HP-41 Programs

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Circular X-Section, Partially Full, Gravity Flow, SOLVER approach

Problem
A 4-foot-diameter finished concrete pipe is laid at a slope of 0.2%. The water depth is 3 feet. Calculate the flow rate and flow velocity using Manning's equation.

Solution

Step 1. Calculate the flow rate (ft3/sec).
- Q for Partially Full Circular X-Section
Q=C÷N((0.5×SIN(ACOS((H−D÷2)÷(D÷2))×2)+π(360−ACOS((H−D÷2)÷(D÷2))×2)÷360)
×(D÷2)^2)^(5÷3)÷(π×D(360−ACOS((H−D÷2)÷(D÷2))×2)÷360)^(2÷3)×S^0.5
Where:
Q = flow rate (ft3/sec, m3/s)
C = 1.49 for English units, 1 for Metric units
N = Manning roughness coefficient
H = depth of water (ft, m)
D = diameter of pipe (ft, m)
S = slope of energy line (decimal)

Step 2. Compute the velocity of flow.
- V for Partially Full Circular X-Section
V=C÷N((0.5×SIN(ACOS((H−D÷2)÷(D÷2))×2)+π(360−ACOS((H−D÷2)÷(D÷2))
×2)÷360)×(D÷2)^2)÷(π×D(360−ACOS((H−D÷2)÷(D÷2))×2)÷360)^(2÷3)×S^0.5
Where:
V = velocity of flow (ft/sec, m/s)
C = 1.49 for English units, 1 for Metric units
N = Manning roughness coefficient
H = depth of water (ft, m)
D = diameter of pipe (ft, m)
S = slope of energy line (decimal)

see attached PDF for Equations & Illustrations.
[attachment=2421]
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