Open channels are crucial in hydraulic engineering, carrying water in rivers, canals, and drainage systems. Uniform flow maintains constant depth and velocity along the channel, balancing gravity and resistance forces. This equilibrium shapes the flow's behavior and energy distribution.
Gradually varied flow (GVF) introduces complexity, with depth and velocity changing gradually along the channel. GVF profiles are classified based on depth relationships and channel characteristics. Understanding these concepts is vital for designing and analyzing open channel systems effectively.
Uniform Flow in Open Channels
Characteristics of uniform channel flow
Top images from around the web for Characteristics of uniform channel flow
File:Velocity-Depth (open channel).png - Wikimedia Commons View original
Is this image relevant?
Flow Rate and Its Relation to Velocity | Physics View original
Is this image relevant?
Fluid Dynamics – University Physics Volume 1 View original
Is this image relevant?
File:Velocity-Depth (open channel).png - Wikimedia Commons View original
Is this image relevant?
Flow Rate and Its Relation to Velocity | Physics View original
Is this image relevant?
1 of 3
Top images from around the web for Characteristics of uniform channel flow
File:Velocity-Depth (open channel).png - Wikimedia Commons View original
Is this image relevant?
Flow Rate and Its Relation to Velocity | Physics View original
Is this image relevant?
Fluid Dynamics – University Physics Volume 1 View original
Is this image relevant?
File:Velocity-Depth (open channel).png - Wikimedia Commons View original
Is this image relevant?
Flow Rate and Its Relation to Velocity | Physics View original
Is this image relevant?
1 of 3
Uniform flow maintains constant depth, velocity, and cross-sectional area along the channel length
Steady flow exhibits no change in flow characteristics over time at a given location
Prismatic channel has a consistent cross-sectional shape and slope (rectangular, trapezoidal)
Balance between gravitational forces and resistance forces drives the flow
Gravitational force determined by the channel slope and fluid weight
Resistance force caused by friction between the fluid and channel boundary (roughness of concrete, natural streambed)
Energy grade line (EGL) and hydraulic grade line (HGL) run parallel to the channel bottom in uniform flow
EGL represents total energy head as the sum of elevation head, pressure head, and velocity head
HGL represents the sum of elevation head and pressure head (piezometric head)
Chezy and Manning equations application
Chezy equation calculates average flow velocity (V) using Chezy coefficient (C), hydraulic radius (R), and channel slope (S): V=CRS
Chezy coefficient (C) depends on channel roughness and flow characteristics (m^(1/2)/s)
Hydraulic radius (R) is the ratio of cross-sectional area (A) to wetted perimeter (P) (m)
Channel slope (S) is dimensionless
Manning equation expresses average flow velocity (V) using Manning's roughness coefficient (n), hydraulic radius (R), and channel slope (S): V=n1R2/3S1/2
Manning's roughness coefficient (n) depends on channel material and surface characteristics (s/m^(1/3))
Tabulated n values available for various channel types (concrete, natural streams)
Continuity equation calculates discharge (Q) as the product of average flow velocity (V) and cross-sectional area (A): Q=VA
Gradually Varied Flow in Open Channels
Analysis of gradually varied flow
Gradually varied flow (GVF) exhibits gradual changes in depth and velocity along the channel length
Flow is steady and non-uniform
Streamlines are nearly parallel with hydrostatic pressure distribution
GVF profiles classified based on the relationship between actual depth (y), normal depth (yn), and critical depth (yc)
Normal depth (yn) occurs in uniform flow for given discharge and channel characteristics
Critical depth (yc) occurs when Froude number (Fr) equals 1
Fr=gyV, where g is acceleration due to gravity and y is flow depth
GVF profiles categorized as mild (M), critical (C), steep (S), horizontal (H), or adverse (A)
M profiles: y>yn>yc
C profiles: y=yc
S profiles: yn>yc>y
H profiles: zero channel slope
A profiles: negative channel slope
Water surface profiles in prismatic channels
Gradually varied flow equation (GVFE) analyzes water surface profiles: dxdy=1−Fr2S0−Sf
dxdy is the slope of the water surface
S0 is the channel bottom slope
Sf is the friction slope (energy grade line slope)
Fr is the Froude number
GVFE is a first-order differential equation solved numerically using methods like:
Direct step method
Standard step method
Boundary conditions required to solve GVFE:
Known water depth at a specific location (downstream control, sluice gate, overfall)
Known discharge and flow regime (subcritical or supercritical)
Computed water surface profile should match expected GVF profile type based on boundary conditions and channel characteristics