ERT 349 SOIL AND WATER ENGINEERING Open Channel Flow Siti Kamariah Md Sa’at PPK Bioproses, UniMAP

Topic Learning Outcomes At the end of this topic, student should be able to: Design the open channel in uniform and non-uniform flow Design the most efficient section channel Calculate the flow in open channel

Introduction “Occur when free water surface in the channel is at atmosphere pressure” Example of open channel: Rivers and streams Drainage Ditches Irrigation canal

Application Interest to hydraulic engineers location of free surface velocity distribution discharge - stage (depth) relationships optimal channel design

Types of channels Man made Natural Channel designed and made by human Examples: earth or concrete lined drainage and irrigation Prismatic channel (no change in geometry with distance) Natural Examples: River and streams Changes with spatial and temporal (non prismatic channel)

TEMPORAL (Time) SPATIAL (Space)

Types of flow Based on temporal (Time, t) and Spatial (Space,x) Time Criteria Steady flow (dy/dt = 0). Water depth at one point same all the time. (Flow constant with time) Unsteady flow (dy/dt ≠ 0). Water depth changes all the time. (Flow variation with time) Space criteria Uniform flow (dy/dx = 0). Water depth same along the whole length of flow. Non-uniform flow (dy/dx ≠ 0). Water depth changes either rapidly or gradually flow

Steady and Non-Steady Flow Flow Rate Steady Unsteady Time Steady and Non-Steady Flow

Uniform and Non-Uniform Flow V1 = V2 A1 = A2 V1 V2 V1 A1 A2 V2 A2 A1 Non-Uniform Flow Uniform Flow

States of flow Flow vary with following forces: Viscous Inertia Gravity Defines by Reynolds number (Re) and Froude numbers (Fr)

Reynolds Number To determine: Laminar flow : Re < 500 (viscous > inertia) Transitional flow : 500 < Re < 1300 Turbulent flow : Re > 1300 (inertia > viscous)

Froude Number The Froude Number, Fr describes the following states of flow: Fr < 1 : flow is subcritical Fr = 1 : flow is critical ( inertia < gravity) Fr > 1 : flow is supercritical ( inertia > gravity)

Froude Number A flow is called critical if the flow velocity is equal to the velocity of a gravity wave having small amplitude. The flow is called subcritical flow, if the flow velocity is less than the critical velocity The flow is called supercritical flow if the flow velocity is greater than the critical velocity.

Critical Flow Characteristics Occurrence Used for flow measurements Unstable surface Series of standing waves Difficult to measure depth Occurrence Broad crested weir (and other weirs) Channel Controls (rapid changes in cross-section) Over falls Changes in channel slope from mild to steep Used for flow measurements Unique relationship between depth and discharge

Parameters of Open Channels Wetted Perimeter (P) :The Length of contact between Liquid and sides and base of Channel Hydraulic Mean Depth or Hydraulic Radius (R): If cross sectional area is A, then R = A/P. Depth of flow section (d) : depth of flow normal to the direction of flow.

Parameters of Open Channels Top width (T) : the width of channel section at the free surface. Hydraulic depth (D) : D = A/T Base slope (So) : So = tan θ

Parameters of Open Channels Freeboard: Vertical distance between the highest water level anticipated in the design and the top of the retaining banks. It is a safety factor to prevent the overtopping of structures. Side Slope (Z): The ratio of the horizontal to vertical distance of the sides of the channel.

Table 1: Maximum Canal Side Slopes (Z) Sand, Soft Clay 3: 1 (Horizontal: Vertical) Sandy Clay, Silt Loam, Sandy Loam 2:1 Fine Clay, Clay Loam 1.5:1 Heavy Clay 1:1 Stiff Clay with Concrete Lining 0.5 to 1:1 Lined Canals

M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008

Continuity Equation Inflow 1 2 A 3 Change in Storage Outflow 3a 3b Section AA Change in Storage Outflow 3a 3b The continuity equation simply says that inflow minus outflow is equal to change in storage. Inflow – Outflow = Change in Storage

Q = vA General Flow Equation Equation 1 Area of the cross-section (m2) Flow rate (m3/s) Avg. velocity of flow at a cross-section (m/s) Area of the cross-section (m2) The general flow equation we are all familiar with says that the flow rate, Q, is equal to the avg. velocity of the flow at a cross-section multiplied by the area of the cross-section. We are talking about the avg. flow rate of the cross-section here. In reality the flow velocity along a boundary such as the channel wall will be zero. Figure 4.2 in the book shows typical flow profiles for different channel cross sections.

Uniform flow in Open Channel

Uniform flow in Open Channel Energy lines i Water Surface Sw Flow yo So For uniform flow (in prismatic channel), i = Sw = So yo= normal depth for uniform flow only

Resistance Equation Chezy Equation Manning Equation By Antoine Chezy (France), 1768 Manning Equation By Robert Manning (Irish), 1889

Chezy Equation Introduced by the French engineer Antoine Chezy in 1768 while designing a canal for the water-supply system of Paris Because i = So, so

Chezy Equation where C = Chezy coefficient = L1/2/T (Unit m1/2/s) where 60 is for rough and 150 is for smooth

Manning Equation Most popular in for open channels around the world C = R1/6 / n SI Unit n = Manning roughness coefficient = T/L1/3 (Unit s/m1/3) T /L1/3 Dimensions of n? (English system) Bottom slope very sensitive to n

Manning roughness coefficient, n n = f (surface roughness, channel irregularity, stage...)

Example 1: Trapezoidal channel: Determine Q if yo = 2.6m. Bottom width = 3.0 m Side slope = 1: 1.5 Base slope = 0.0016 Manning coefficient = 0.013 Determine Q if yo = 2.6m.

M.Hanif Chaudry, Open Channel Flow 2nd Edition, Springer, 2008

Determination of yo If Q, So and n given or known and you need to estimate yo, direct calculation cannot give you answer. So there are another method can be use: Try and error Graphical Curves chart

Example 2: A rectangular channel with n = 0.017 with width 6 meter, base slope 0.0016 and to carry 10 m3/s flowrate. Determine yo with: Try and error Graphical Curves chart