CVEN3502 Study Notes
Trimester 2, 2019
Water Engineering
DEFINITIONS OF FLOW
• The two types of water flows:
o Open channel flow has an open surface and hence is not
pressurised
o Closed conduit flow is confined in all directions and is
pressurised
• Engineers must be able to analyse free surface flows in order to:
o Predict floods
o Conduct water quality studies
o Understand the movement of sediments/materials in waterways
• A steady flow will not change through time in terms of depth and
velocity
• Unsteady flows have ever-changing depth and velocity
• For steady flows, the various head lines can be plotted against
distance travelled throughout the flow
o The channel bottom line will decrease at a rate of S0/L
o The water surface line will decrease at a rate of Sws/L
o The energy grade line will decrease at a rate of Sf/L
• The energy grade line will be a vertical distance of ‘v2/2g’ above the
water surface line
• The difference in height of the energy grade line across a given
distance is its overall head loss (hf) due to friction
• In closed conduit flow, the hydraulic grade line will be a distance
above the centre line of the pipe due to a finite pressure head
• For a given flow cross-section:
o The hydraulic radius equals the Area/Wetted Perimeter
o Hydraulic diameter equals 4*Area/Wetted Perimeter
• In pipe flow, due to the constraint of area, flow volume tends to be
roughly proportional to velocity (one degree of freedom)
• With surface flow, both velocity and depth can vary, which means that
flow volume is related heavily to both factors (two degrees of
freedom)
UNIFORM FLOW
• Ideal flow is purely theoretical and does not have any losses due to
friction
• In uniform flow, the flow runs with constant depth and velocity
• In real life flows, energy is loss due to friction, yet there is a point on
the slope at which friction and gravity forces are balanced which is
when the flow stops accelerating
• Shear force is equivalent to a friction stress multiplied by the length of
the flow, multiplied by the wetted perimeter (this considers flow in 3D)
• On flow boundaries, shear stress is equal to weight force, which leads
to an equation: Shear Stress = Weight*Hydraulic Radius*S
, • Shear stress can be approximated to be proportional to the square of
the mean flow velocity
• However for turbulent flow, shear stress will equal: K*ro*v2
• The Chezy coefficient equals: sqrt(g/K)
o This is usually in the range of 30-60m0.5/s and is a measure of
smoothness
• Therefore, velocity equals: v = C*sqrt(Rh*S) where S=slope
• The Colebrook-White equation can be used to relate the Chezy
coefficient to the Darcy friction factor: C = sqrt(8*g/f)
• The Darcy-Weisbach equation states that head loss is as follows: hf =
f*L*v2/(D*2g)
• Turbulent flow can be classified as hydraulically smooth when the
roughness height is less than 2/7ths of the width of the viscous
sublayer
• Turbulent flow will be classified as hydraulically rough when the
roughness height is more than 2/7ths of the width of the viscous
sublayer
• Flow is considered laminar when the Reynolds number is less than
500 and is considered turbulent when the Reynolds numbers is more
than 1000 for pipe flow or 2000 for open surface flow
• The Manning equation is an empirical formula for flow velocity as a
function of hydraulic radius, slope and the Manning coefficient
o This is NOT considered to be an accurate equation
o A comprehensive table of values for Manning coefficients
(based on visual characteristics) are displayed in ‘Open-
Channel Flow’ (1959) by Chow
o The slope factor used in the Manning equation is considered
proportional to the square of velocity, meaning that this is only
valid for hydraulically rough turbulent flow
• The Chezy and Darcy equations are directly related
• The Darcy friction factor ‘f’ can be calculated using three equations
depending on whether the flow is laminar, transitional or turbulent
o The Colebrook-White iterative equation is used when the flow is
turbulent
CHANNEL CROSS SECTIONS
• For a given cross sectional shape, the area and perimeter can be used
to calculate the hydraulic radius
• It is extremely difficult to calculate the flow within circular cross sections
which are NOT full, this is covered in a postgraduate course at UNSW
• A hydraulically optimal cross-section gives the maximum discharge
for a given discharge area
o It is in the interest of the engineer to design a flow channel with
a hydraulically optimal cross-section, since this is the most
