3. What is an Open Channel flow?
An open channel refers to any passage through which a liquid flows with an exposed
surface. This surface, typically where the liquid meets another fluid like air, remains at
constant pressure. In most civil engineering scenarios, this liquid is water, and the free
surface is in contact with air at atmospheric pressure. Hence, our main focus is on
water flowing with a free surface.
The main force that drives water in open channels is gravity. Whether it is a small
roadside gutter, a large river like the Ganga or Brahmaputra, or an irrigation canal, they
all operate under similar physical laws due to the presence of a free surface.
Open channels can be natural, such as rivers and streams, or man-made, such as canals
used for irrigation, water supply, sewage systems, hydropower generation, or
navigation routes.
4. What is a pipe flow?
When a liquid (water) flows within a closed conduit then it’s called pipe flow. There is no free surface
in this type of flow and also does not exert direct atmospheric pressure like open channel flow. But it
exerts hydraulic pressure on the conduit. Like open Channel flow, not all flow within a closed conduit
is pipe flow.
PIPE FLOW
6. Flow is called steady if the fluid characteristics like depth of flow (y), velocity (V), and discharge or rate of flow (Q) do
not change with time at a given location.
Mathematically: dy/dt = 0, dV/dt = 0, dQ/dt = 0 ● Example: A river flowing at a constant rate throughout the
day.
WHAT IS A STEADY FLOW?
7. Unsteady flow refers to a condition where one or more flow parameters such as velocity, pressure, or depth change
with time at a given location. This means that if you observe the flow at a fixed point, the conditions you measure
will vary from moment to moment. Unsteady flow commonly occurs in natural systems like rivers during floods,
where the water level continuously rises or falls. It is also seen in engineered systems during operations such as the
starting or stopping of a pump, or when a gate in a channel is suddenly opened. These changes make unsteady flow
more complex to analyze compared to steady flow, where flow parameters remain constant over time.
Mathematically: dy/dt ≠ 0, dV/dt ≠ 0, dQ/dt ≠ 0
● Example: Water level in a storage tank being filled or emptied.
WHAT IS AN UNSTEADY FLOW?
Uniform flow occurs when the flow characteristics such as depth, velocity, slope, and cross-sectional area remain
constant at every point along the length of the channel. In this type of flow, the water moves in a consistent manner
without any variation in its profile or speed from one section of the channel to another. Uniform flow is typically
found in long, straight, and evenly sloped channels where the conditions do not change over distance. Since all flow
parameters remain the same along
WHAT IS A UNIFORM FLOW?
8. the channel, analyzing uniform flow is simpler compared to non-uniform flow, where these properties vary from
point to point.
Mathematically: dy/dl = 0, dV/dl = 0
Example: Water flowing through a long straight rectangular channel.
NON-UNIFORM FLOW
Non-uniform or varied flow refers to a situation where the flow parameters, particularly depth or velocity, change
along the length of the channel. This means that as you move from one point to another along the channel, the
water level or speed is not constant. Such flow commonly occurs in natural streams, curved channels, or when
there are changes in slope, cross-section, or obstructions like gates and weirs. Because the flow characteristics vary
from place to place, non-uniform flow is more complex to analyze than uniform flow and is often divided further
into gradually varied and rapidly varied flow depending on how quickly the changes occur.
Mathematically: dy/dl ≠ 0, dV/dl ≠ 0
9. Flow in an open channel can be classified as either laminar or turbulent, based on the value of the Reynolds number
(Re). The Reynolds number is a dimensionless quantity used to determine the type of flow and is calculated using the
formula:
Re = (ρVR) / μ,
LAMINAR FLOW & TURBULENT FLOW
10. where V is the average velocity of flow, R is the hydraulic radius (the ratio of the flow area to the wetted perimeter), ρ
is the density of the fluid, and μ is the dynamic viscosity. When the Reynolds number is less than 500, the flow is
considered laminar, meaning the water particles move in smooth, parallel layers with minimal mixing. If the Reynolds
number is greater than 2000, the flow becomes turbulent, where there is significant mixing, eddies, and irregular
motion. Values of Reynolds number between 500 and 2000 indicate a transitional flow, where the behavior is
unstable and can shift between laminar and turbulent depending on slight changes in conditions.
CRITICAL, SUBCRITICAL, SUPER-CRITICAL FLOW IN RELATION TO FROUDE’S NUMBER
Critical flow is that flow which occurs when specific energy is at its minimum.
