Single Pump Results
Single Pump Calculations
Impeller Diameter (D) 114mm
Venturi inlet diameter (AP) 27.2mm
Venturi throat diameter (AT) 18.5mm
All calculations done assuming ρ= 1000 kg/m3
1. Graphs for the single pump test
Figure 3: Percentage efficiency plotted against the flow rate in litres per second
2. Analysis of single pump graphs
The graph in Figure 1 demonstrates an inverse correction that exists between flow rate and the size of the head. According to the curve, the fluid flow exhibits a maximum head (16.20795m) at zero flow (Derakhshan and Ahmad 807). On the other hand, the fluid flow demonstrates a minimum head (4.99490m) at the moment when the flow rate is at its highest value (1.905979 Ls-1). The valve closes given that the speed of the bump is maintained at a constant rate. In other words, the energy that initially went into the water is currently converted into water pressure (Gülich 238.).This conversion of energy leads to an increase in the total head (Haaland 90).
The shape of the graph is supported by the equations of the total head loss and the flow rate available in Appendix A.
The graph in Figure 2 represents the relationship that exists between the total power (PE) and the hydraulic power (PH) plotted against the flow rate in litres per second. As evident from the curve, the lowest total power (159 W) is realized at zero flow. On the other hand, the relationship realizes the maximum total power at the maximum flow rate (1.905979 Ls-1). Similarly, the flow exhibits a maximum hydraulic power (129.6680 W) at a flow rate of 1.3794 Ls-1. It is imperative to note that at any point in the curve, the values of hydraulic power are never higher than those of the total power (Cooper and George 6). That is, the values of the total power are always greater than those of hydraulic power. This relationship between the hydraulic power and the total power can be elaborate by the principle that the system efficiency (η=PH/PE) is always less than 100%.
At the initial stages, the graph in Figure 3 indicates a positive and direct correlation between the flow rate and the efficiency (Hergt et al 96). Tit is evident from the curve that the highest efficiency (41.077228%) is attained when the flow rate is equal to 1.1004175 Ls-1. The efficiency begins to gradually drop to a minimum of 24.904792% when the flow rate is at its highest point (1.905979 Ls-1). The shape of the curve flawlessly follows the distances between the two sets of power values (Hooper 89).
3. Specific speed of pump
According to Houghtalen, Robert and Ned (342), it is imperative to point out that the specific speed (NS) of a pump is a crucial value that should be considered when choosing a pump for a specific function (Ito 140). The value of the specific speed, NS is the speed needed to release 1m3/s against 1m head. As a consequence, the physical size of the unit for a given discharge will always be at a minimum when the specific speed value is at a maximum. According to Medvitz (383), specific speed is without dimensions when using consistent units.
NS=ωQ(gH)34 (Williams 59)
4. Head coefficient vs. flow coefficient & Power coefficient vs. flow coefficient
Figure 4: Head coefficient values plotted against the flow coefficients
Figure 5: Power coefficient values plotted against the flow coefficients
5. Analysis coefficient graphs plotted
Figure 4 outlines the curve of head coefficient plotted against the flow coefficient. It indicates the relationship that exists between the head coefficient and the flow coefficient. According to the curve, the flow exhibits a maximum head coefficient 0.123963 at a zero flow coefficient. On the other hand, the head coefficient attains a minimum at the moment when the flow rate coefficient is at its highest (0.004094998). Similarly, the relationship that exists between the power coefficient and the flow coefficient is demonstrated by Figure 5. It is apparent from the curve that the maximum power coefficient 0.000215686 is attained at the moment when the flow coefficient is at 0.00295684. According to Murakami and Kiyoshi (1295), it is imperative to note the close similarity that exists between the two graphs and the curve of power against the flow rate. The similarity can be attributed to the fact every variable in the coefficient equations remain constant. Furthermore, the slight change is due to the fluctuation in the values of ω (Šavar, Mario and Igor 659).
Two Pumps Results
Two Pumps Calculations
Figure 8: Percentage efficiency plotted against the flow rate in litres per second
7. Pump Head Discussion
It is imperative to point that the maximum head attained from utilizing the two pumps is higher than that obtained from using a single pump. The two pumps recorded a maximum head of 25.38226 m while the single pump recorded a maximum head of 16.20795 m. It is worth noting that connecting the two pumps in series present a different effect to the values of the maximum head (Varley 989). The pumps are connected in series so that the discharge of the first pump is linked to the suction section of the second pump. This connection results into a head with double the size of a single pump. Vocadlo and Prang (74) assert that the value of the total head is achieved by summing up the individual head (H) values from each pump.
HT=H1+H2, H1=H2 (Hamill, 1995).
The radial component of the velocity in both pumps will be fixed to zero since the two pumps exhibit the same flow rate, possess the same shape and pipe diameter. Additionally, the velocity component that exists along the pipe will be the same in both pumps. Water does not exhibit a rotational velocity as it enters the first pump. However, it gains rotational velocity in the pump. The water enters the second pump after it has accessed rotational velocity. This rotational velocity results to a reduction in the size of the head in the second pump: (H1 > H2). As a consequence, a reduction in the size of the total head is witnessed.
Appendix A
Formulae and sample calculations used both experiments
Total head H
H=PO-PI⍴g (Walker and Apostolos 45)
Flow Rate Q
Q=CdAT2∆pρ(1-(ATAP)2 (Williams 59)
Efficiency η
η=PHPE (Walker and Apostolos 45)
Pump Speed N1
N1=3000 r/min
Head Coefficient CH
CH=gHω2D2
Flow Coefficient CQ
CQ=QωD3 (Williams 69)
Power Coefficient CP
CP=PHρω3D5 (Williams 53)
Works Cited
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