Engineering lab report rewrite(paraphrasing) Fan

Thermal-Fluids Lab

CENTRIFUGAL FAN EXPERIMENT

PROFESSOR:

PERFORMED: August 7, 2018

REPORT SUBMITTED: August 24, 2018

Group #4

Abstract

Engineers design ducting systems based on the selected air flow rate and the calculated pressure to overcome in order to let the air flow. Fans are chosen for this application, but to determine the perfect fan for the suited application, the efficiency needs to be determined. The Purpose of this experiment is to find the efficiency of a fan under two rotational speed settings 900 RPM and 1300 RPM. The experiment was carried on successfully and the highest efficiency for the 900 RPM rotational speed was 8.30 ±0.84% when the air flow rate was 2.07 CFS, and the highest efficiency for the 1300 RPM was 10.70 ±1.80% when the air flow rate was 1.60 CFS.

Introduction

Centrifugal fans are mostly used to transfer or deliver air from a location to another. In general, fans chosen to design a ducting system are limited to low pressure applications. To design a ducting system, the designer needs to choose a flow rate for the air then predict the pressure that is needed to overcome in order to let the air flow in the system. After that, a fan with the required specifications needs to be figured. The best fan chosen should develop the selected flow rate and operate near its peak efficiency. Therefore, the objective of this experiment is to find the efficiency of a fan under two rotational speed settings. First, to estimate the flow velocity, V, and flow rate, Q, the following equations are used:

V = (2 Pdynamic / ρ) 0.5 … (1)

Q = V * (π D2 / 4) … (2)

Where:

Pdynamic is the dynamic pressure at the duct exit.

ρ is the density of air.

D is the ducting system diameter.

To calculate the fan head, hf, the following equation was used:

hf = ( Pstatic + Pdynamic ) / γ … (3)

Where:

Pstatic is the static pressure at the exit of the duct.

γ is the specific weight of air.

To evaluate the efficiency, η, the ideal work rate and the shaft work rate need to determined using the following:

Ẇideal = γ Q hf … (4)

Ẇshaft = T ω … (5)

η = Ẇideal / Ẇshaft … (6)

Where:

T is the shaft input torque.

ω is the rotational speed of the shaft.

Description of Work

Before operating the fan, all the pressure manometers (Figure 1) and the weight scale (Figure 2) were zeroed. Then the fan was turned on at two different rotational speeds (900 RPM & 1300 RPM). At the first rotational speed setting, the exit cone (Figure 3) was set to 0 position, and the dynamic pressure, static pressure, and the reaction force were recorded. Then the exit cone were set to position -2 and the same data were recorded. This step was repeat several times while changing the position of the exit cone with increments of -2. After reaching the -6 position, increments of -1 were chosen instead for the exit cone position.

Figure 1: weight scale.

Figure 2: Dynamic and static pressure manometers.

Figure 3: Exit cone.

Results and Discussion

First, the pressures were converted from inches of water to lb/ft2 by dividing them by 12 then multiplying by the water specific weight. Similarly, the force was converted to torque by multiplying by the arm length. Also the rotational speed was converted to rad/s by dividing by a factor of 9.55. All data are shown in Table 1 for 900 RPM, and Table 2 for 1300 RPM below. It is clear to note the dynamic pressure is decreasing while the static pressure is increasing. Also the 1300 RPM has higher values of dynamic pressure, static pressure, and torque.

Table 1: Calculated torque of input shaft with the converted pressures at 900 RPM.

Table 2: Calculated torque of input shaft with the converted pressures at 1300 RPM.

After that, using equations (1), (2), (3), (4), (5), and (6), Tables 3 and 5 were constructed. Obviously the air velocity and flow rate are decreasing since they are related to the dynamic pressure only, while the fan head was increasing since it relies on the total pressure which was increasing. Both ideal work rate and shaft work rate are decreasing, but not at the same rate. So the efficiency tends to increase until it reaches its peak (at 8.3% for 900 RPM at 2.07 CFS) and (at 10.7% for 1300 RPM at 1.60 CFS) then it decreases significantly. The uncertainties were calculated using the propagation of error equations, and can be seen in Tables 4 and 6.

Table 3: Velocity, flow rate, fan head, ideal work, shaft work, and efficiency for 900 RPM.

Table 4: Uncertainties for 900 RPM.

Table 5: Velocity, flow rate, fan head, ideal work, shaft work, and efficiency for 1300 RPM

Table 6: Uncertainties for 1300 RPM.

Figure 4: Static pressure as a function of flow rate.

Figure 5: Fan head as a function of flow rate.

Figure 6: Shaft power as a function of flow rate.

Figure 7: Efficiency as a function of flow rate.

Conclusion

The purpose of the experiment is to figure the efficiency of two different rotational speed settings of a fan in a ducting system. To calculate the efficiency, both the ideal work rate and the actual shaft input work rate needed to be calculated. The efficiencies were determined and the highest were 8.3% for air flow of 2.07 CFS at 900 RPM and 10.7% for air flow of 1.60 CFS and at 1300 RPM. It is believed that human error could have contributed to reading the manometers and the weight scale not accurately. One of these errors can be due to the fact the manometer is tilted and it is hard to read the actual reading of it. Another is that the weight scale reading was not static but it was moving rapidly across a range of values. All in all, the experiment can be somehow found to be successful.

