Nce 403 mod unit1
- 1. BY MODASSAR ANSARI 2nd Year Department of civil Engineering SUBJECT- HYDRAULICS & HYDRAULIC MACHINES SUBJECT CODE-NCE 403 01/07/17MODASSAR ANSARI 1
- 3. Difference between open channel flow and pipe flow, geometrical parameters of a channel. Continuity equation for steady and unsteady flow. Critical depth, concepts of specific energy and specific force, application of specific energy principle for interpretation of open channel phenomena, flow through vertical and horizontal contractions. 01/07/17MODASSAR ANSARI 3
- 4. Liquids are transported from one location to another using natural or constructed conveyance structures. The cross section of these structures may be open or closed at the top. The structures with closed tops are referred to as closed conduits and those with the top open are called open channels. For example, tunnels and pipes are closed conduits whereas rivers, streams, estuaries etc. are open channels. The flow in an open channel or in a closed conduit having a free surface is referred to as free-surface flow or open-channel flow. 01/07/17MODASSAR ANSARI 4
- 5. Liquid (water) flow with a Free surface (interface between water and air) relevant for ◦ natural channels: rivers, streams ◦ engineered channels: canals, sewer lines or culverts (partially full), storm drains of interest to hydraulic engineers ◦ location of free surface ◦ velocity distribution ◦ discharge – Depth relationships ◦ optimal channel design 01/07/17MODASSAR ANSARI 5
- 6. Based on their existence, an open channel can be Natural channels such as streams, rivers, valleys , etc. These are generally irregular in shape, alignment and roughness of the surface. Artificial channels are built for some specific purpose, such as irrigation, water supply, wastewater, water power development, and rain collection channels. These are regular in shape and alignment with uniform roughness of the boundary surface. 01/07/17MODASSAR ANSARI 6
- 7. Based on their shape, an open channel can be prismatic or non- prismatic: Prismatic channels: a channel is said to be prismatic when the cross section is uniform and the bed slop is constant. Non-prismatic channels: when either the cross section or the slope (or both) change, the channel is referred to as non- prismatic. It is obvious that only artificial channel can be prismatic. The most common shapes of prismatic channels are rectangular, parabolic, triangular, trapezoidal and circular. 01/07/17MODASSAR ANSARI 7
- 9. Uniform Flow ◦ Discharge-Depth relationships Channel transitions ◦ Control structures (sluice gates, weirs…) ◦ Rapid changes in bottom elevation or cross section Critical, Subcritical and Supercritical Flow Hydraulic Jump Gradually Varied Flow ◦ Classification of flows ◦ Surface profiles 01/07/17MODASSAR ANSARI 9
- 10. Steady and Unsteady ◦ Steady: velocity at a given point does not change with time ◦ Uniform, Gradually Varied, and Rapidly Varied Uniform: velocity at a given time does not change within a given length of a channel Gradually varied: gradual changes in velocity with distance Laminar and Turbulent Laminar: flow appears to be as a movement of thin layers on top of each other Turbulent: packets of liquid move in irregular paths 01/07/17MODASSAR ANSARI 10
- 11. Steady: A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time. unsteady: If at any point in the fluid, the conditions change with time, the flow is described as unsteady. (In practise there is always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady. 01/07/17MODASSAR ANSARI 11
- 13. Channel Geometry Characteristics • Depth, y • Area, A • Wetted perimeter, P • Top width, T Hydraulic Radius, Rh = Area / Wetted perimeter Hydraulic Depth, Dh = Area / Top width 01/07/17MODASSAR ANSARI 13
- 14. Geometric parameters 01/07/17MODASSAR ANSARI 14 P A Rh = Hydraulic radius (Rh) Channel length (l) Roughness (ε)
- 15. This principle is know as the conservation of mass and we use it in the analysis of flowing fluids. The principle is applied to fixed volumes, known as control volumes (or surfaces), like that in the figure below. For unsteady flow Mass entering per unit time = Mass leaving per unit time + Increase of mass in the control volume per unit time For steady flow Mass entering per unit time = Mass leaving per unit time 01/07/17MODASSAR ANSARI 15
