Calculation of Equilibrium Discharge:

Given:
Catchment area = 72 km2
Unit hydrograph duration = 2 hours

To calculate the equilibrium discharge using the S curve method, we need to follow these steps:

Step 1: Calculate the time of concentration (tc):
The time of concentration represents the time taken for the runoff from the farthest point of the catchment to reach the outlet. It is calculated using the Kirpich equation:

tc = 0.025 * √(L * S)
Where:
L = Longest flow path in km
S = Average slope of the catchment in m/m

Since the length of the flow path is not provided in the question, we cannot calculate the exact value of tc. However, for the purpose of this question, let's assume that tc is 3 hours.

Step 2: Calculate the peak discharge (Qp):
The peak discharge is calculated using the unit hydrograph method, which involves the convolution of the unit hydrograph with the rainfall excess hydrograph. In this case, we are given that the unit hydrograph duration is 2 hours.

Since the time of concentration (tc) is assumed to be 3 hours, we need to extend the unit hydrograph to match the tc. We can do this by reflecting and shifting the unit hydrograph in time.

Assuming the unit hydrograph has a peak value of 1, the extended unit hydrograph would look like this:

```
Time (hours) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
Unit Hydrograph | 0 | 1 | 0 | -1 | 0 | 0 | 0 |
```

The peak discharge can be obtained by multiplying the extended unit hydrograph values with the runoff volume for each time period and summing them up. Since we are given that the catchment area is 72 km2, we can assume a runoff volume of 1 m3/sec for each hour.

Using this information, the peak discharge (Qp) can be calculated as follows:

Qp = (1 * 1) + (1 * 0) + (0 * (-1)) + (-1 * 0) + (0 * 0) + (0 * 0) + (0 * 0) = 1 m3/sec

Step 3: Calculate the equilibrium discharge (Qe):
The equilibrium discharge is given by the formula:

Qe = Qp * (A / Ac)
Where:
Qp = Peak discharge
A = Catchment area in km2
Ac = Contributing area in km2

Since the catchment area (A) is given as 72 km2, and the contributing area is assumed to be equal to the catchment area, we can substitute these values into the equation to calculate the equilibrium discharge:

Qe = 1 * (72 / 72) = 1 m3/sec

Conclusion:
Therefore, the equilibrium discharge obtained by 2-hour unit hydrograph summation for a catchment area of 72 km2 is 1 m3/sec.