FLUIDS MECHANICS LABORATORY THE HYDRAULICS BENCH The Hydraulics Bench is a service module designed to accommodate a range of accessories, each of which demonstrates an aspect of hydraulic theory. A

self-priming centrifugal pump draws water from the sump tank and delivers into a vertical transparent pipe. A panel mounted bench control valve is used to regulate the flow in the delivery pipe which terminates in a quick release pipe connector situated in the bed of a channel. Water discharging from the accessory on test is collected in the volumetric measuring tank. This tank is stepped to accommodate low or high flow rates and incorporates a stilling baffle to reduce turbulence. MEASUREMENT OF VOLUMETRIC FLOW RATE The molded bench top incorporates a volumetric measuring tank which is stepped to accommodate low or high flow rates. A remote sight gage, consisting of a sight tube and scale is connected to a tap in the base of the tank, and gives an instantaneous indication of water level. The scale is divided into two zones corresponding to the volume above and below the step in the tank. To make a volumetric flow reading, the ball of the dump valve is lowered, retaining the water in the tank. Timings are taken as the water level rises in the tank. Low flow rates are monitored on the lower portion of the scale corresponding to the small volume beneath the step. Larger flow rates are monitored on the upper scale corresponding to the main tank. When not used for volumetric determinations, the water drains back to the sump by lifting the dump valve. F1-10 Hydraulics Bench Drain Valve 0 Water Inlet Stilling Baffle Sight Tube and Scale Location of Hook & Point 1 Centrifugal Service Pump Bench Control Valve Weir Carrier Stilling Baffle Dump Valve RCD Pump ON/OFF Switch LEARNING OBJECTIVES Flow Control Valve Outlet Pipe Inlet Pipe E2: FLOW METER DEMONSTRATION Investigate the operation and characteristics of three different basic types of flow meters (variable area, orifice plate, venturi). Determine the accuracy and energy losses of each meter. 2 Orifice Plate C₁A₂ -(1/)* Air Bleed Screws Tap Venturi Meter Figure 1: Detailed description of the Flow Meter apparatus (front and side views). THEORY OF THE EXPERIMENT Variable area meter Eight-bank manometer The hydraulics bench and a stopwatch are used to determine the flow rate through the flow meter apparatus. Manometers are used to measure the associated pressure losses of the three flow meters connected in series. Application of the Bernoulli equation yields the following result for the volumetric flow rate for both the Venturi meter and the orifice plate flow meter. √2gAh C is the discharge coefficient for the meter [dimensionless] A₁ is the area of the test pipe upstream of the meter [m²] A₂ is the throat area of the meter [m²] Hand Pump Equation 1 where Ah is the head difference determined from the manometer readings for the appropriate device [m] g is the acceleration due to gravity [m/s²] Use of a discharge coefficient, Cd, is necessary because of the simplifying assumptions made when applying the Bernoulli equation. Values of this coefficient are determined experimentally. Pipe assembly components (including flow meters) cause some resistance to flow and thus an energy loss. This is commonly expressed in terms of a head loss and this can be determined from the difference in readings of manometers placed before and after the component in the flow path. The flow meter apparatus is capable of analyzing the head losses of the flow meters (so-called secondary loss), but this will not be computed in this experiment. EXPERIMENTAL PROCEDURE This accessory is positioned above the top channel of the Hydraulics Bench. The Venturi meter, variable area meter and the orifice plate are installed in a series configuration to permit direct comparison. Flow through the test section is regulated using a flow control valve. This together with the bench control valve permits variation of the system static pressure. Pressure taps in the circuit are connected to an eight-bank manometer which incorporates an air inlet/outlet valve in the top manifold with facilities to connect a hand pump. This enables the levels in the manometer bank to be adjusted to a convenient level to suit the system static pressure. The pressure taps for the manometers are placed to give a set of readings around the flow meters in the system. STEPS 1. Start the pump and open the bench control valve and the test rig flow control valve to flush the system. 