OPEN CHANNEL FLOW
Velocity Distribution
where,
V_{0.2} = velocity at a depth of 0.2 y_{0} from the free surface.
V_{0.8} = Velocity at a depth of 0.8 y_{0} from the free surface.
Terms related to open channel flow
(a) Depth of Flow (y) : Vertical distance between the lowest point of the channel section (bed of the channel) to the free liquid surface.
(b) Top width (T) : Width of channel section at free liquid surface.
(c) Wetted Area (A) : Cross sectional area of the channel normal to the direction of flow.
(d) Channel slope (S) : Inclination of channel bed is called channel slope and is given by,
S = tan a » sin a = (h/I)
where h = vertical fall in length ℓ of channel.
(e) Wetted Perimeter and Hydraulic mean depth
(f) Hydraulic depth (D) : It is the ratio of wetted area A to the top width T.
(D=A/T)
(g) Hydraulic Grade Line (HGL)
(h) Energy Grade Line (EGL) or Total energy Line (TEL)
Difference between TEL/EGL and HGL at any section
where a = Kinetic energy correction factor
Specific Energy
If the datum coincides with the channel bed at the section, the resulting expression is known as SPECIFIC ENERGY and is denoted by E. Thus.
Critical Depth
Equation (i) & (ii) are basic equations for critical flow conditions in a channel.
at critical flow F = 1 at y = y_{c}
Uniform Flow
Velocity Formulae in Uniform Flow
(a) Chezy Equation
S = bottom slope
Relationship between ‘C’ and friction factor ‘f’
where,
h_{f} = head loss due to friction
D = Diameter of pipe
f = friction factor
L = length of pipe
2. Manning’s Formula
where, n = a roughness coefficient known as Manning’s ‘n’.
Relationship between Manning’s ‘n’ ‘c’ & ‘f’ :
(By comparing chezy and Manning’s formula)
(3) Ganguillet and Kutter Formula
where, n = manning’s coefficient.
HYDRAULICALLYefficient channel sections
A = (B + ny) y = Constant
(ii) The trapezoidal channel should be part of regular hexagon.
(iii) The side slopes should be 60° with the horizontal.
(iv) Half top width is equal to one of the sloping sides
(c) Triangular Section
(i) q = 45°
(ii)
(d) Circular Section
Case 1 : Condtion for maximum discharge :
y = depth of flow
(i) y » 0.95 D and
(ii) hydraulic radius, R » 0.29 D
Case 2 : Condition for maximum mean velocity
(i)y » 0.81D
(ii)R » 0.30D
Basic Assumptions of Gradually Varied Flow Analysis
(i) The pressure distribution at any section is assumed to be hydrostatic.
(ii) The resistance to flow at any depth is given by the corresponding uniform flow equation, such as Manning’s formula with the condition that the slope term to be used in the equation is energy slope and not the bed slope.
Dynamic Equation of GVF
Classification of Water Surface Profiles
M Mild slope y n > yc
C Critical slope yn = yc
S Steep slope yn < yc
H Horizontal So = O
A Adverse So < O
RAPIDLY VARIED FLOW (RVF)
Hydraulic Jump
From specific force curve we can find the sequent depths y_{1} and y_{2} for a given discharge in a given horizontal channel.
Condition for Critical Flow :
Hydraulic Jump in a rectangular channel :
(a) Sequent depth ratio
F_{1} = Froude number at (i)
(b) Energy Loss
(i) EL = E1 – E2
(ii)
(c) Height of Jump = y_{2} – y_{1 }
(d) Length of jump = 5 to 7 times Height of Jump
(e) Ratio of energy loss to initial energy :
Classification of Jumps
Type F_{1} 
Undular Jump 1 – 1.7 Weak Jump 1.7 – 2.5 Oscillating Jump 2.5 – 4.5 Steady Jump 4.5 – 9 Stronger choppy > 9.0 
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1. What is open channel flow in mechanical engineering? 
2. What are the different types of open channel flow? 
3. How is flow rate calculated in open channel flow? 
4. What are the factors that affect open channel flow? 
5. What are some applications of open channel flow in mechanical engineering? 

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