1. Reynolds’s number
For open channel flow of any cross section:
Re = VR / ν
For flow in pipe of diameter D
Re = VD / ν
Where,
Re : Reynold’s Number (Dimensionless)
V : Cross- sectional mean velocity in m/sec
D : Diameter of pipe
R : Hydraulic Radius (A/P) in m
ν : Kinematic Viscosity in m2/sec
P : wetted perimeter in m
Re gives a dimensionless number, which is called Reynold’s number. It determines whether the flow is laminar or turbulent. It is found that in open-channel, flow is laminar when Re ≤ 500 and turbulent when Re > 1000,
whereas in pipe flow, the flow is laminar when Re ≤ 2000 and flow is turbulent when Re > 4000.
2. Specific Energy Es: It is defined as the energy of the flow with reference to the channel bed as the datum.
Es = Y+ V2/2g
Where,
Y : Depth of water
V : Mean cross section velocity
g : Acceleration due to gravity
Es : Specific energy
3. Froude number
Fr = V / (gDm) 1/2
Where,
Fr : Froude number (Dimensionless)
V : Mean velocity in m/sec
Dm : Hydraulic mean depth in m (cross section area of flow/width of the channel)
g : acceleration due to gravity in m/sec2
4. Critical flow: The general equation for Critical flow:
Q2B/gA3 = 1
Where,
Q : Discharge, m3/sec
B : Width of water surface, m
A : Cross section area of water flow, m2
g : Acceleration due to gravity, m/sec2
For a fixed discharge, the specific energy is minimum at critical depth. For all other values of specific energy, there are two alternate depths, one is subcritical depth when flow depth is greater than critical depth and other is supercritical depth when flow depth is less than critical depth. In steady Uniform flow, the flow depth is known as normal depth. The slope at normal depth is said to be mild slope, at critical depth the slope is said to be critical slope and at supercritical depth, the slope is known as steep slope
5. Manning’s Equation
Manning’s Equation for uniform gravity flow:
V = (1/n) x R2/3x S1/2
Manning’s Equation for uniform flow in terms of discharge:
Q = (1/n) x (A5/3/P2/3) x S1/2
For circular section:
Q = (0.3118/n) xD8/3x S1/2
Where,
V : Velocity of flow in m/sec
R : Hydraulic radius (Flow area (A)/Wetted perimeter (P)) in m.
S : Slope of Hydraulic Gradient
n : Manning’s coefficient of roughness for Channels / conduits
P : Wetted perimeter in m
A : Area of cross section of water area in m2
Q : Discharge in m3/sec
D : Diameter of pipe in m
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Urban Infrastructure and Network Study notes for M. plan Sem-III
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