MECHANICS of FLUIDS LABORATORY - Mechanical Engineering

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Performance Map A performance map is to be drawn to summarize the performance of the pump over its operating range. The performance map is a graph if the total head ∆H versus flow rate Q (horizontal axis). Four lines, corresponding to the four pre-selected rotational speeds, would be drawn. Each line has 6 data points, and the efficiency at each point is calculated. Lines of equal efficiency are then drawn, and the resulting graph is known as a performance map. Figure 18.2 is an example of a performance map. Total head in ft 40 30 20 10 3600 rpm 2700 1760 900 65% Efficiency in % 75% 80% 85% 75% 0 0 200 400 600 800 Volume flow rate in gallons per minute 65% FIGURE 18.2. Example of a performance map of one impeller-casing-motor combination obtained at four different rotational speeds. Dimensionless Graphs To illustrate the importance of dimensionless parameters, it is prudent to use the data obtained in this experiment and produce a dimensionless graph. A dimensional analysis can be performed for pumps to determine which dimensionless groups are important. With regard to the flow of an incompressible fluid through a pump, we wish to relate three variables introduced thus far to the flow parameters. The three variables of interest here are the efficiency η, the energy transfer rate g∆H, and the power dW/dt. These three parameters are assumed to be functions of fluid properties density ρ and viscosity µ, volume flow rate through the machine Q, rotational speed ω, and a characteristic dimension (usually impeller diameter) D. We therefore write three functional dependencies: η = f 1 (ρ, µ, Q, ω, D ) dW dt = f 3 (ρ, µ, Q, ω, D) Performing a dimensional analysis gives the following results: where ρωD η = f 1 ⎛ 2 ⎞ ⎝ µ , Q ωD 3 ⎠ g∆H ω 2 D 2 = f 2 ⎝ ⎛ ρωD 2 µ , Q ωD ⎠ ⎞ 3 dW/dt ρω 3 D 5 = f 3 ⎝ ⎛ ρωD 2 µ , Q ωD ⎠ ⎞ 3 g∆H ω 2 D2 = energy transfer coefficient Q ωD 3 ρωD 2 µ dW/dt ρω 3 D 5 = volumetric flow coefficient = rotational Reynolds number = power coefficient Experiments conducted with pumps show that the rotational Reynolds number (ρωD 2 /µ) has a smaller effect on the dependent variables than does the flow coefficient. So for incompressible flow through pumps, the preceding equations reduce to Q η ≈ f 1 ⎛ ⎞ ⎝ ωD 3 (18.4) ⎠ g∆H ω 2 D 2 ≈ f 2 ⎝ ⎛ Q ωD ⎠ ⎞ 3 (18.5) dW/dt ρω 3 D 5 Q ≈ f 3 ⎛ ⎞ ⎝ ωD 3 (18.6) ⎠ For this experiment, construct a graph of efficiency, energy transfer coefficient, and power coefficient all as functions of the volumetric flow coefficient. Three different graphs can be drawn, or all lines can be placed on the same set of axes. g∆H = f 2 (ρ, µ, Q, ω, D) 48
Specific Speed A dimensionless group known as specific speed can also be derived. Specific speed is found by combining head coefficient and flow coefficient in order to eliminate characteristic length D: ω ss = ⎝ ⎛ or ω ss = Q ⎞ ⎠ ωD 3 1/2 ωQ 1/2 (g∆H) 3/4 ω ⎛ 2 D 2 ⎞ ⎝ g∆H ⎠ 3/4 [dimensionless] Exponents other than 1/2 and 3/4 could be used (to eliminate D), but 1/2 and 3/4 are customarily selected for modeling pumps. Another definition for specific speed is given by ω s = ωQ1/2 ∆H 3/4 ⎣ ⎡ rpm = rpm(gpm)1/2 ⎦ ⎤ ft 3/4 in which the rotational speed ω is expressed in rpm, volume flow rate Q is in gpm, total head ∆H is in ft of liquid, and specific speed ω s is arbitrarily assigned the unit of rpm. The equation for specific speed ω ss is dimensionless whereas ω s is not. The specific speed of a pump can be calculated at any operating point, but customarily specific speed for a pump is determined only at its maximum efficiency. For the pump of this experiment, calculate its specific speed using both equations. 49
Page 1 and 2: A Manual for the MECHANICS of FLUID
Page 3 and 4: TABLE OF CONTENTS Item Page Report
Page 5 and 6: as its strong points. Suggest exten
Page 7 and 8: EXPERIMENT 1 FLUID PROPERTIES: DENS
Page 9 and 10: EXPERIMENT 2 FLUID PROPERTIES: VISC
Page 11 and 12: L level R i y zeroing weight torus
Page 13 and 14: 5. Is a low value of the standard d
Page 15 and 16: pivot balancing weight lever arm wi
Page 17 and 18: Questions 1. Can a similar procedur
Page 19 and 20: actual flow rate (measured in the l
Page 21 and 22: manometer orifice meter venturi met
Page 23 and 24: otameter tank valve motor static pr
Page 25 and 26: Pressure Measurement Equipment A Wi
Page 27 and 28: EXPERIMENT 10 DRAG FORCE DETERMINAT
Page 29 and 30: Experiment II For a number of wings
Page 31 and 32: axis) versus (Q 2 /b 2 h 0 3 g). De
Page 33 and 34: Therefore, Q = ∫ 0 Integration gi
Page 35 and 36: Develop a hydraulic jump in the cha
Page 37 and 38: At any upstream (of the hump) locat
Page 39 and 40: EXPERIMENT 16 MEASUREMENT OF VELOCI
Page 41 and 42: Incompressible Flow Through a Meter
Page 43 and 44: TABLE 16.1. Summary of equations fo
Page 45 and 46: placed on the torque arm to reposit
Page 47: ∆H = H 2 - H 1 = p 2 ρg + V 2 2
Page 51 and 52: 1 large orifice volume flow rate in

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