HYDRAULIC STRUCTURES Hydraulic structures form part of most major water engineering schemes e.g. irrigation, water supply, drainage, sewage networks and treatment, hydropower etc. Hydraulic structures are classified as follows: a) Flow measuring structures e.g. weirs and flumes b) Regulation structures e.g. gates and valves c) Discharge structures e.g. spillways 1. Rectangular sharp crested weir The primary purpose of a weir is to measure discharge. A y1 U12/2g P1/ρg h1 crest Z1 1 A nappe Z2 2 The simplest method of developing a numerical model which represents a weir is to use the Bernoulli equation as the starting point applied along one streamline (due to uneven distribution of volume) Total energy of streamline A-A at 1 At section 2, the liquid passes over the weir and forms an over spilling jet whose lower nappe is exposed to the atmosphere. Total energy at 2 Assumptions Velocities upstream are uniform and steady therefore pressure there varies according to the hydrostatic equation Pressure throughout nappe is atmospheric therefore P2 = 0 Effects of viscosity and surface tension are negligible From the energy principle H1 = H2 The ideal discharge through an elemental strip of width b and depth δZ is; δQideal = Assumptions i. ii. Elevation of water surface at section 2 is the same as that at1 (elevation of free surface is horizontal) Datum is raised to crest of weir Thus integrating to obtain Q at weir Integrating with respect to Z2 For practical purposes h1 >>>> therefore equation 1.4 reduces to: The streamlines approaching the weir converge downstream of the weir. This causes a contraction or venacontracta which implies that actual discharge is less than Q ideal and account must be taken of this by the coefficient of discharge Cd. Hence; 2. Triangular / Vee – Notch weir (sharp crested) Rectangular weirs have the disadvantage of loss of accuracy at low flows. The vee – notch weir overcomes this problem since b varies with height and therefore offers greater sensitivity. However the vee – notch weir is inappropriate for large flows because its construction would be very uneconomical. The theory and assumptions for the vee – notch weir are the same as for the rectangular sharp crested weir. δQideal = b θ Z δZ b is not constant b = f (θ, Z) b = 2 Z2 tan ( Integrating; The approach velocity, U1 is almost always negligible for vee – notch weirs in view of the smaller discharges for which they are designed. Therefore: From which; 3. Broad Crested Weir The broad crested weir is an obstacle and the water upstream of the weir needs to gather just enough specific energy to overcome the obstacle. Thus given a sufficient weir height ∆Z the flow over the weir will be critical. For the derivation of the equation of flow over a broad crested weir, refer to earlier notes on open channel hydraulics; section 1.19.1. 4. Venture Flume This refers to a device in which the flow is locally accelerated due to a streamlined lateral contraction within the channel sides. Flumes are usually designed to achieve critical flow in the narrowest section (throat). Flumes are especially applicable where depositions of solids must be avoided e.g. in sewage works and irrigation canals. Deposition at weirs results in gradual change of the weir coefficients. Additionally the use of weirs results in a relatively large head loss. For the derivation of the equation of flow in a venture flume, refer to earlier notes on open channel hydraulics; section 1.19.3. 5. DAMS Dams are interruptions in the flow of rivers, streams etc. that result in impounded reservoirs. There are 4 main types of dams; Gravity Dam: usually made from concrete and masonry and depends on its weight for stability. Arch Dams: transmit most of the horizontal thrust of the water behind them to the abutments by arch action and have thinner cross-sections compared to gravity dams. Buttress Dam: consists of a sloping membrane which transmits the water load to a series of buttresses at right angles to the axis of the dam. There are several types of buttress dams; the most important being the flat slab and the multiple arch. Earth Dams: These are embankments of suitable rock or earth with provision for controlling seepage by means of an impermeable zone and an upstream blanket. These earth dams are common in dry areas. 6. SPILLWAYS The majority of impounding reservoirs are formed as a result of construction of a dam. There are times when the reservoir is full and the stream flow exceeds the demand. The excess water must therefore be discharged safely from the reservoir. In most cases, to allow the water to simply overtop the dam would result in failure of the structure. For this reason, carefully designed overflow passages are incorporated as part of the design. The spillway must be sufficient to accommodate large flood discharges likely to occur in the life of a dam. Because of the high velocities of flow often attained on spillways, some form of energy dissipation and a scour prevention system at the base of the spillway must be provided for. This often takes the form of a stilling basin. Gravity (Ogee) Spillways The discharge relationship for a spillway is of the same form as other weirs. L Hd h + Hd Where; Q = discharge Cw = coefficient L = Length of crest h = head on spillway (vertical distance from crest of spillway to reservoir level) Vo = approach velocity Hd = height of spillway related to the downstream floor level Siphon Spillway Head Water Datum 1 3 Crown/prime 2 Tail Water If a large capacity is not necessary and space is limited; the siphon spillway could be a practical selection. A siphon spillway is a structure in which the flow is below atmospheric pressure Applying Bernoulli’s equation to points 1, 2 and 3 in the above figure But P1 = P2 = 0 (pressure is atmospheric) From (i); But V2 = V3 (same cross-sectional area of conduit) Q = A2V2 = A3V3 Negative pressure The Stilling Basin Stilling basin and check weir The flow discharged from the spillway outlet is usually highly supercritical. If this were left uncontrolled, severe erosion at the toe of the dam would be experienced. This flow is controlled by a dissipating or stilling device. A typical device of this nature is the stilling basin. It consists of a short level apron at the foot of the spillway. It must be constructed of concrete to resist scour. The function of the basin is to decelerate the flow sufficiently to ensure the formation of a hydraulic jump within the basin. The jump dissipates much of the energy and returns the flow to the subcritical state. 7. FLOW UNDER A VARYING HEAD Q1(t) A ∆h h1 h(t) Q(t) a Q = a. Velocity. Cd From Torricelli; velocity Vt = Thus Q(t) = a. Cd. (i) Volume of water in the tank; V = Ah Change in volume; dV = Adh Velocity in tank; Vtank = Q(t) = A. Vtank = Equating (i) to (ii) If there is an inflow Q1(t) then dV = - Adh + Q1(t) In general; (ii) HOMEWORK 1. A pipeline 1000m long, 100mm diameter with a roughness coefficient 0.0186 discharges water from a tank having a cross-sectional area of 1000m2. Find the time taken for the water level to fall from 20m to 15m above the pipe inlet (minor losses are 1.5 ) 2. A pyramidal vessel has a 15cm orifice at the bottom. If the water level in the vessel is 1.8m at the beginning, find the time taken for the level to fall to 90 cm given that C d = 0.62. Assume a square cross-section.