8.9) A long rectangular channel 3.0m wide with a flow rate of 11.6 m³/s has a specific energy, E = 3.40m. a.) Determine two possible depths of flow and their corresponding Froude numbers. b.) What is the critical slope for this discharge if the channel is made of concrete with a Manning's n = 0.014?
8.9) A long rectangular channel 3.0m wide with a flow rate of 11.6 m³/s has a specific energy, E = 3.40m. a.) Determine two possible depths of flow and their corresponding Froude numbers. b.) What is the critical slope for this discharge if the channel is made of concrete with a Manning's n = 0.014?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:8.9) A long rectangular channel 3.0m wide with a flow rate of 11.6 m³/s has a specific
energy, E = 3.40m.
a.) Determine two possible depths of flow and their corresponding Froude numbers.
b.) What is the critical slope for this discharge if the channel is made of concrete with a
Manning's n = 0.014?
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How about using this formula for the froudea number
Transcribed Image Text:In pipe flow, viscous forces predominate. We define the dimensionless number known as
Reynold's number, NR, as being the ratio of the inertia force to the viscous force in the flow.
In open-channel flow, gravity forces predominate and we define the Froude number, NF, as
being the ratio of the inertia force to the gravity force in the flow.
ARET 3400 Chapter 8 - Open-Channel Flow
When
NE
We have
V
√gD
It turns out that √gD is the speed of a small gravity or surface wave travelling over the
water surface. The Froude number, NF is also then the ratio of the mean flow velocity to the
speed of a small wave travelling on the water surface.
= √gD, NF = 1 and the flow is critical
v<√gD, NF < 1 and the flow is subcritical
v> √gD, NF > 1 and the flow is supercritical.
For a rectangular channel, at critical conditions:
v = √gD or v² = gD
Substitution of the continuity equation yields an expression in terms of Q:
Q²
= = gD, but for a rectangular channel D = dc and A = bd..
A²
Q²
b²d²
dc
Sumar
=gd, or
Q²
Page 115
96²
gb
(8.17)
(8.18)
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