12. In essence when fr=1 : flow is critical, when fr<1 : flow is sub-critical , when fr>1; flow is super critical
1. Chezy’s formula
2. Manning’s formula.
for uniform flow in open channels, the following formulae will be discussed
CHEZY’S FORMULAR
Chezy’s formula for uniform flow. Chezy's formula for uniform flow describes the relationship between flow velocity,
hydraulic radius, slope, and the Chezy coefficient in open channel flow. It's a fundamental equation in fluid
mechanics used to estimate mean flow velocity. It is an empirical formula used to calculate the mean flow velocity,
particularly in steady, turbulent conditions. The formula is: V= c✓RS Where: • v: is the average flow velocity (m/s). •
C: is the Chezy coefficient, which accounts for roughness of the channel (m^2/s) • R: is the hydraulic radius, which is
the cross-sectional area of flow divided by the wetted perimeter (m) • i: is the slope of the channel (m/m or
dimensionless). Chezy Coefficient (C): This coefficient is determined experimentally and depends on the channel's
roughness, the hydraulic radius, and the Reynolds number.
13. MANNINGS FORMULAR
Example 1: Using Chezy’s Formula
Find the rate of flow and conveyance for a rectangular channel 7.5 m wide, carrying uniform flow at a depth of 2.25
m. The bed slope of the channel is 1 in 1000. Take Chezy’s constant C = 55.
Solution:
Width of channel, b = 7.5 m
Depth of flow, y = 2.25 m
Bed slope, S = 1/1000 = 0.001
Chezy’s constant, C = 55
14. Area of flow, A = b × y = 7.5 × 2.25 = 16.875 m²
Wetted perimeter, P = b + 2y = 7.5 + 2(2.25) = 12 m
Hydraulic radius, R = A / P = 16.875 / 12 = 1.40625 m
Using Chezy’s formula:
Q = A × C × √(R × S)
Q = 16.875 × 55 × √(1.40625 × 0.001)
Q = 16.875 × 55 × √0.00140625
Q ≈ 16.875 × 55 × 0.0375 ≈ 34.85 m³/s
Conveyance, K = A × C × √R
K = 16.875 × 55 × √1.40625
K = 16.875 × 55 × 1.1867 ≈ 1100.5
15. Example 2: Using Manning’s Formula
A trapezoidal channel has a bottom width of 3 m and side slopes of 1:1. Water flows to a depth of 1.5 m. If the bed
slope is 0.001 and Manning’s roughness coefficient (n) is 0.015, determine the discharge using Manning’s formula.
Solution:
Given:
Bottom width, b = 3 m
Depth, y = 1.5 m
Side slope = 1H:1V ⇒ z = 1
Bed slope, S = 0.001
Manning’s n = 0.015
Top width = b + 2zy = 3 + 2×1×1.5 = 6 m
Area, A = (b + zy) × y = (3 + 1×1.5) × 1.5 = 4.5 × 1.5 = 6.75 m²
Wetted perimeter, P = b + 2√(1² + z²) × y = 3 + 2×√2×1.5 = 3 + 4.243 = 7.243 m
Hydraulic radius, R = A / P = 6.75 / 7.243 ≈ 0.9325 m
Using Manning’s formula:
Q = (1/n) × A × R^(2/3) × S^(1/2)
Q = (1/0.015) × 6.75 × (0.9325)^(2/3) × (0.001)^(1/2)
Q ≈ 66.67 × 6.75 × 0.965 × 0.0316 ≈ 13.65 m³/s
16. in open channel design, the most efficient section refers to a cross-sectional shape that conveys the maximum
discharge using the least amount of material for construction or excavation. This is crucial in engineering because it
helps reduce costs while ensuring effective water transport. Efficiency in this context means achieving the largest
hydraulic radius, which minimizes frictional losses and maximizes flow for a given area and slope. Designing channels
with the most efficient section is essential in irrigation, drainage, and water supply systems
MOST ECONOMICAL SECTIONS FOR DIFFERENT SECTIONS
Rectangular section channel
21. REFERENCES
Subramanya, K. (2009). Flow in Open Channels (3rd ed.). Tata
McGraw-Hill Education.
Ven Te Chow (1959). Open-Channel Hydraulics. McGraw-Hill Book
Company.
Modi, P. N., & Seth, S. M. (2017). Hydraulics and Fluid Mechanics
Including Hydraulic Machines (20th ed.). Standard Book House.
https://www.howtocivil.com/differences-pipe-flow-open-channel-flow/
RAJPUT FLUID MECHANICS
Ranga Raju, K. G. (2015). Flow Through Open Channels (2nd ed.).
Universities Press.
French, R. H. (1985). Open-Channel Hydraulics. McGraw-Hill Series in
Water Resources and Environmental Engineering.
https://youtu.be/G00W672DIEg?si=EdMJDghVKrrxCBXZ