2. In order to bleed air from the pressure tap points and manometers, close both the bench and test rig valves, open the air bleed and allow flow through the manometer tubes to purge them of air. Once air bubbles are out, close air bleed valve, then close bench control valve. Now open the air bleed screw slightly to allow air to be drawn into the top of the manometer tubes. Re-tighten the screw when the manometer levels reach a convenient height (about the 100 mm level on the manometers is a good starting point). Check that all manometer levels are on scale, at the maximum flow rate (full-scale reading on the variable area meter). These levels can be adjusted further by using the air bleed screw or the hand pump supplied. 5. Ensuring you can read each manometer level, adjust the bench control valve for a flow rate (perhaps starting at 4 L/min as indicated by the variable area meter). Do not change the control valve settings while reading and recording all manometer heights and the variable area meter readings. 3. 4. 6. Carry out a timed volume collection using the volumetric tank and sight gage. Record the time it takes for the water to reach a certain volume (such as 5 L). 7. 5. Repeat steps 3 and 4 for a total of 8 different flow rates of your choosing (for example, adjust the bench control valve and take readings when the variable area meter reads 4, 7, 10, 12, 14, 16, 18, and 20 L/min). Record data in Table 1. RESULTS Use a spreadsheet to compute and display the data for the various meters as indicated by Table 2 (note that SI units are called for). Some parameters are provided in the information boxes below. Values to Calculate: . Convert variable area reading, Q₁, to m³/s by dividing reading by 60,000 Q[m³/s], Timed (captured) flow rate= V/t [converted as appropriate to obtain m³/s] Q, [m³/s], Venturi flow rate. Calculate from Equation 1 using C₁ = 0.98 and Ah, Qo [m³/s], Orifice flow rate. Calculate from Equation 1 using C₁=0.63 and Aho Head difference in meters (Ah, and Aho). See formulas in information box below. Data to Collect: Volume collected in tank, V (L) Time to collect given volume in tank, t (s) • hl-h8, mm Data known: For Venturi Meter Upstream Pipe Diameter = 0.03175 m Cross sectional area of upstream pipe A₁ = 7.92x 10+ m² Throat diameter = 0.015 m Cross sectional area of throat A₂ = 1.77 X 10+ m² Upstream Taper = 21 degrees Downstream Taper = 14 degrees C₁ = 0.98 Data known: For Orifice Plate Upstream Pipe Diameter = 0.03175 m Cross sectional area of upstream pipe A₁ = 7.92x 10¹ m² Throat diameter = 0.020 m Cross sectional Area of Throat A² = 3.14 x 104 m² C₁=0.63 Data to convert to SI units: (hl-h2)/1000 = Venturi head difference, Ah, (m) (h6-h7)/1000 = Orifice plate head difference, Ah, (m) Data not used in this experiment: (hl-h3)/1000 = Venturi meter head loss (m) (h4-h5)/1000 = Variable area meter head loss (m) (h6-h8)/1000 = Orifice plate meter head loss (m) Data Analysis and Questions for Lab Reports 1. Calculate and tabulate the flow rate errors as percentages (take the timed flow rate Q to be the correct value), i.e., find for each flow meter: (Percent Error)x= [(Qx-Q/QJ (100%) where x = v, a, or o. 2. Comment on the differences in accuracy in meters. Could these differences be due to experimental error? A(2g) *(¹-(+²)²³)` 3. On a single graph, plot the flow rates Q₁, Qy, and Q, vs. the flow rate determined experimentally (Q.). Also plot Q₂ vs. Q, to provide the slope = 1 line to represent ideal performance of a flow meter. 4. What does it mean if a flow meter curve is consistently above the ideal performance (slope = 1) line? What does it mean if a flow meter curve is below the ideal performance line? 5. Take the timed (or captured) flow rate (Q) data to be correct and calculate the discharge coefficient (Ca) as indicated by your experiments for the venturi and orifice plate flow meters. A good way to do this is to plot Q vs. venturi head loss and Q² vs. orifice plate head loss and relate the slopes to the following derived from Equation 1: Q² = c² -(Ah) thus for Q vs. Ah plot: slope = C A(2g) (¹- (²²³)²) and solve for C, Be sure to use SI units for all parameters. Be sure your plot has Q on the vertical axis and Ah on the horizontal axis (this is what is meant by Q vs. Ah plot). Compare to the Ca values given above for discharge coefficient for the venturi and orifice plate flow meters. Table 1: Data Collected in Lab for Comparing Various Flow meters Q₂ hl h5 Trial (L/min) (mm) (mm) 2 3 5 6 7 8 h2 (mm) h3 (mm) h4 (mm) h6 (mm) h7 (mm) h8 Volume (mm) (L) Time (s) 2 112 109 110 110 38 39 40 41 5 2:16.33 Ч 128 114 121 123 46 50 48 51 3 1:07.83 b 138 117 125 124 55 52 45 49 5 46.48 8 151 118 132 128 59 56 42 47 5 33.45 46 38 46 5 28.40 23.28 62 38 10 168 115 140 135 64 12 187 111 150 141 70 71 30 42 3 14 210 167 165 130 72 73 23 40 ≤ 20.40 16 233 100 180 160 88 90 10 35 5 17.46