space and economically efficient design
• Maximum discharge occurs when perimeter is at a minimum
• For a trapezium, the perimeter is a function of both the depth of water
AND the angle of the slant
• Optimum possible design for a waterway is a half circle
, o The reason why not all waterways are built as semi-circles is
due to the cost of construction
• The pressure on a point of fluid acts perpendicular to the bed of the
channel, meaning that the pressure head is always overestimated
using the common methods if the channel is on a slope
• The existence of a boundary layer means that velocity will always
vary within a stream, meaning that a coefficient must be used to correct
the velocity head to that of an averaged value
SPECIFIC ENERGY
• Specific energy measures the energy at a point relative to the energy
at the channel bed
• This is useful for analysing channel transitions (i.e. changes in the
dimensions of the channel), flow control and flow states
• Total head (H) = z + y*cos2(theta) + a*v2/(2g)
• Since specific energy (E) is relative to the channel bed, total head also
equals: H = z + E
• In open channel flow, there are two types of losses that occur:
o Friction losses over distance
o Local energy losses due to transitions
• A contraction or expansion of flow will create an eddy current which
leads to a loss of energy (hf)
• If there are no channel transitions present along a short distance of
flow, frictional losses can usually be neglected (total head would
remain constant)
o This means that over a short distance, if elevation increases
then specific energy must decrease and vice versa
• For rectangular channels, the flow per unit width (q) simple equals: v*y
• The specific energy formula can be rewritten in terms of ‘q’, which
provides a new equation: (E-y)*y2 = q2/(2g)
o This can be plotted with depth ‘y’ on the vertical axis and
specific energy on the horizontal axis
o Being a cubic, this equation has 2 real solutions for depth ‘y’
o The two asymptotes represent states where specific energy
purely equals elevation and another where there is zero
elevation
o Along the curve, the depth associated with the point of minimum
specific energy (Emin) is known as the critical depth
Trimester 2, 2019
Water Engineering
DEFINITIONS OF FLOW
• The two types of water flows:
o Open channel flow has an open surface and hence is not
pressurised
o Closed conduit flow is confined in all directions and is
pressurised
• Engineers must be able to analyse free surface flows in order to:
o Predict floods
o Conduct water quality studies
o Understand the movement of sediments/materials in waterways
• A steady flow will not change through time in terms of depth and
velocity
• Unsteady flows have ever-changing depth and velocity
• For steady flows, the various head lines can be plotted against
distance travelled throughout the flow
o The channel bottom line will decrease at a rate of S0/L
o The water surface line will decrease at a rate of Sws/L
o The energy grade line will decrease at a rate of Sf/L
• The energy grade line will be a vertical distance of ‘v2/2g’ above the
water surface line
• The difference in height of the energy grade line across a given
distance is its overall head loss (hf) due to friction
• In closed conduit flow, the hydraulic grade line will be a distance
above the centre line of the pipe due to a finite pressure head
• For a given flow cross-section:
o The hydraulic radius equals the Area/Wetted Perimeter
o Hydraulic diameter equals 4*Area/Wetted Perimeter
• In pipe flow, due to the constraint of area, flow volume tends to be
roughly proportional to velocity (one degree of freedom)
• With surface flow, both velocity and depth can vary, which means that
flow volume is related heavily to both factors (two degrees of
freedom)
UNIFORM FLOW
• Ideal flow is purely theoretical and does not have any losses due to
friction
• In uniform flow, the flow runs with constant depth and velocity
• In real life flows, energy is loss due to friction, yet there is a point on
the slope at which friction and gravity forces are balanced which is
when the flow stops accelerating
• Shear force is equivalent to a friction stress multiplied by the length of
the flow, multiplied by the wetted perimeter (this considers flow in 3D)
• On flow boundaries, shear stress is equal to weight force, which leads
to an equation: Shear Stress = Weight*Hydraulic Radius*S
