1. Non-uniform flow occurs when
depth and velocity changes along the
channel length.
•Types:
• Gradually Varied Flow
(GVF): Flow depth changes
over a long distance due to bed
slope or obstruction.
• Rapidly Varied Flow (RVF):
Flow depth changes suddenly
over a short distance, often due
to hydraulic jumps or
spillways.
Introduction to Non-Uniform Flow
2. • Steady flow with gradual changes in water surface profile.
• The water surface profile in GVF is influenced by factors such as channel slope,
shape, and roughness. The governing equation for GVF is derived from the energy
equation, considering the balance between gravitational forces and frictional
resistance.
• This results in a differential equation that describes the variation of flow depth
along the channel. Solving this equation helps in predicting the water surface
profiles under various flow conditions
•Fundamental Assumption:
• Small slope angle (i.e., sinθ ≈ θ).
•Governing Equation
•where:
• S
0 = Channel bed slope
• Sf= Friction slope (calculated using Manning’s equation)
Gradually Varied Flow (GVF)
3. •Flow conditions based on channel slope:
Classification of Water Surface Profiles (As per OCF)
6. Ques: A rectangular channel with a bottom width of 4.0 m and a bottom slope of 0.0008 has
a discharge of 1.50 m3/s. In a gradually varied flow in this channel, the depth at a certain
location is found to be 0.30 m. Assuming n = 0.016, determine the type of GVF profile
7. • Flow depth changes abruptly due to an obstruction or transition.
• A common example of RVF is the hydraulic jump, which occurs when
supercritical flow transitions to subcritical flow, leading to a sudden rise in the
water surface. This phenomenon is associated with significant energy
dissipation and turbulence. Hydraulic jumps are utilized in engineering
applications to dissipate energy and reduce erosion downstream of hydraulic
structures.
•Examples in Open Channel Flow:
• Flow over a spillway crest
• Flow at a sluice gate
• Hydraulic jumps in stilling basins
•Momentum principle governs RVF:
• The energy equation is not valid due to energy losses.
Rapidly Varied Flow (RVF)
8. A hydraulic jump is a specific type of RVF
where there is a sudden transition from high-
velocity, low-depth (supercritical) flow to
low-velocity, high-depth (subcritical) flow.
This transition results in a turbulent flow
region with considerable energy loss.
Hydraulic jumps are often employed in
engineering designs to dissipate excess
energy, thereby protecting downstream
structures from potential damage due to high-
velocity flows.
•Why does it occur?
• Happens when the downstream water level forces a transition from
supercritical to subcritical flow.
•Engineering Significance:
• Used in stilling basins for energy dissipation.
Hydraulic Jump
9. Applying the linear momentum equation in the
longitudinal direction to the control volume:
P - P - F + W sin
₁ ₂ ₛ θ = M - M
₂ ₁
For a horizontal channel (θ = 0), W sinθ = 0.
• P =
₁ γ A cos
₁ ȳ₁ θ → Pressure force at Section
1
• P =
₂ γ A cos
₂ ȳ₂ θ → Pressure force at Section
2
• F → Shear force on the control surface
ₛ
• W sinθ → Longitudinal component of water
weight
• M =
₂ β ρ
₂ QV → Momentum flux at the outlet
₂
• M =
₁ β ρ
₁ QV → Momentum flux at the inlet
₁
For small θ, (W sinθ - F ) is negligible.
ₛ
10. Putting the value of different terms of moment equation and solving we will get the
subsequent depth ratio.
Here y1 and y2 subsequent depths
F denotes the Froude Number that varies with type of flow i.e subcritical, critical and
super critical.
Subsequent Depths Ratio
Classification of Hydraulic Jumps:
•Based on Froude number (Fr1
):
• 1.0 < Fr1 < 1.7 : Undular jump
• 1.7 < Fr1 < 2.5 : Weak jump
• 2.5 < Fr1 < 4.5 : Oscillating jump
• 4.5 < Fr1 < 9.0: Steady jump (well-defined energy loss)
• Fr1 > 9: Strong jump (high turbulence, high energy dissipation)
13. Ques: A hydraulic jump takes place in a rectangular channel with sequent depths of
0.25 m and 1.50 m at the beginning and end of the jump respectively. Estimate the
(i) discharge per unit width of the channel and
(ii) energy loss.
14. Ques: A 3.6 m wide rectangular channel conveys 9m ^ 3 / s of water with a velocity of 6 m/s.
(1)Is there a condition for hydraulic jump to occur? If so, calculate the height, length and
strength of the jump.
(2)What is loss of energy per kg of water?
15. Applications of Hydraulic Jumps in Engineering
i. Spillways of dams (stilling basins)
ii. Energy dissipation structures
iii. Flood mitigation systems
iv. Wastewater treatment plants (for aeration and mixing)
v. Irrigation canals and sluice gates
