Essay: Afflux and back water curve

Let us discuss the terms: 1. Afflux and 2. Back water curve and Derive an expression for the length of the back water curve.
Whenever an obstruction comes across the width of the channel, the water surface in the upstream side of the obstruction no longer remains parallel to the bed but the depth of water will be rising thus forms a curved surface. Upstream profile of the curved surved with the concavity upwards is called a backwater curve and it is shown in figure 5.
The amount by which the water is rising is known as afflux.
Then afflux = y2 – y1
Figure 5. Backwater curve
where y1 – depth of water at the point where the water
starts rising up.
y2 – maximum height of rising water from bed.
The distance along the bed of the channel between the section where the water level starts rising from its normal depth to the section where the water level is having the maximum height is called the length of the backwater curve.
Length of back water is obtained by applying Bernoulli’s equation at section (1) (1) and (2) (2) of channel in which depth of water is rising as shown in figure 6.
Let y1 → depth of flow at section on (1)
y2 → depth of flow at section (2)
V1 → velocity of flow at section (1)
V2 → velocity of flow at section (2)
S0 → bed slope of channel
Sf → energy line slope and
L → length of back water curve
Applying Bernoulli’s equation at section (1) (1) and (2)
(2)
hL – loss of energy due to friction = Sf × L
Z1= S0 × L
Figure 6. Length of back water curve
Value of Sf is calculated either by Manning’s formula or by Chezy’s formula. The mean values of velocity, depth of flow, hydraulic mean depth are used between section (1) (1)
and (2) (2) for calculating the value of Sf.
3.5 Hydraulic jumps
Let us discuss the energy loss in a hydraulic jump
When hydraulic jump takes place, a loss of energy due to eddies formation and turbulence occurs. This loss of energy is equal to the difference of specific energies at section 1-1 and 2-2.
Loss of energy due to hydraulic jump
hL = E1 -E2.
Let us discuss the conditions for the formation of hydraulic jump
• The flow is uniform and pressure distribution is due to hydrostatic before and after the jump.
• Losses due to friction on the surface of the bed of the channel are small and hence neglected.
• The slope of the bed of the channel is small, so that the component of the weight of the fluid in the direction of flow is negligibly small.
Let us discuss the uses of formation of hydraulic jump in a channel
The uses are:
1) Energy dissipation
2) Mixing of chemicals
3) Flow measurement
4) Desalination of seawater
5) Aeration of streams.
Let us Derive an expression for loss of head in Hydraulic Jump.
When hydraulic jump takes place, a loss of energy occurs due to eddy formation and turbulence. This loss of energy is equal to the difference of specific energies.
Loss of energy due to hydraulic jump, hL = E1 – E2.
From equation,
9
Substituting q2 in equation (1).
Define energy dissipation.
Let us discuss the energy dissipation.
Hydraulic jump is useful means of dissipating excess energy of water flowing over spillways and other hydraulic structures.
1. Undular jump: Energy dissipation is very low and it will be less than 5%
2. Weak jump: The energy loss in the jump is low and in the range of 5 to 15%
3. Oscillating jump: Energy dissipation in the range of 15 to 45%
4. Steady jump: The energy dissipation may be in the range of 45 to 70%. The jump is well established, the roller and jump action is fully developed to cause appreciable energy loss.
5. Strong jump: The energy dissipation may be upto 85%.
What are the various applications of momentum principle? Explain.
Let us discuss the various applications of momentum principle
Ans: Momentum principle states that “the rate of change of momentum is proportional to the imposed force and takes place in the direction in which force acts”.
It is derived from Newton’s second law of motion. According to Newton’s second law of motion,
Force, F = Mass × Acceleration = m × a
The equation (1) is knwon as the momentum principle. This equation can be written as:
F dt = d(mv) … (2)
The equation (2) is known as impulse momentum equation. The quantity F dt represents the impulse of applied force, while the quantity d(mv) represents the change in momentum.
