient, $C=0.60$
- Times of entry to the outfall from the corners A, B, C, and D are 10, 20, 15, and 25 minutes, respectively.

Step 2: Determine the Time of Concentration ($t_c$)
The time of concentration is the time required for runoff to travel from the hydraulically most remote point of the catchment to the outlet. In this case, it is the maximum of the entry times from all the corners:
$$t_c=max(10,20,15,25)=25\text{minutes}$$

Step 3: Calculate the Rainfall Intensity ($I$)
Using the intensity-duration relationship with $t=25\text{minutes}$:
$$I=\frac{25}{t+10}=\frac{25}{25+10}=\frac{25}{35}=\frac{5}{7}\text{cm/h}$$

Convert the rainfall intensity from cm/h to m/h:
$$I=\frac{5}{7}\times {10}^{-2}\text{m/h}$$

Step 4: Calculate the Design Flowrate ($Q$)
Substitute the values into the Rational Method equation:
$$Q=0.60\times (\frac{5}{7}\times {10}^{-2}\text{m/h})\times (7\times {10}^4{\text{m}}^2)$$

Simplifying the expression:
$$Q=0.60\times \frac{5}{7}\times 7\times {10}^2{\text{m}}^3\text{/h}$$

$$Q=0.60\times 5\times 100{\text{m}}^3\text{/h}$$

$$Q=3\times 100=300{\text{m}}^3\text{/h}$$

Thus, the design flowrate of the storm-sewer at the outfall is 300 ${\text{m}}^3\text{/h}$.