Appendix

Table 7: Raw data for 900 RPM.

Table 8: Raw data for 1300 RPM.

Table 9: Used constants and measured values.

Sample Calculation

· To convert pressure from inches of water to lb/ft2:

P = 0.0650 (in. of water) / 12 * 62.4 (lb/ft3)

P = 0.338 lb/ft2.

· To calculate the air velocity, V = (2 Pdynamic / ρ) 0.5 :

V = (2 * 0.338/ 0.0748) 0.5

V = 3.004 ft/s.

· To calculate the ideal work rate, Ẇideal = γ Q hf :

Ẇideal = 2.46 * 2.36 * 0.348

Ẇideal = 2.025 ft-lb/sec.

Static pressure vs. flowrate

900 RPM 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 0.01 0.01 2.3597174974403989 2.2671432382001493 2.0696091544292163 1.6031123576525537 1.308935758866296 0.92555735123191751 0.65446787943314799 0.1 0.14000000000000001 0.22 0.3 0.34 0.38 0.4 1300 RPM 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 3.7022294049276701 3.4631185001198275 2.8527593482424538 2.3597174974403989 1.851114702463835 1.6031123576525537 0.92555735123191751 0.22 0.32 0.46 0.68 0.76 0.84 0.88

Flow rate (cfs)

Static pressure (inches of water)

Fan head vs. Flowrate

900 RPM 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 8.3333333333333339E-4 2.3597174974403989 2.2671432382001493 2.0696091544292163 1.6031123576525537 1.308935758866296 0.92555735123191751 0.65446787943314799 0.34831323833881384 0.42219786465310766 0.56996711728169525 0.69662647667762756 0.75995615637559377 0.82328583607355987 0.85495067592254292 1300 RPM 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46 280378228493779 3.7022294049276701 3.4631185001198275 2.8527593482424538 2.3597174974403989 1.851114702463835 1.6031123576525537 0.92555735123191751 0.80217594284090454 0.97105508870214774 1.1715990744123739 1.5726870458328261 1.6887914586124306 1.8365607112410178 1.8787804977063287

Flow rate (cfs)

Fan head (ft)

Shaft power vs. Flowrate

900 RPM 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 2.3597174974403989 2.2671432382001493 2.0696091544292163 1.6031123576525537 1.308935758866296 0.92555735123191751 0.65446787943314799 35.811518324607334 35.811518324607334 34.86910994764397 33.926701570680635 31.099476439790578 28.272251308900522 23.560209424083769 1300 RPM 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 3.7022294049276701 3.4631185001198275 2.8527593482424538 2.3597174974403989 1.851114702463835 1.6031123576525537 0.92555735123191751 99.3717277486911 100.7329842931937 99.3717277486911 93.926701570680621 85.759162303664922 68.062827225130889 57.172774869109944

Flow rate (cfs)

Shaft power (ft-lb/sec)

Efficiency vs. Flowrate

900 RPM 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 0.18193232911762164 0.18929724471082557 0.20724143403983877 0.26731582272430171 0.32730494632253432 0.46280378228493779 0.65447675616167844 4.4239650213593008E-3 5.5667277190622503E-3 8.4210728042368923E-3 1.3567902158471942E-2 1.9738097598299888E-2 3.3215933406175617E-2 5.8514095050641084E-2 4.4239650213593008E-3 5.5667277190622503E-3 8.4210728042368923E-3 1.3567902158471942E-2 1.9738097598299888E-2 3.3215933406175617E-2 5.8514095050641084E-2 2.3597174974403989 2.2671432382001493 2.0696091544292163 1.6031123576525537 1.308935758866296 0.92555735123191751 0.65446787943314799 5.6535933339990893E-2 6.5839960940947018E-2 8.3332532926179648E-2 8.1084829304748487E-2 7.8789999739757879E-2 6.6391257200922357E-2 5.8501574806770235E-2 1300 RPM 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 0.11729053282740783 0.12499108765713642 0.15087860526105684 0.18193232911762164 0.23159010950545481 0.26731582272430171 0.46280378228493779 2.3874239787817606E-3 3.0204188672529188E-3 4.418872084559558E-3 7.5370323490956924E-3 1.125662699681652E-2 1.7799936197553153E-2 3.7473495066511361E-2 2.3874239787817606E-3 3.0204188672529188E-3 4.418872084559558E-3 7.5370323490956924E-3 1.125662699681652E-2 1.7799936197553153E-2 3.7473495066511361E-2 3.7022294049276701 3.4631185001198275 2.8527593482424538 2.3597174974403989 1.851114702463835 1.6031123576525537 0.92555735123191751 7.3618578139630214E-2 8.2235024708250851E-2 8.2851165674093508E-2 9.7326377187907723E-2 8.9793754456023472E-2 0.10655567218844991 7.4921663874244579E-2

Flow rate (cfs)

Efficiency

12