Instruction Manual. Equipment for Engineering Education


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1 Equipment for Engineering Education Instruction Manual HM15007 Bernoulli s Principle Demonstrator GUNT Gerätebau GmbH PO Box 1125 D Barsbüttel Germany Phone (040) Fax (040)
2 Instruction Manual Puplication No A /95
3 Contents 1 Unit description 2 2 Performance of experiment 4 3 Assessment of experiment 6 31 Velocity Profile Venturi Tube 8 32 Pressure Distribution Venturi Tube Determining the Flow Rate Factor 12 4 Technical Data 13 1
4 1 Unit description The HM15007 is used to investigate Bernoulli s law The measurement object is a venturi tube with 6 pressure measurement points The 6 static pressures are displayed on a board with 6 water pressure gauges The overall pressure can also be measured at various locations in the venturi tube and indicated on a second water pressure gauge Measurement is by way of a probe which can be moved axially with respect to the venturi tube The probe is sealed by way of a compression gland Water is supplied either from the HM150 Fluid Mechanics Basic Module or from the laboratory mains The HM150 enables a closed water circuit to be constructed Possible experiments:  Demonstration of Bernoulli s law  Pressure measurements along venturi tube  Determination of flow rate factor K 1 Unit description 2
5 Components: Assembly board 2 Single water pressure gauge 3 Discharge pipe 4 Outlet ball cock 5 Venturi tube with 6 measurement points 6 Compression gland 7 Probe for measuring overall pressure (can be moved axially) 8 Hose connection, water supply 9 Ball cock at water inlet 10 6fold water pressure gauge (pressure distribution in venturi tube) 1 Unit description 3
6 2 Performance of experiment  Arrange the experimentation setup on the HM150 such that the discharge routes the water into the channel  Make hose connection between HM150 and unit  Open discharge of HM150  Set cap nut [1] of probe compression gland such that slight resistance is felt on moving probe Open inlet and outlet ball cock  Close drain valve [2] at bottom of single water pressure gauge  Switch on pump and slowly open main cock of HM150  Open vent valves [3] on water pressure gauges  Carefully close outlet cock until pressure gauges are flushed  By simultaneously setting inlet and outlet cock, regulate water level in pressure gauges such that neither upper nor lower range limit [4,5] is overshot or undershot 4  Record pressures at all measurement points Then move overall pressure probe to corresponding measurement level and note down overall pressure 5  Determine volumetric flow rate To do so, use stopwatch to establish time t required for raising the level in the volumetric tank of the HM150 from 20 to 30 litres 2 Performance of experiment 4
7 ATTENTION! The experimental setup should be arranged absolutely plane to avoid falsification of measurement results (use of spirit level recommended) For taking pressure measurements, the volumetric tank of the HM150 must be empty and the outlet cock open, as otherwise the delivery head of the pump will change as the water level in the volumetric tank increases 80 mm This results in fluctuating pressure conditions A constant pump delivery pressure is important with low flow rates to prevent biasing of the measurement results The zero of the single pressure gauge is 80 mm below that of the 6fold pressure gauge Allowance is to be made for this fact when reading the pressure level and performing calculations Both ball cocks must be reset whenever the flow changes to ensure that the measured pressures are within the display ranges 2 Performance of experiment 5
8 3 Assessment of experiment The measured values are to be compared to Bernoulli s equation Bernoulli s equation for constant head h: ρ + w = p 2 ρ + w = const p 1 Condition 1 Condition 2 Allowance for friction losses and conversion of the pressures p1 and p2 into static pressure heads h1 and h2 yields: p 1 : h 1 : w 1 : p 2 : h 2 : w 2 : h 1 + w 2 1 2g = h 2 + w 2 2 2g + h v Pressure at crosssection A1 Pressure head at crosssection A1 Flow velocity at crosssection A1 Pressure at crosssection A2 Pressure head at crosssection A2 Flow velocity at crosssection A2 ρ: Density of medium = constant for incompressible fluids such as water Pressure loss head h v 3 Assessment of experiment 6
