To understand why the minimum width to which the channel can be contracted without affecting the upstream flow condition is 4m, we need to consider the concept of critical flow in open channels.

Critical flow is the condition at which the specific energy of the flow is at its minimum for a given discharge. At critical flow, the flow velocity is maximum and the water surface slope is equal to the channel slope. If the channel width is reduced below a certain limit, it can disrupt the critical flow condition and cause the flow to become subcritical or supercritical.

Here's an explanation of why the correct answer is option 'A' (4m):

1. Critical Flow Condition:
In open channels, the critical flow condition is achieved when the Froude number (Fr) is equal to 1. The Froude number is defined as the ratio of the flow velocity to the velocity of small waves that can propagate on the water surface. Fr = V / sqrt(gd), where V is the flow velocity, g is the acceleration due to gravity, and d is the flow depth.

2. Width-Contraction Coefficient:
The width-contraction coefficient, also known as the contraction coefficient (Cc), is a dimensionless parameter that represents the reduction in channel width. Cc is defined as the ratio of the contracted width to the original width of the channel. Cc = Wc / Wo, where Wc is the contracted width and Wo is the original width of the channel.

3. Minimum Channel Width:
To maintain the critical flow condition, the minimum channel width can be determined using the following equation: Wo / Wc = 1 + (2/g)(Fr^2 - 1), where Wo is the original width and Wc is the contracted width.

4. Calculation:
Substituting the values, we have: Wo / Wc = 1 + (2/g)(1 - 1)
Simplifying further: Wo / Wc = 1

From the equation, we can see that the contracted width (Wc) should be equal to the original width (Wo) to maintain the critical flow condition. Therefore, the minimum width to which the channel can be contracted without affecting the upstream flow condition is 4m (option 'A').