To determine the maximum height of a jump without causing afflux in a rectangular channel, we need to consider the specific energy at the upstream section and the minimum specific energy.

Specific energy is defined as the sum of the velocity head and the elevation head of a fluid particle in an open channel flow. It represents the total energy per unit weight of the fluid.

The specific energy at the upstream section is given as 3 m, and the minimum specific energy is given as 2.5 m. This means that the specific energy at the downstream section should not be less than 2.5 m in order to avoid afflux, which is the rise in water level due to a sudden change in flow conditions.

To calculate the maximum height of the jump, we can use the specific energy equation:

Specific Energy = Velocity Head + Elevation Head

In a rectangular channel, the velocity head can be calculated as:

Velocity Head = (V^2) / (2g)

Where V is the velocity of flow and g is the acceleration due to gravity.

To avoid afflux, the specific energy at the downstream section should be equal to or greater than the minimum specific energy. Therefore, we can set up the following equation:

Specific Energy at Downstream = (V^2) / (2g) + H

Where H is the height of the jump.

Since the specific energy at the downstream section should be equal to or greater than 2.5 m, we can write the equation as:

2.5 m = (V^2) / (2g) + H

Simplifying the equation, we get:

H = 2.5 m - (V^2) / (2g)

To find the maximum height of the jump without causing afflux, we need to find the minimum velocity of flow. This can be calculated using the specific energy equation at the upstream section:

3 m = (V^2) / (2g)

Simplifying the equation, we get:

V^2 = 6g

V = √(6g)

Substituting this value of V into the equation for H, we get:

H = 2.5 m - (6g) / (2g)

H = 2.5 m - 3 m

H = -0.5 m

Since the height cannot be negative, the maximum height of the jump without causing afflux is 0.50 m.