9 The mass flow is constant in closed systems m 1 = m 2 m 1 m 2 Given m = V ρ : V 1 V 1 ρ = V 2 = V 2 Given V ρ = A w : A 1 w 1 = A 2 w 2 = V = const 3 Assessment of experiment 7
10 31 Velocity profile in venturi tube The venturi tube used has 6 measurement points The table below shows the standardised reference velocity w This parameter is derived from the geometry of the venturi tube w i = A 1 A i Point i reference velocity w Di [mm] A [m ] 1 28,4 6, ,5 3,97 1, ,0 1,54 4, ,2 2,32 2, ,2 4,60 1, ,4 6,33 1 Multiplying the reference velocity values with a starting value, the student can calculate the theoretical velocity values w calc at the 6 measuring points of the venturi tube At constant flow rate, the starting value for calculating the theoretical velocity is found as: w 1 = V A 1 The results for the calculated velocity w calc can be found in the following table 3 Assessment of experiment 8
11 The following values were determined for various flow rates: i h1 [mmws] h2 [mmws] h3 [mmws] h4 [mmws] h5 [mmws] h6 [mmws] hstat htotal hdyn wmes 0,420 0,626 1,826 1,320 0,852 0,594 wcalc 0,435 0,692 1,785 1,185 0,592 0,4355 hstat htotal hdyn wmes 0,396 0,594 1,715 1,250 0,816 0,671 wcalc 0,404 0,644 1,662 1,100 0,556 0,404 hstat htotal hdyn wmes 0,140 0,280 1,057 0,800 0,520 0,396 wcalc 0,262 0,418 1,073 0,715 0,362 0,262 t für 10 l V [l/s] 36,29 0,275 39,0 0,256 60,0 0,166 The table makes allowance for the following relationships Calculation of dynamic pressure head: h dyn = h tot 80mm h stat 80 mm must be subtracted, as there is a zeropoint difference of 80 mm between the pressure gauges The velocity w meas was calculated from the dynamic pressure w meas = 2 g h dyn 3 Assessment of experiment 9
12 Graphical representation The graph below illustrates the measured and calculated velocity profile along the venturi tube at a flow rate of 0,275 l/s The deviations can be attributed to inexact measurements w [m/s] Flow velocity 1,8 1,4 1,0 0,6 0,2 Calculated Measured Measurement points i on venturi tube 3 Assessment of experiment 10
13 32 Pressure Distribution Venturi Tube Graphical representation The pressure changes in the venturi tube can be represented in a graph directly: 400 Pressure Distribution Venturi Tube 350 htotal 300 hdyn in mm WC hstat hdyn Measuring Point The graph shows, that the equation h dyn = h tot 80mm h stat is fullfilled at every point in the venturi tube Furthermore, it becomes clear, that there is a slight overall pressure loss in the venturi tube 3 Assessment of experiment 11
14 33 Determination of Flow Rate Factor p:: A venturi tube can be used for flow rate measurements In comparison with orifice or nozzle, there is a far more smaller pressure loss during measurements of flow rate The pressure loss p between largest and smallest diameter of the tube is used as measure for the flow rate: V = K p The flow rate factor K is generally made available for the user by the manufacturer of a venturi tube If the flow rate factor is unknown, it can be determined from the pressure loss p:: V K = p The following table shows the pressure loss for various flow rates as well as the flow rate factor K V =0,275 l/s V =0,256 l/s V =0,166 l/s Measuring p K p K p [mm WC] K Point [mm WC] l [ s bar ] [mm WC] l [ s bar ] l [ s bar ] , ,1 65 2,1 3 The pressure loss is read off from the six tube manometer in mm water column and set in the equation as bar The flow rate can be used with unit l/s 3 Assessment of experiment 12
15 4 Technical Data Water multi tube manometer 6fold: 300 mm H2O Total pressure tube manometer 1fold: 530 mm H2O Venturi meter nom diameter: min diameter: 284 mm 14 mm Overall dimension (L x W x H): 1100 x 640 x 900 mm Weight: 40 kg 4 Technical Data 13
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