Web www.lightmypump.com 
1.0 SOLVED PROBLEMS
1.1 Does it take longer to cook a 4 min egg in Mexico city than on the beach? Are you kidding 4 minutes is 4 minutes? I mean to get an egg to the same consistency as a typical 4 min egg, how long would it take in Mexico city vs. somewhere at sea level?
1.2 In a multiple and identical pump system, if one pump is in poor running order what is the effect on the discharge header head and the flow to the system?
1.3 What happens if the damaged pump's performance curve has all points at a lower head than the good pump's performance curve?
1.4 Ever wonder how it occurs that you can get partially full pipes in what appears to be a pressurized system? What would the difference in Total Head be for the same flow rate for a system with partially full pipes and a system with full pipes?
1.5 How long does it take to empty a tank?
1.6 How to calculate the pump flow, total head or efficiency based on power consumed by the motor.
1.1 Does it take longer to cook a 4 min egg in Mexico city than on the beach ? Are you kidding 4 minutes is 4 minutes? I mean to get an egg to the same consistency as a typical 4 min egg, how long would it take in Mexico city vs. somewhere at sea level?
Different liquids boil at different temperatures for a given air pressure. For example, water boils at a temperature of 212 °F at an air pressure of 14.7 psia (the pressure at sea level). However, a temperature of 189 °F is required to boil water at a pressure of 11 psia which is the air pressure at 8,500 feet above sea level, the altitude of Mexico city. Just because water boils at a lower temperature in Mexico city doesn't mean that it takes a shorter time to boil an egg. The same amount of heat transfer is required to get the egg to the right consistency regardless of water temperature. It will take longer to transfer enough heat to cook the egg if the water is boiling at a lower temperature than a higher one. We are so used to water boiling at the same temperature that it is very surprising to find that it takes longer than 4 minutes to boil a 4 minutes egg in Mexico city. How much longer I don't know, I'd have to go to Mexico city. If there are any Mexico city residents out there on the web, please try the experiment and let me know.
1.2 In a multiple and identical pump system, if one pump is in poor running order what is the effect on the discharge header head and the flow to the system?
Consider a two pump system where one of the pumps is in poor running condition as compared to the other. This could be due to: worn or damaged impeller, worn casing, worn bearings and shaft, wrong impeller, etc. Any or a combinations of these factors will have an effect on the pump's performance. The efficiency of the pump will be affected as well as the head and flow. It is difficult to predict the resulting performance curve without doing tests. However, unless the pump has gaping holes, the performance curve should look similar to that of the good pump but with a lower capacity and head. Let's assume that there is negligible friction loss between the discharges of pumps A or B and the header and also the head at the inlet of both pumps is the same. The operating point is point 1 on curve A which corresponds to 500 USGPM and 96 ft. The curve for the bad pump B, being slightly lower will contribute 265 USGPM at 96 ft since it must operate at the same head as pump A. Therefore, the total flow will be 765 USGPM. If we had two good pumps the total flow would be 1000 USGPM instead of 765 USGPM. The head is not affected since it is the pump with the higher head which will control the pressure head in the discharge header by forcing the other pump to reduce its flow to match the higher pressure head. This what is meant when people say that one pump is fighting the other. Improperly designed suction or discharge piping can have this effect also.
1.3 What happens if the damaged pump's performance curve has all points at a lower head than the good pump's performance curve?
The best that the damaged pump can do is to produce the head corresponding to its shutoff head H_{C} (point 2) at 0 flow. Since the head produced by the good pump is higher, there will be flow through the damaged pump in the reverse direction. The flow however will be impeded since the pump can produce some head. The system behaves as a branch system. The branch flow sees a head drop which is the sum of the shutoff head of the damaged pump, plus any friction loss, plus the static head of the suction tank on the inlet of the damaged pump.
1.4 Ever wonder how it occurs that you can get partially full pipes in what appears to be a pressurized system? What would the difference in Total Head be for the same flow rate for a system with partially full pipes and a system with full pipes?
What conditions are required for a fluid to completely fill the piping throughout a system? Consider Figure B1 a system with a long discharge pipe, sloping gradually down from point 3 to point 2. A fluid under positive pressure will completely fill the available volume in the pipes. However, certain areas may remain unfilled if the pressure drops to zero or less. This can occur when the fluid rises above its discharge point. Under these conditions, if air enters the system, an air pocket can establish itself at the high point of the line. From there, it can expand with the help of negative pressure towards the end of the pipe, collapsing the fluid and causing the line to be partially full. A combination of pipe size, flow rate and system geometry can produce conditions causing certain locations of the piping to be partially full.
Q.: What is the difference in the Total Head (at the same flow rate) when all the discharge piping is full compared to when it is partially empty? A.: The answer depends which of these two terms is greater: the elevation difference between the collapse point (point 3) and the end point (point 2, the discharge end of the pipe) and the friction head for a full pipe between these two same points. If the friction head is greater, then it requires more energy to pump the fluid if the pipe is full. If the friction head is smaller then it requires less energy to pump the fluid with a collapsed line for the same flow rate.
1. Determine the Total Head of the system with a full pipe.
The general system equation for a single inlet single outlet system is:
(B1)

