STEADY UNIFORM FLOW IN OPEN CHANNEL

Transcription

1 11/4/018 School of Environmental Engineering STEY UNIFORM FLOW IN OEN CHNNEL ZULKRNIN BIN HSSN COURSE OUTCOMES CO1: ble to analyze and design the steady flow in pipeline (O1) CO: ble to analyze and design the steady flow in open channel (O1) CO3: ble to apply a dimensional analysis of a physical system incorporating many variables (O) CO4: ble to conduct and demonstrate open channel experiments (O4) OUTLINES (WEEKS 9 & 10) Steady Uniform Flow in Open Channel Classification of flow, Roughness equation, Open channel design INTROUCTION OEN CHNNEL Open-channel flow is a flow with a free surface touching an atmosphere, like a river, canal or a flume. Mainly governed by gravity (i.e. channel bed slope). Open channel hydraulics is of great importance in civil engineers Channels constructed for water supply, irrigation, drainage, and Sewers, culverts, and Tunnels flowing partially full; and Natural streams and rivers. Muda River (Kedah & enang) Klang River (Selangor & Kuala Lumpur) Muda River near to Sungai etani is overflow due to heavy rainfall (image from StarTV, 017) 1

2 11/4/018 CLSSIFICTION OF OEN-CHNNEL Natural Channels Natural open channels include all channels that exist naturally on the earth. They are generally very irregular in shape. CLSSIFICTION OF OEN-CHNNEL rtificial Channels rtificial open channels are the channels develops by human. They are usually designed with regular geometric shapes. Sg Sedim (Kedah) Concrete drainage Swale (USM, enang) IE N OEN CHNNEL FLOWS ipe Flow The liquid completely fills the pipe and flow under pressure. The flow in a pipe takes place due to difference of pressure (pressure gradient), The flow in a closed conduit is not necessarily a pipe flow. Open Channel Flow Flow takes place due to the slope of the channel bed (due to gravity). The flow must be classified as open channel flow if the liquid has a free surface. ipe Flow HGL = hydraulic grade line EGL = energy grade line WSL = water surface line ipe Flow: WL = HGL = pressure head + head = (/y) + h Velocity head = V /g E = HGL + velocity head 1 ρg + z 1 + v 1 g h L = E E 1 ipe Flow HGL = hydraulic grade line EGL = energy grade line WSL = water surface line Open-Channel Flow Open-Channel Flow: WSL = head = y + z Velocity head = V /g E = WSL + velocity head y 1 + z 1 + v 1 g CLSSIFICTIONS OF OEN CHNNEL FLOW h L = E E 1

3 11/4/018 CLSSIFICTION BSE ON THE TIME CRITERION 1. Steady Flow (time independent) (discharge and water depth do not change with time) CLSSIFICTION BSE ON THE SCE CRITERION 1. Uniform flow (are mostly steady) (discharge and water depth remains the same at every section in the channel) Where, V is the velocity, Q is the discharge, y is the water depth, and t is the time.. Unsteady Flow (time dependent) (discharge and water depth at any section change with time) Uniform flow conditions are commonly encountered in practice in long straight sections of channels with constant slope, constant roughness, and constant cross section. The flow depth in uniform flow is called the normal depth y n, which is an important characteristic parameter for open-channel flows. CLSSIFICTION BSE ON THE SCE CRITERION (CONT ) Values showing isovelocity contours. Non-uniform Flow (or called as Varied Flow) (discharge and water depth change at any section in the channel) a) Gradually varied flow (GVF) where the depth of the flow changes gradually along the length of the channel. b) Rapidly varied flow (RVF) where the depth of flow changes suddenly over a small length of the channel. Reynolds number (Laminar and Turbulent): where υ = verage velocity of flow, R = hydraulic radius, and v = Kinematic viscosity of the fluid. If N R < 500, the flow is laminar and N R > 000, it is turbulent. Froude number (Sub or Super-Critical): For rectangular Open Channel Laminar - Uniform Steady Turbulent - Hydraulic Jump Where, y h called the hydraulic depth and T is the width of the free surface of the fluid at the top of the channel. If N F < 1, it is sub-critical flow, and N F > 1, it is supercritical. Classifications of Open Channel Flow 3

