HYDRAULIC 1 CVE 303

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HYDRAULIC 1CVE 303

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Basics of Fluid Flow

• Types of flow The type of flow depends on the
  manner in which the particles unite, the
  particles group themselves in a variety of ways
  e.g. regular or irregular. The type of flow is
  identified by the Reynolds number.
• Flow of an IDEAL FLUID No Viscousity
• Flow of a REAL FLUID Viscousity included
• Laminar (low velocity, motion in layers)
• Turbulent Flow ( high velocity, chaotic motion)
• Steady flow (conditions at any point remain
  constant, may differ from point to point)
• Uniform Flow ( velocity is the same at any given
  point in the fluid)
• Flow lines Path lines, Stream lines and Streak
  lines
• Straight line streamlines of moving particle- One
  dimensional flow (Flow in pipes)
• Curve Two dimensional flow (Flow over a
  spillway)
• Streamlines represented in space Three
  dimensional (flow in a river bed)
• Motion of Fluid Particles
• Lagrangian method
• Eulerian method

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• Equation of continuity of a liquid flow If an
  incompressible liquid us is continuously flowing
  through a pipe or a channel (whose
  cross-sectional area may or may not be constant)
  the quantity of liquid passing per second is the
  same at all sections.
• Questions
• Water is flowing through a tapered pipe having
  end diameter of 150m and 50m respectively. Find
  the discharge at the larger end and velocity head
  at the smaller end if the velocity of water at
  the larger end is 2m/s.
• A circular pipe of 250 mm diameter carries an oil
  of specific gravity 0.8 at the rate of 120
  litres/s and under a pressure of 20kPa. Calculate
  the total energy in meters at a point which is 3m
  above the datum line.
• A horizontal pipe 100 m long uniformly tapers
  from 300 mm diameter to 200 mm diameter. What is
  the pressure head at the smaller end, if the
  pressure at the larger end is 100 KPa and the
  pipe is discharging 50 litres of water per
  second. (5 marks

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Bernoullis Equation and its applications

• Introduction
• Energy of liquid in motion
• Potential Energy a liquid posses by virtue of
  its position
• Kinetic Energy posessed by a liquid by virtue of
  its motion
• Pressure head of a liquid particle in motion
• Total Energy This is the sum of a liquids
  Potential, Kinetics and Pressure energy
• Total Head of a liquid in motion

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Bernoullis equation (contd.)

• Definition For a perfect incompressible fluid,
  flowing in a continuous stream, the total energy
  of a particle remains the same, while the
  particles moves from one point to another.
• Limitations of Bernoullis equation
• Practical application of Bernoullis equation
• Venturimeter ( Convergent cone, throat,
  divergent cone)
• Discharge through a venturimeter
• Inclined venturimeter
• Orificemeter
• Pitot tube

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• Questions
• A pipe 500 m long has a slope of 1 in 100 and
  tapers from 1 m diameter at the higher end to 0.5
  m at the lower end. The quantity of water flowing
  is 900 l/sec. If the pressure at the higher end
  is 70KPa. Find the pressure at the lower end.
• A pipe AB branches into two pipes C and D. The
  pipe has a diameter of 0.45 m at A, 0.3 m at B,
  0.2 m at C and 0.15 m at D. Find the discharge at
  A if the velocity of water at A is 2 m/s also
  find the velocities at B and D if the velocity at
  C is 4 m/s.
• A venturimeter with a 150 mm diameter at inlet
  and 100 mm at throat is laid with its axis
  horizontal and is used for measuring the flow of
  oil specific gravity 0.9. The oil mercury
  differential manometer shows a guage difference
  of 200 mm. Assume coefficient of meter as 0.98.
  Calculate the discharge in litres per minute
• A venturimeter has 400 mm diameter at the main
  and 150 mm at the throat. If the difference of
  pressure is 250 mm of mercury and the metre
  coefficient is 0.97, calculate the discharge of
  oil (specific gravity 0.75) through the
  venturimeter

