Essay: Open channel flow

Open channel flow:
Flow of liquid with a free surface through any passage with atmospheric pressure acting on its surface is known as open channel flow. The liquid flowing through any closed passage without touching the top can also treated as open channels.
Examples:
1. Flow in natural waterfalls, river and streams.
2. Flow in artificial or man-made channels such as irrigation channels and flumes.
3. Flow in sewer and drainage channels.
Pipe flow:
Pipe flow a branch of hydraulics and fluid mechanics is a type of liquid flow within a closed conduit.In Pipe flow there exist no direct atmospheric flow but hydraulic pressure only.
Pipe flow Open channel flow
In open channels flow usually occur due to the slope of channel bottom and the slope of liquid surface. The main difference in the open channel flow and pipe flow is that in pipe flow usually the cross section of channel is fixed and confined while on the other hand open channel flow is unconfined. Open channels flow is difficult to analyze than the pipe flow. That’s why in open channel flow measurement empirical approach is adopted. The velocity of flow in open channel can be computed by help of Manning’s formula:
V = 1/n x R0.66 x S0.5
In pipe flow the conduit (pipe for movement of fluid) usually completely fills with water for the development of pipe pressure, while in the conduit which is partially filled can have open channel flow. There is no restriction for the conduit in case of open channel flow to be completely filled.
 
Differences between pipe flow and open channel flow:
 
1.2 Types of Flow
Specific energy:
The total energy of a channel flow referred to datum is given by.
 
If the datum coincides with the channel bed at the section, the resulting expressions is know as specific energy and is denoted by E.
 
When cos  = 1.0 and  = 1.0
 
The condition of minimum specific energy is known as the critical-flow condition and corresponding depth yc is known as the critical depth.
Based on specific energy concept the following flows are possible.
(i) Critical Flow:
Froude number is the defined as the square root of the ratio of the inertia force of flowing fluid to the gravity force.
 
V => Velocity
g => Acceleration due to gravity
D => Depth.
If the Froude number is equal to one, the flow said to be critical flow.
Fe = 1.0.
(ii) Sub-Critical Flow:
When the depth of flow in a channel is greater than the critical depth (yc), the flow is said to sub-critical flow or streaming flow or tranquil flow. This type of flow the, Froude number is less than one.
Fe < 1.0.
(iii) Super Critical Flow:
When the depth of flow in a channel is less than the critical depth of the flow is said to be super critical flow or torrential flow. For this type of flow, the Froude number is greater than one.
Fe > 1.0.
Types of flows in channels:
Flow in open channel can be classified into different types based on different criteria.
(i) Steady flow and unsteady flow.
(ii) Uniform flow and non uniform flow.
(iii) Laminar flow and Turbulent flow.
(iv) Sub critical, critical and super critical flow.
(i) Steady flow and Unsteady flow: Time is the criterion
Flow in open channel is said to be steady when the depth of flow, mean velocity of flow, rate of flow at any point do not change with time. It is expressed as
 
When these quantities change with time, then the flow is said to be unsteady flow.
 
(ii) Uniform flow and Non uniform flow: Space is the criterion
If the flow properties such as the velocity of flow, depth of flow, slope of the channel and cross section remain constant along the length of the channel at any given instant then the flow is said to be uniform.
 
When the above flow properties vary along the channel at any given instant, then the flow is known as non uniform flow.
 
Non uniform flow in open channel is also called varied flow, which is classified into 2 types.
1. Rapidly varied flow (RVF)
2. Gradually varied flow (GVF)
Rapidly varied flow is defined as that flow in which depth of flow changes abruptly over a small length of the channel.
Example: Hydraulic Jump occurring below a spill way or a sluice gate.
 
Uniform flow and non uniform flow
Gradually varied flow (GVF):
If the depth flow in a channel changes gradually over a long length of channel, the flow is said to be gradually varied flow and is denoted by GVF.
Example: Flow behind a dam.
Non uniform flow or varied flow can be either steady or unsteady.
Varied flow assumes that no flow is externally added to or taken out of the system. If some flow is added to or abstracted from the system, then the resulting varied flow is known as a spatially varied flow.
(iii) Laminar flow and Turbulent flow: Reynolds Number as the criterion
The flow in the open channel may be characterised as laminar or turbulent depending upon the value of Reynolds Number, which is nothing but the ratio of inertia force to viscour force.
 
where ρ density of liquid.
μ viscosity of liquid.
V Mean velocity of liquid.
R Hydraulic radius on hydraulic mean depth.
 
When Re < 500 – flow is laminar
Re > 2000 – flow is turbulent
500 < Re < 2000 – flow is transitional
(iv) Subcritical flow, critical flow and super-critical flow: Froude Number as the criterion
Since gravitational force is a predominant force in the case of channel flow, therefore Froude Number is an important parameter for analysing open channel flow which is the ratio of inertia force and gravity force.
 
where V and D are mean velocity of flow and hydraulic depth of channel respectively.
 
Depending upon froude Number the channel flow may be characterised as
(i) When the flow is described as subcritical (or streaming)
(ii) When Fr = 1 the flow is said to be in critical state
(iii) When Fr > 1 the flow is said to be super critical (or rapid or shootin