Flow Measurement and the Bernoullis Equation - Lab Report Example

FLUID MECHANICS LAB: FLOW MEASUREMENT Name: Lab Instructor: Institution: Date: Introduction The orifice, venturi flow meters and rotameters apply the Bernoulli equation to determine the rate of fluid flow through these devices using the difference in pressure through the obstructions in the channel of flow. A fluid flow through a venturi meter is accelerated to flow through a converging cone, and the difference in pressure between the throat and the upstream side of the converging cone is measured to determine the rate of flow. An orifice consists of a circular plate with a centrally drilled hole through which the fluid flows, and there are pressure taps upstream and downstream (Paul J. LaNasa, 2014). Rotameters consist of a float within a tube and are used to measure fluid flow within the closed tube. In any flow measuring device that is based on Bernoulli’s principle, the pressure downstream after obstruction or constriction will be lower compared to the upstream pressure. In order to understand how these devices operate, it is essential to explore the Bernoulli equation. The Bernoulli’s Equation Assuming that the flow is horizontal through section 1 and 2, the physical phenomenon of fluid flow is described by Bernoulli’s Equation and the equation of continuity. (Bernoulli’s equation) (Continuity equation) Where:  - pressure  - density - flow velocity A – cross-section area - elevation height For a given geometrical flow, the rate of flow can be determined by measuring the difference in pressure between the two sections and applying Bernoulli’s equation. The three typical devices used in the measurement of flow of incompressible fluids include; the venturi meter, the orifice and the rotameter. Bernoulli’s equation find wide applications in many situations. In addition to pipe flows, Bernoulli’s equation is applied in the flow measurement devices, such as venturi meters, orifices and rotameter, for measurement of fluid flow. It is also applied in open channels, such as flow over weirs and notches, as well as sizing of pumps, pitot tube, ejectors, siphon, flow sensors, carburetor etc (Sawhney, 2011). Aims of the experiment To familiarize with methods of measuring discharge of incompressible fluid whilst giving applications of the steady-flow energy equation and Bernoulli’s equation. To determine discharge using a venture meter, an orifice plate meter and a rotameter. To determine head losses associated with rapid enlargement and right-angled elbow. Experimental Procedure The equipment used in this experiment was a “Flow Measurement Apparatus” from TecQuipment Ltd. After setting up the equipment, measurements were taken. First, the control valve was kept fully open. The test section was divided into nine sections as explained in figure 2. The equipment valve was opened to ensure that the rotameter had a reading of about 10mm. After achieving a steady flow, the flow was measured with a Hydraulic Bench. The readings of the manometers and other measurement devices were recorded in a table. This procedure was repeated in nine trials for a 10mm interval rotameter readings until the manometer recorded the maximum pressure. Below is a figure of the TecQuuipment that was used in the experiment. Figure 1: TecQuuipment for Flow Measurement Below in figure 3 is an explanatory diagram of the equipment showing the location of pressure manometers and how the flow measurement devices are arranged in the flow measurement equipment shown in figure 1. Figure 2: Explanatory diagram of the flow measurement apparatus Results and Calculations Table 1: Results Test No. 1 2 3 4 5 6 7 8 9 Manometer Levels (mm) A 331 334 339 346 352 360 372 390 400 B 328 332 328 336 328 328 330 340 342 C 330 330 336 342 348 356 364 382 392 D 330 330 336 342 346 352 360 370 388 E 330 330 336 344 348 356 366 310 390 F 326 326 327 324 320 320 313 330 326 G 329 326 327 326 326 326 326 338 336 H 329 326 326 326 325 325 324 336 334 I 224 230 226 224 222 222 220 234 230 Rotameter (cm) 10 20 30 40 50 60 70 80 90 Mass Flowrate (kg/s) 0.05 0.07 0.09 0.11 0.14 0.16 0.18 0.20 0.23 H/Inlet Kinetic Head Venturi 1.98 -5.93 1.62 2.37 0.99 0.74 1.13 0.95 0.82 Orifice 104.92 -157.37 64.38 157.37 91.80 88.52 99.30 -31.47 86.83 Rotameter 3002.11 -3602.53 603.29 587.78 209.36 127.39 76.75 41.71 22.88 Diffuser 0.94 0.94 0.94 0.94 1.43 1.68 1.50 2.36 1.35 Elbow 0.00 0.00 8.62 0.00 3.95 2.96 4.51 3.79 3.27 Calculation of inlet kinetic heads The calculations shown in this section have been done using the results of the first test. Since there are nine tests, all the calculations may not be shown here, but have been done in the same way as those that have been done using the results in the first test. Venturi Meter The Bernolli equation is applied between section A and B. The mechanical energy equation is applied between section A and C. Continuity equation: Energy equation: Combining the continuity and energy equation, we have the equation, we have: 328 = (331-330) = 1mm Venturi inlet kinetic head / -1 = 0.51 mm Head loss = (1/0.51) = 1.96 inlet kinetic heads Wide-angled Diffuser Applying the following equation: The area ratio of the inlet to outlet of the diffuser is 1: 4. Therefore, the ratio of inlet kinetic head to outlet kinetic head of the diffuser 1:16. 330 mm and 330 mm Inlet kinetic head = 0.51 mm Therefore, Outlet kinetic head = Head loss = ( Thus, head loss = 0.94 mm Orifice Meter The mechanical energy equation is not applied in orifice meter because the value that will be obtained will show excessive head loss due to the ram pressure on the plate wall. Generally, the head loss between points and is determined by the correlation: Therefore, Orifice inlet kinetic head = 1/16 (venturi inlet kinetic head) mm Orifice head loss = (/ orifice inlet kinetic head) = inlet kinetic heads Right angled bend Applying the following equation and assuming the outlet kinetic head is equal to inlet kinetic head: = 329-329=0 Right angled bend Inlet kinetic head = Orifice inlet kinetic head Head loss at Right angled bend = inlet kinetic heads Rotameter The mechanical energy equation is applied between sections H and I. The rotameter diverges gradually, and therefore, assuming a minimal change in kinetic head and flow speed between points H and I on the rotameter; =-10+ (329-224) =95 mm Rotameter inlet kinetic head= 1/16 (venturi inlet kinetic head) mm Rotameter head loss = = = 3002.11inlet kinetic heads Calculation of mass flow rate The mass flow rate are approximated using the linear rotameter calibration curve. For Flow rate from the characteristic linear calibration curve Flow rate = 3L/min = 0.05kg/sec. Conclusion As a fluid flows through various measuring devices and obstructions, there is loss of pressure head. The loss in pressure head is determined by the velocity and pressure of the fluid flow. The fluid velocity and fluid pressure are inversely related, i.e. increase in fluid velocity results to decrease in head pressure and vice-versa. The phenomenon of fluid flow in these devices is governed by the Bernoulli’s equation and equation of continuity. The flow measurement device used in this experiment provides situations where the Bernoulli’s equation is practically applied in determination of fluid flows in pipes, thus, meeting the objectives of the experiment. References Read More