Q1 — Manhole invert elevation
Answer: C. 243.32 ft
Given:
MH-1 Inv Out = 246.20 ft
Pipe slope = 1.20%
Distance from Sta. 12+00 to Sta. 14+40 = 240 ft
Flow is east from MH-1 to MH-2
Calculation:
Drop = 240 × 0.012 = 2.88 ft
Invert at MH-2:
246.20 − 2.88 = 243.32 ft
So the correct answer is C. 243.32 ft.
Q2 — Culvert cover
Answer: B. 3.62 ft
Step 1: Find proposed roadway elevation at Sta. 13+20.
From profile:
PVI 10+00 Elev. = 307.20
PVI 14+00 Elev. = 308.80
Grade:
308.80 − 307.20 = 1.60 ft over 400 ft
Grade = 1.60 / 400 = 0.004 = 0.40%
Sta. 13+20 is 320 ft after Sta. 10+00.
Elevation increase:
320 × 0.004 = 1.28 ft
Proposed roadway elevation:
307.20 + 1.28 = 308.48 ft
Step 2: Find culvert invert at centerline.
Culvert length = 48 ft
Road crosses at mid-length
Distance from north inlet to centerline = 24 ft
Culvert slope = 1.00% downward south
Invert drop:
24 × 0.01 = 0.24 ft
Invert at centerline:
302.10 − 0.24 = 301.86 ft
Step 3: Find top of pipe.
36-inch pipe = 3.00 ft diameter
Top of pipe:
301.86 + 3.00 = 304.86 ft
Step 4: Find cover.
Cover:
308.48 − 304.86 = 3.62 ft
So the correct answer is B. 3.62 ft. this is worng correct answer is 3.38 which is not in answers
Q3 — Top of crest vertical curve
The question I wrote had a problem: the choices do not match the correct calculation. So technically, none of the listed choices is exactly correct.
Correct answer should be:
Sta. 22+28, Elev. 423.12 ft
Given:
PVI = Sta. 22+00
PVI Elev. = 424.80 ft
g1 = +3.00% = +0.030
g2 = −2.00% = −0.020
L = 280 ft
Step 1: Find BVC station.
BVC = PVI − L/2
BVC = 22+00 − 140 ft = Sta. 20+60
Step 2: Find BVC elevation.
BVC Elev. = PVI Elev. − 140 × 0.030
BVC Elev. = 424.80 − 4.20 = 420.60 ft
Step 3: Find distance from BVC to high point.
For a crest vertical curve, the high point is where the grade becomes zero.
A = g2 − g1
A = −0.020 − 0.030 = −0.050
x = −g1L / A
x = −(0.030)(280) / (−0.050)
x = 168 ft from BVC
High point station:
Sta. 20+60 + 168 ft = Sta. 22+28
Step 4: Find elevation at high point.
Vertical curve equation:
Elevation = BVC Elev. + g1x + A x² / 2L
Elevation = 420.60 + 0.030(168) + [−0.050(168²)] / [2(280)]
Elevation = 420.60 + 5.04 − 2.52
Elevation = 423.12 ft
So Q3 should have this correct choice:
Sta. 22+28, Elev. 423.12 ft
The earlier multiple-choice options for Q3 need to be corrected.