4 11/4/018 UNIFORM FLOW IN OEN CHNNEL UNIFORM FLOW IN OEN CHNNEL Uniform flow in an open channel must satisfy the following main features: 1. The water depth y, flow area, discharge Q, and the velocity distribution V at all sections throughout the entire channel length must remain constant.. The slope of the energy gradient line (S e ), the water surface slope (S ws ), and the channel bed slope (S 0 ) are equal. S e = S ws = S 0 UNIFORM FLOW USING CHEZY S FORMUL ϴ UNIFORM FLOW USING CHEZY S FORMUL (CONT ) If F 1 =F (due to hydrostatic forces at ends) and sin ϴ = tan ϴ = S o W 1 Wsinϴ + F 1 F F f = 0 This is possible when the gravity force (W sin q) component equal the resistance to the flow (F f ) Wsinϴ + F 1 F F f = 0 W W 1 = W x cos (90- ϴ) = W x sin (ϴ) W = γv = γl γlsinθ γls o Hence, γls o + 0 (Kv )L = 0 v = γ K S o F f = τ o L=(Kv )L Where, τ o is the resisting force per unit area of channel and K is constant of proportionality C = v = UNIFORM FLOW USING CHEZY S FORMUL (CONT ) γ K γ K S o R h = = hydraulic radius = Chezy constant (Chezy s resistance factor) Hence, v =C R h S o = Chezy s Formula UNIFORM FLOW USING MNNING S FORMUL Correlation of the Chezy s equation and Manning s coefficient, n: C = 1 n R 1 6 h where n is the Manning s coefficient for the channel roughness Substituting into Chezy s equation: v = 1 R n h 3S 1 or Q = 1 R n h 3S 1 Where, v is the flow (m/s), R h is the hydraulic radius (m), and S is the slope (m/m). 4

5 Normal Flow Flood Normal Flow 11/4/018 Typical design values of n are listed in Table 14.1 for materials commonly used for artificial channels and natural streams. The roughness of the flood plains will be different (generally rougher) than that of the main channel Q = 3 1R R + 3 3R 3 n 1 n n 3 1 S o EXMLE 1 etermine the hydraulic radius, R of the triangular section sd shown in the Figure. m 4m 5

6 11/4/018 EXMLE Water floes in the canal as shown in the Figure. The bottom drops 0.4m per 305m of length. The canal is lined with new finished concrete. etermine, a) The flow rate, and b) The Froude number for this flow. m 4m EXMLE 3 Calculate the minimum slope on which the channel shown in Fig must be laid if it is to carry m 3 /s of water with a depth of 0.61 m. The sides and bottom of the channel are made of formed, unfinished concrete. m 4m EXMLE 4 Water flow along the drainage canal having the properties shown in the Figure. The bottom slope is Estimate the flowrate when the depth is 0.4m n 1 = 0.00 n 3 = n = m 0.9m 0.6m 0.9m 6

7 11/4/018 HYRULIC EFFICIENCY OF OEN CHNNEL SECTIONS HYRULIC EFFICIENCY OF OEN CHNNEL SECTIONS section of a channel is said to be most economical when the cost of construction of the channel is minimum. But the cost of construction of a channel depends upon the excavation and the lining. To keep the cost down or minimum, the wetted perimeter, for a given discharge, should be minimum. This condition is utilized for determining the dimensions of economical sections of different forms of channels. HYRULIC EFFICIENCY OF OEN CHNNEL SECTIONS (CONT ) Q V C R S C h e 1 S const.* e ECONOMICL RECTNGULR CHNNEL B, B d should be minimum for a given area; 0 d d B B 0 d B R h R B 4 h B So, the rectangular channel will be most economical when either: the depth of the flow is half the width, or the hydraulic radius is half the depth of flow. (Bn ) ECONOMICL TREZOIL CHNNEL B B 1n ( n ) 1n d 0 d n d 1 n n 0 d (Bn) B n 1n n or B B n ( B n ) B n Rh ( ) ( B n ) Rh 1n n Bn 1n 7

8 11/4/018 ECONOMICL TREZOIL CHNNEL (CONT ) Bn 1n B ( 1 n n) BBn( Bn) B n n 1 n ( n ) 1n n Now, from equations: ( B n ) B n d dn n 1 n ECONOMICL TREZOIL CHNNEL (CONT ) 0 d 4 [( 1 n ) *( n) 1] dn 1 4n 1 n n n 1 tanq q The best side slope is at 60 o to the horizontal, i.e.; of all trapezoidal sections a half hexagon is most economical. However, because of constructional difficulties, it may not be practical to adopt the most economical side slopes. Some book (Crowe, John Wiley & Son) 45, indicate real work for less excavation cost. 60 squaring both sides 4( ) 4 ( 1 n n) CONCLUSION efinition of open channel flow ifferences of pipe flow vs open channel flow Classification of open channel ble to design steady flow in open channel using the Chezy and Manning s equations Simulate velocity or discharge esign open-channel (dimension or slope) ble to design with considering the economical section of every channel shape. 8