Answer:
The minimum channel width that can be used without affecting the upstream water level is 14.44 m.
Step-by-step explanation:
To determine the minimum channel width without affecting the upstream water level, we need to ensure that the specific energy of the flow remains constant. Specific energy (E) is the sum of potential energy (P) and kinetic energy (K) per unit weight of fluid. For a rectangular channel, specific energy can be expressed as:
E = P + K = gy + V^2/2g
where:
g is the acceleration due to gravity (9.81 m/s^2)
y is the flow depth (4 m)
V is the average velocity of the flow (m/s)
The average velocity can be calculated using the discharge (Q) and channel width (B):
V = Q/B
Substituting the expressions for V and y into the specific energy equation:
E = gy + (Q/B)^2/2g
For the original channel width of 50 m, the specific energy is:
E_original = 9.81 * 4 + (200/50)^2/2 * 9.81 = 49.04 J/kg
To maintain the same specific energy without affecting the upstream water level, the revised channel width (B_revised) should satisfy the following equation:
E_original = 9.81 * 4 + (200/B_revised)^2/2 * 9.81
Solving for B_revised, we get:
B_revised = 14.44 m
This reduction in channel width will significantly shorten the length of the bridge required.
There are other formulas but I am truly sorry if I didn't got the formula u asked for...
Hope that helps!