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OPEN CHANNEL FLOW

• General Definition An open channel is a passage
  through which the water flows under the force of
  gravity and atmospheric pressure e.g. canals,
  sewers, aqauduct. It is also known as
  free-surface flow or gravity flow. The flow here
  is not due to pressure as in the case of pipe
  flow. Most open channel flow are turbulent flow
  and froude number is the relevant parameter here
• Types of open channel flow
• Natural streams and rivers
• Artificial canals, flumes
• Sewers, tunnels, partially full pipelines
• Gutters
• Applications of artificial channels
• Water power development
• Irrigation
• Water supply
• Drainage
• Flood control
• Reynolds no. for pipes
• Reynolds no. for open channels
• Wetted perimeter Length of cross-sectional
  border in contact with water. Length where
  friction acts.
• Slopes in open channel flow

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Open channel flow (contd.)

• Uniform flow through open channels
• Chezys formula
• Values of Chezys constant in the formula for
  discharge in open channel
• Mannings formula
• Basins formula
• Kutters formula
• Geometric properties of cross-sections
• Trapezoidal channels
• Triangular channels
• Rectangular channels

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• Exercises
• A trapezoidal channel 3.5 m wide at the bottom
  has side and bed slopes of 11 and 11000
  respectively. Using mannings formula, find the
  discharge through the channel, if the depth of
  water is 0.5 m. Take N 0.03.
• A non symmetrical trapezoidal cross-section with
  b 1.2 m, m1 2 and m2 1, So 0.00009, Q
  120 m3/s and y 0.6 m, find the mannings
  roughness factor n.
• Unnatural streams cross-section can be
  approximated by a parabolic shape with B 4m and
  a depth y 2 m. If the stream is laid on a slope
  of 0.001 m/m and n 0.028, determine the
  discharge.

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SPECIFIC ENERGY

• Introduction
• Specific energy diagram
• Critical conditions
• E Emin i.e.
• Critical depth
• Critical velocity
• Subcritical y1 gt yc tranquil, upper stage flow
  V lt Vc
• Supercritical y1 lt yc rapid, lower stage flow V
  gtVc
• Froudes number
• Critical depth in non rectangular channels
• Occurrence of critical flow

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• Critical energy
• Occurrence of Critical Flow
• Change from mild to steep slope in a channel
• Entrance from a reservoir into a steep slope
  channel
• Free fall from mild slope channel
• Free fall from steep slope channel
• Humps and Contractions
• Questions
• A rectangular channel 3.25 m wide discharges
  2600 litres of water per second. What is the
  critical depth and critical velocity?
• A channel of rectangular section 8 m wide is
  discharging water at the rate of 12 m3/s with an
  average velocity of 1.2 m/s. Find the type of
  flow?
• A rectangular channel 3 m wide carries 4 m3/s of
  water in subcritical uniform flow at a depth of
  1.2 m, a frictionless hump is to be installed
  across the bed. Find the critical hump height?

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HYDRAULIC JUMP

• Introduction Local non-uniform flow phenomenon
  supercritical flow going into subcritical. The
  shooting flow is an unstable type of flow and
  does not continue on the downstream side, the
  flow transform itself to the streaming flow by
  increasing its depth. The rise in water level
  which occurs during the transformation of the
  unstable shooting flow to the stable streaming
  flow is called hydraulic jump.
• Depth relations
• Energy losses
• Types of jumps
• Stilling basins

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• Questions
• A horizontal rectangular channel of constant
  breadth has a sluice opening from the bed
  upwards. When the sluice is partially opened
  water issues at 6 m/s with a depth of 600 mm.
  Determine the loss of head per KN of water.
• A discharge of 1000 l/s flows along a
  rectangular channel 1.5 m wide. If a standing
  wave is to be formed at a point where the
  upstream depth is 180 mm. What would be the rise
  in water level?
• Water flows at the rate of 1 m3/s along a channel
  of rectangular section of 1.6 m width. If a
  standing wave occurs at a point where upstream
  depth is 250 mm. Find the rise in water level
  after the hydraulic jump. Also find the loss of
  head in the standing wave.