Answer:
To find the required values, we can use the Manning's equation for open channel flow:
Q = (1/n) * (A * R^(2/3) * S^(1/2))
Where:
Q is the discharge (flow rate)
n is the Manning's roughness coefficient
A is the cross-sectional area of flow
R is the hydraulic radius
S is the slope of the channel
We are given:
Diameter of the culvert (d) = 3.00 ft
Depth of uniform flow (y) = 1.6200 ft
Slope of the channel (S) = 0.0012 ft/ft
Manning's roughness coefficient (n) = 0.025
We can calculate the required values as follows:
Cross-sectional area (A) of flow:
Since the culvert is circular, the cross-sectional area can be calculated using the formula:
A = (π/4) * d^2
A = (π/4) * (3.00 ft)^2
Hydraulic radius (R):
The hydraulic radius can be calculated as:
R = A / P
where P is the wetted perimeter of the flow.
For a circular culvert, the wetted perimeter is equal to the circumference of the circle:
P = π * d
Now, we can substitute the calculated values into the Manning's equation to find the discharge (Q).
Once we have the discharge (Q), we can calculate the velocity (V) using the formula:
V = Q / A
The required values are:
(a) Discharge (Q)
(b) Velocity (V)
Let's calculate these values:
(a) Discharge (Q):
A = (π/4) * (3.00 ft)^2
P = π * 3.00 ft
R = A / P
Q = (1/n) * (A * R^(2/3) * S^(1/2))
(b) Velocity (V):
V = Q / A
By substituting the calculated values into the equations, we can find the answers.