Flow over Weir

Introduction A weir is an opening in the sidewall of a tank at top. The stream of liquid coming out the weir is known as a nappe, sheet or vein. There is no difference between a notch and weir except that the former is a small structure and has sharp edges. A weir generally an overflow structure, with a broad crest, build across an open channel. The terms air and weirs are used synonymously in general. The top of weir wall over which the liquid flows is known as the sill or crest. The head under which the weir is discharging is measure from the crest to the free surface.
A weir or notch is generally used for measuring the flow of liquids. In this experiment, we ar using the rectangular weir and triangle weir. Rectangular weir and triangular weir (v-notch) ore often used in water supply, wastewater and sewage system. They consists of a sharp edge plane with rectangular and triangular profile for the water flow. Broad-crested weirs can be observed in dam spillways where the broad edge is beneath the water surface across the entire stream. Flow measurement installations ith broad-crested weirs will meet accuracy requirement only if they are calibrated. objective To determine the characteristics of open channel flow over; * A rectangular notch * A triangular (v-notch) * To determine values of the discharge coefficient for both notches Method General features of the flow can be determined by direct observation. Discharge coefficient values can be determined from measurements of the height of the free surface of water above the notch base and corresponding volume flow rate Equipment In order to complete the experiment, we need a number of pieces of equipment * The F1-10 haudralics bench which allows us to measure flow by timed volume collection * The F1-13 stilling baffle The F1-13 rectangular and Vee notch * Vernier Height Gauge (supplied with F1-13) * Stopwatch * Spiril level 4 4 2 2 5 5 8 8 7 7 6 6 3 3 1 1 Figure 1: Flow over Weirs – Figure 2: Flow over Weirs – vee notch weir rectangular notch weir 1 1 5 5 2 2 6 6 Hydraulics BenchBasket of glass spheres 3 3 Weir channelVolumetric measuring tank 4 4 (V) Vee notch weir7 7 Rectangular weir Hook & point gauge Hook Gauge and Scale8 8 There are different shapes of weirs that can be used to measure the volumetric flow rate. These shapes with their dimension are shown in fig 3 below. Figure 3: Details of weirs
Technical Data The following dimension from the equipment are used in the appropriate calculation. If required these values may be checked as part of the experimental procedure and replace with your own measurements. * Width of rectangular notch, b= 0. 030 * Angle of vee notch, o=90 degree Theory Because the depth of flow above the base of notch is related to the volume flow rate through it, the notch forms a useful flow measurement device. The classical result for flow over notch are obtained by an application of the Bernoulli equation, from a point well up stream to a point just above the notch.

This approach requires a number of very substantial assumptions and it yields the following results: For Rectangular Notch, the formula is given by; Qt=Cd23b(2g)H32 For Vee-notch, the formula is given by; Qt=Cd815tan(? 2)(2g)H52 Where; Qt= Volume flow rate H = height above notch base B = width of rectangular notch ? = angle of the vee in triangular notch; Cd= the discharge coefficient, which has to be determined by experiment These can be rearrange to give; Cd=3Qt2b2gH32 For rectangular notch Cd=15Qt8tan? 22gH52 Foe vee notch. Discussion.
From the experiment, we are about to determine the discharge coefficient of the both rectangular and the triangular notches. The discharge coefficient for the rectangular notch are influence by its H and also its volumetric flow rate while the triangular notch are influence by its o, H and also its volumetric flow rate. From the result, we can see that the volumetric flow rate of both notches are increase. This showed show that the water outflow increase as the H increased. These is suppose to happened as, the water level increase, the Water outflow from the notch increase over the time.
But from discharged coefficient, we can see that the value of both notches are not stable. This may be from the friction at the head of the notches during the starter of experiment. The friction will affect the time taken to collect 1liter of water for V-notch and 5 litre of water for the Rectangle notch. Thus it will effect the volumetric flow rate and also the discharge coefficient as the volumetric flow rate influence the value of Cd. The aim of this experiment is to determine the value of the discharge coefficient for both notches of rectangular notch and also triangular (V-notch).
The discharge coefficient values can be determine from the measurements of the height of free surface of water above the notch base and corresponding volume flow rate For discharge coefficient of Rectangular Notch, the formula is given by; Cd=3Qt2b2gH32 For discharge coefficient of V-notch, the formula is given by; Cd=15Qt8tan? 22gH52 In comparison, for rectangular notch, the theoretical value of its discharge coefficient, Cd, is ——. However, the experimental value of Cd turns out to be 2. 31. Based on experiment that we conducted, the percentage error for rectangular notch is–.
This is due to some errors that ccur during experiment. For example parallax error. However, for V-notch, the theoretical value is —, but theoretical value is—. There is not much of a difference between its theoretical value and actual value. This mean that the flow is laminar, and not much energy is loss through friction. The derivation of values are contributed by the error during handing the experiment, if we take it as overall error, most of error occurred when step of taking the height started. First, we have to careful about the height of datum. For convenience, is is advice that to take your first datum as zero.
Other than that, it is also advice that th time should be taken 3 times so that we can take the average so that the error can be minimize. Besides, The theory does not put energy loss or viscosity of the water flow into consideration, but it only depends on the flow rate, the width of the notches and height of the notches. However, in reality, water currents or flow rate may not be constant all the time and it is difficult to maintain the water level height above the notches as what he want. The cross section area over the weir with flowing water at lower rates is small compare to high rates.
This is because at lower flow rates, the time for collection of water varies a lot compare to higher flow rates. It require a longer time to collect a specific amount of water to measure the flow rate at lower flow rate due to viscosity of water. Moreover, energy is conserved due to slower speed of flow of water. At higher flow rates, water flowing may already have the energy to create a constant water flow. Whereas at an even higher rat, water flow is difficult to control in order for it to be in constant height above notch base because the water current is too high.

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