To solve this problem, we can use the concept of the continuity equation, which states that the discharge through a channel is equal to the product of the cross-sectional area and the velocity of flow.

Let's assume that the original depth of the channel is H and the original discharge is Q.

1. Calculate the cross-sectional area of the channel:
The cross-sectional area is given by A = W * H, where W is the width of the channel. Let's assume the width remains constant.

2. Calculate the velocity of flow:
The velocity of flow can be calculated using the equation Q = A * V, where V is the velocity of flow.

3. Calculate the new depth:
The new depth of the channel is increased by 10%, so the new depth is H + 0.1H = 1.1H.

4. Calculate the new cross-sectional area:
The new cross-sectional area is given by A' = W * (1.1H).

5. Calculate the new velocity of flow:
The new velocity of flow can be calculated using the equation Q = A' * V', where V' is the new velocity of flow.

6. Calculate the new discharge:
The new discharge can be calculated by equating the original discharge to the new discharge:
Q = A * V = A' * V'
=> Q = W * H * V = W * (1.1H) * V'
=> Q = 1.1W * H * V'
=> V' = V / 1.1

7. Calculate the percentage increase in discharge:
The percentage increase in discharge can be calculated using the formula:
Percentage increase = (New discharge - Original discharge) / Original discharge * 100
=> (V' - V) / V * 100
=> (V / 1.1 - V) / V * 100
=> (0.1V / 1.1) / V * 100
=> 0.1 / 1.1 * 100
=> 10 / 110 * 100
=> 1000 / 110
=> 9.09%

Therefore, the percentage increase in discharge is approximately 9.09%, which is closest to option D (17.2%). Hence, the correct answer is option D.