Six-Minute Solutions, 3rd Edition, Question 26:
Given: Concrete rectangular channel [assume n=0.013], 8m wide by 1.5m deep, velocity = 2.5 m/s at 0.002m/m slope. Transition 50m beneath a highway [DISTRACTOR!!!] to a circular 9 FOOT diameter concrete concrete culvert of same slope and "n" value, flowing half-full.
Find: Number of 9' diameter culverts required.
The answer is "four", but that is beside the point.
My initial inclination was to use Manning's equation to find Qchannel upstream, then find Qcircular [9-foot diameter half-full] for a single pipe downstream, and then divide and round up to the nearest whole number to determine the number of 9-foot diameter pipes required.
NOT!!! Intuitively wrong again. I spent two hours working on this to gain conceptual understanding, and the best I can figure is that the velocity changes downstream [to 2.67 m/s] which negates this concept.
Does this make sense? The solution offered is to find V2 downstream, determine A2 for a single circular 9' pipe, and use the continuity equation. Is it true that the change in downstream velocity is the reason why my initial inclination is wrong?
I wait with bated breath for the wise and sagacious CEs to enlighten me...
Given: Concrete rectangular channel [assume n=0.013], 8m wide by 1.5m deep, velocity = 2.5 m/s at 0.002m/m slope. Transition 50m beneath a highway [DISTRACTOR!!!] to a circular 9 FOOT diameter concrete concrete culvert of same slope and "n" value, flowing half-full.
Find: Number of 9' diameter culverts required.
The answer is "four", but that is beside the point.
My initial inclination was to use Manning's equation to find Qchannel upstream, then find Qcircular [9-foot diameter half-full] for a single pipe downstream, and then divide and round up to the nearest whole number to determine the number of 9-foot diameter pipes required.
NOT!!! Intuitively wrong again. I spent two hours working on this to gain conceptual understanding, and the best I can figure is that the velocity changes downstream [to 2.67 m/s] which negates this concept.
Does this make sense? The solution offered is to find V2 downstream, determine A2 for a single circular 9' pipe, and use the continuity equation. Is it true that the change in downstream velocity is the reason why my initial inclination is wrong?
I wait with bated breath for the wise and sagacious CEs to enlighten me...