, • Shear stress can be approximated to be proportional to the square of
the mean flow velocity
• However for turbulent flow, shear stress will equal: K*ro*v2
• The Chezy coefficient equals: sqrt(g/K)
o This is usually in the range of 30-60m0.5/s and is a measure of
smoothness
• Therefore, velocity equals: v = C*sqrt(Rh*S) where S=slope
• The Colebrook-White equation can be used to relate the Chezy
coefficient to the Darcy friction factor: C = sqrt(8*g/f)
• The Darcy-Weisbach equation states that head loss is as follows: hf =
f*L*v2/(D*2g)
• Turbulent flow can be classified as hydraulically smooth when the
roughness height is less than 2/7ths of the width of the viscous
sublayer
• Turbulent flow will be classified as hydraulically rough when the
roughness height is more than 2/7ths of the width of the viscous
sublayer
• Flow is considered laminar when the Reynolds number is less than
500 and is considered turbulent when the Reynolds numbers is more
than 1000 for pipe flow or 2000 for open surface flow
• The Manning equation is an empirical formula for flow velocity as a
function of hydraulic radius, slope and the Manning coefficient
o This is NOT considered to be an accurate equation
o A comprehensive table of values for Manning coefficients
(based on visual characteristics) are displayed in ‘Open-
Channel Flow’ (1959) by Chow
o The slope factor used in the Manning equation is considered
proportional to the square of velocity, meaning that this is only
valid for hydraulically rough turbulent flow
• The Chezy and Darcy equations are directly related
• The Darcy friction factor ‘f’ can be calculated using three equations
depending on whether the flow is laminar, transitional or turbulent
o The Colebrook-White iterative equation is used when the flow is
turbulent
CHANNEL CROSS SECTIONS
• For a given cross sectional shape, the area and perimeter can be used
to calculate the hydraulic radius
• It is extremely difficult to calculate the flow within circular cross sections
which are NOT full, this is covered in a postgraduate course at UNSW
• A hydraulically optimal cross-section gives the maximum discharge
for a given discharge area
o It is in the interest of the engineer to design a flow channel with
a hydraulically optimal cross-section, since this is the most
space and economically efficient design
• Maximum discharge occurs when perimeter is at a minimum
• For a trapezium, the perimeter is a function of both the depth of water
AND the angle of the slant
• Optimum possible design for a waterway is a half circle
, o The reason why not all waterways are built as semi-circles is
due to the cost of construction
• The pressure on a point of fluid acts perpendicular to the bed of the
channel, meaning that the pressure head is always overestimated
using the common methods if the channel is on a slope
• The existence of a boundary layer means that velocity will always
vary within a stream, meaning that a coefficient must be used to correct
the velocity head to that of an averaged value
SPECIFIC ENERGY
• Specific energy measures the energy at a point relative to the energy
at the channel bed
• This is useful for analysing channel transitions (i.e. changes in the
dimensions of the channel), flow control and flow states
• Total head (H) = z + y*cos2(theta) + a*v2/(2g)
• Since specific energy (E) is relative to the channel bed, total head also
equals: H = z + E
• In open channel flow, there are two types of losses that occur:
o Friction losses over distance
o Local energy losses due to transitions
• A contraction or expansion of flow will create an eddy current which
leads to a loss of energy (hf)
• If there are no channel transitions present along a short distance of
flow, frictional losses can usually be neglected (total head would
remain constant)
o This means that over a short distance, if elevation increases
then specific energy must decrease and vice versa
• For rectangular channels, the flow per unit width (q) simple equals: v*y
• The specific energy formula can be rewritten in terms of ‘q’, which
provides a new equation: (E-y)*y2 = q2/(2g)
o This can be plotted with depth ‘y’ on the vertical axis and
specific energy on the horizontal axis
o Being a cubic, this equation has 2 real solutions for depth ‘y’
o The two asymptotes represent states where specific energy
purely equals elevation and another where there is zero
elevation
o Along the curve, the depth associated with the point of minimum
specific energy (Emin) is known as the critical depth