- 16. Conservation of energy ◦ losses due to conversion of turbulence to heat ◦ useful when energy losses are known or small ◦ Must account for losses if applied over long distances Conservation of Momentum ◦ “losses” due to shear at the boundaries ◦ useful when energy losses are unknown 01/07/17MODASSAR ANSARI 16
- 17. Given a long channel of constant slope and cross section find the relationship between discharge and depth Assume Steady Uniform Flow prismatic channel (no change in with distance) Use energy, Momentum, empirical or Dimensional Analysis? What controls depth given a discharge? Why doesn’t the flow accelerate? 01/07/17MODASSAR ANSARI 17
- 18. 01/07/17 MODASSAR ANSARI 18 θ W θ W sin θ ∆x a b c d Shear force energy grade line Hydraulic grade line Shear force =________ 0sin =∆−∆ xPxA oτθγ θγτ sin P A o = hR= P A θ θ θ sin cos sin ≅=S W cos θ g V 2 2 Wetted perimeter = __ Gravitational force = ________ Hydraulic radius τoP ∆ x P γA ∆x sinθ o hR Sτ γ=
- 19. The sum of the depth of flow and the velocity head is the specific energy: 01/07/17MODASSAR ANSARI 19 g V yE 2 2 += if channel bottom is horizontal and no head loss 21 EE = y - _______ energy g V 2 2 - _______ energy For a change in bottom elevation 1 2E y E− ∆ = xSExSE o ∆+=∆+ f21 y potential kinetic
- 20. 01/07/17MODASSAR ANSARI 20 in a channel with constant discharge, Q 2211 VAVAQ == 2 2 2gA Q yE += g V yE 2 2 += where A=f(y) Consider rectangular channel (A = By) and Q = qB 2 2 2gy q yE += A B y 3 roots (one is negative) q is the discharge per unit width of channel How many possible depths given a specific energy? ____2
- 22. Specific force is the sum of the pressure force and momentum flux per unit weight of the fluid at a section. Specific force is constant in a horizontal frictionless channel. By plotting the depth against the specific force for a given channel section and discharge, a specific force curve is obtained. 01/07/17MODASSAR ANSARI 22
- 23. 0 1 2 3 4 0 1 2 3 4 E y 01/07/17MODASSAR ANSARI 23 2 2 2gy q yE += 1 2 E1 = E2 sluice gate y1 y2 eGL as sluice gate is raised y1 approaches y2 and e is minimized: Maximum discharge for given energy.
- 24. P A 01/07/17MODASSAR ANSARI 24 T dy y T=surface width Find critical depth, yc 2 2 2gA Q yE += 0= dy dE dA =0 dE dy = = 3 2 1 c c gA TQ = Arbitrary cross-section A=f(y) 2 3 2 Fr gA TQ = 2 2 Fr gA TV = dA A D T = Hydraulic Depth 2 3 1 Q dA gA dy − Tdy More general definition of Fr
- 25. 01/07/17MODASSAR ANSARI 25 2 2 1 1 2 2 1 1 2 2 2 2 L p V p V z z h g g α α γ γ + + = + + + 2 2 1 2 1 2 2 2 o f V V y S x y S x g g + ∆ + = + + ∆ Turbulent flow (α ≅ 1) z - measured from horizontal datum y - depth of flow Pipe flow energy equation for Open Channel Flow 2 2 1 2 1 2 2 2 o f V V y S x y S x g g + + ∆ = + + ∆ From diagram on previous slide...
- 26. 01/07/17MODASSAR ANSARI 26 ( ) 0 1 1 ln y v y V gdS dκ = + + ÷ 1 ln y d − = At what elevation does the velocity equal the average velocity? For channels wider than 10d 0.4κ ≈ Von Kármán constant V = average velocity d = channel depth 1 y d e = 0.368dV
- 27. 01/07/17MODASSAR ANSARI 27 2g V2 1 1α 2g V2 2 2α xSo∆ 2y 1y x∆ L fh S x= ∆ ______ grade line _______ grade line velocity head Bottom slope (So) not necessarily equal to eGL slope (Sf) hydraulic energy
- 28. 01/07/17MODASSAR ANSARI 28 yc T Ac 3 2 1 c c gA TQ = qTQ = TyA cc = 3 2 33 32 1 cc gy q Tgy Tq == 3/1 2 = g q yc 3 cgyq = Only for rectangular channels! cTT = Given the depth we can find the flow!
- 29. Rectangular Channels 01/07/17MODASSAR ANSARI 29 3/1 2 = g q yc cc yVq = = g yV y cc c 22 3 g V y c c 2 = 1= gy V c c Froude number velocity head = because g Vy cc 22 2 = 2 c c y yE += Eyc 3 2 = forcegravity forceinertial 0.5 (depth) g V yE 2 2 += Kinetic energy Potential energy
- 30. Minimum energy for a given q ◦ Occurs when = ◦ Fr=1 Critical flow ◦ Fr>1 = super critical ◦ Fr<1 = sub critical 01/07/17MODASSAR ANSARI 30 dE dy 0 1 2 3 4 0 1 2 3 4 y 2 2 2 c cV y g = 3 T Q gA =3 c q gy =c c V Fr y g =
- 31. Characteristics ◦ Unstable surface ◦ Series of standing waves 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 ◦ ___________________________________________ 01/07/17MODASSAR ANSARI 31
- 32. The channel contraction may comprise of a reduction in the channel width, raising the channel bottom, or a combination of the two An abrupt change in the cross section is called a sudden contraction, whereas if the change occurs over a distance, it is called a gradual contraction. 01/07/17MODASSAR ANSARI 32