The impulse force F to acting on a fluid mass ‘m’ over a short interval of time dt is equal to the change in momentum d(mv) in the direction of force.
The momentum principle is applied to the following fluid flow situations:
• When the flow passage by a stream of fluid as it changes its direction, magnitude or both.
Example: pipe bends, reducers, moving vanes, jet propulsion.
• To find the flow characteristics when there is abrupt change in flow section.
Example: sudden enlargement of pipe, hydraulic jumps in changes.
Write about backwater curves.
Let us discuss about backwater curves.
Whenever there is an obstruction across the flowing liquid, water surface will be rising forming curved surface in the upstream side of the obstruction called back water curve.
Define the term Afflux.
Let us discuss the term Afflux.
Afflux is defined as the maximum increase in water level due to obstruction in the path of flow of water.
A river of 45 m width has a normal depth of flow of 3 m and an average bed slope of 1 in 10,000. A weir is build across the river raising the water surface level at the weir site for 5 m above the bottom of the river. Assuming that the back water curve is an arc of circle; calculate the approximate length of the curve. Manning’s n = 0.025.
Let us discuss the problem A river of 45 m width has a normal depth of flow of 3 m and an average bed slope of 1 in 10,000. A weir is build across the river raising the water surface level at the weir site for 5 m above the bottom of the river. Assuming that the back water curve is an arc of circle; calculate the approximate length of the curve. Manning’s n = 0.025.
Given:
b = 45 m
h2. – h1 = 5 – 3 = 2m
N = 0.025
A1 = b h1 45 × 3 = 135 m2
P1 = b + 2h1 = 45 + 2 × 351 m
P2 = b + 2h2 = 45 + 2 × 5 = 55m
il/2 = (0.0064)
i = 0.00004
3.5.1 Types
Let us discuss Detail about jump
Definition:
The rise of water level which take places due to transformation of unstable shooting flow (super critical) to stable streaming flow (sub critical).
Types of Jump
1) Undular Jump
– 1 0 < F ≤ 1.7
– water surface is undulating with a very small ripple on the surface
– EL / E1 – Practically zero.
2) Weak Jump
– 1.7 < F1 ≤ .5
– Energy dissipation is very small
– EL / E1 – 5% at F1 = 1.7
– EL / E\\ – 18% at F1 = 2.5
– Water surface is smooth after the jump.
3) Oscillating Jump
– 2.5 < F1 ≤ 4.5
– Characterised by an instability of the high-velocity flow in the jump which oscillates in random manner between the bed and the surface.
– EL / E1 – 45% at F1 = 4.5.
4) Steady Jump
– 4.5 < F1 ≤ 9.0
– Roller and Jump action is fully developed to cause appreciable energy loss
– EL/E1 – 70% at F1 = 9.0
– Steady Jump – least sensitive in terms of the toe-position to small fluctuation in the tail water elevation.
5) Strong/Choppy Jump
– F1 > 9
– water surface is rough and choppy
– El/E1 – > 70%.
3.6 Energy dissipation
3.7 Surges and surge through channel transitions
Let us see the cause of surge to occur in a flow
The cause of surge is sudden change in discharge or depth or both.
Types:
1) Positive surge
2) Negative surge.
Let us discuss the surges and its types
Whenever there is a sudden change in discharge or depth or both in an open channel a rapidly varied unsteady phenomenon known as surge develops. Such situation occurs during sudden operation of a control gate. A surge producing an increase in depth is known as positive surge and the one which causes a decrease an depth is known as negative surge. Positive surges have steep fronts, more like hydraulic jump and the wave does not change during its translation. They are also known as moving hydraulic jumps. Hence surge is defined the moving wavefront which results is an abrupt change of depth of flow.
The surge can move either in the upstream or in downstream direction resulting in 4 basic types of surges as shown in figure 5.
Figure 5. Types of surges
1. Positive surge moving downstream
2. Positive surge moving upstream
3. Negative surge moving downstream
4. Negative surge moving upstream