where H_{P}: pump Total Head
H_{F12}: head loss due to friction between points 1 and 2
H_{EQ12}: head loss due to equipment between points 1 and 2
v_{2}: average pipe velocity at point 2
v_{1}: average pipe velocity at point 1
z_{2}: elevation at point 2
z_{1}: elevation at point 1
H_{2}: head at point 2
H_{1}: head at point 1
Since the suction and discharge tanks are unpressurized and there is no equipment in the line then H_{1} = 0, H_{2} = 0, H_{EQ12} = 0. In addition the velocity at the surface of the suction tank is quite low, v_{1}=0. The Total Head for the system assuming that all the piping is completely full is:
(B2)

If the fluid is going to collapse, the collapse will occur at a position where the pressure is zero or less. The zero pressure position is at point O (see Figure B1). Point O is however in the vertical portion of the pipe run and the fluid will fill the pipe at this position. The collapse will have to occur further down at or near the change of direction to horizontal of the piping .
2. Determine the head at point 3.
The general equation for the head at any point in a single inlet single outlet system is:
(B3)

where point X is the point where the head is required. By applying this equation and substituting 3 for X, the head at point 3 can be determined. The terms v_{1} = 0, H_{1} = 0,
H_{EQ1X} = 0, the above equation becomes:
(B4)

Substitute H_{PFULL} from equation B2 in the above equation, with v_{2} = v_{3, }we obtain:
(B5)

3. Determine the Total Head of the system assuming the fluid has collapsed at point 3
If the fluid has collapsed at point 3, then the exit point of the system will be point 3. Point 3 is the exit point since the fluid runs downhill from 3 to 2 without the system providing energy. Or in other words, if the system were cut at point 3, there would be no effect on the remaining system. By applying equation B1, the subscript 2 which identifies the exit point 2 is replaced with 3, the new exit point. and H_{1} = 0, H3 = 0, H_{EQ13} = 0, v_{1} = 0. The Total Head for a system with a single inlet and outlet with the outlet at point 3:
(B6)

4. Establish the difference between the Total Head for a full line and a collapsed line.
The difference between the Total Head for a full line and a collapsed line is equation B2  equation B6:
(B7)

Our analysis compares the two cases at equal volumetric flow rates. This means that velocities are equal (v_{3} = v_{2}),that is that v_{3} in the collapse fluid case equals v_{2} in the full pipe case. By rearranging the terms in equation B5:
and substituting into equation B7 then:
(B8)

Therefore, the difference between pumping into a nonfull vs. a full discharge line is affected by the value of the head at point 3. By analyzing the value of H_{3} , the conditions that make H_{3} negative, positive or zero will tell us if it is more difficult to pump into a full or nonfull line.
(B9)

Since H_{F12}  H_{F13} = H_{F32,} equation B5 becomes:
H_{3} can be negative or positive depending on the value of the two terms in equation B9. If the friction component is greater than the static head between points 2 and 3:
If the friction component is less than the static head:
If it is necessary to avoid collapse, then a simple remedy is to add a restriction on the end of the pipe. This will add friction to the system and ensure that the complete pipe can be pressurized.
1.5 How long does it take to empty a tank?
To answer this question, we must first write the system equation assuming that the tank is kept full and that we have a constant flow (see Figure 1).
Figure 1
A simple system with a pump has the following system equation:
(1)

Since there is no pump in this system then, H_{P} = 0,and
(2)

Let's assume that the entire friction loss for this system is an exit loss and the friction loss of a manual valve (butterfly). Therefore :
(3)

There is no equipment so that H_{EQ} = 0.
V_{P} is the velocity through the pipe which is so short that we can neglect the friction loss. There is a relationship between v_{1}, v_{2} and v_{P}.
(4)

where Q is the flow rate, A_{1}, A_{2} and A_{P} are respectively the crosssectional areas of the tank, the outlet pipe and the pipe velocity. In this case, the outlet velocity equals the pipe velocity v_{2 }= v_{P}.
The system is open to atmosphere therefore H_{1}= H_{2} = 0. We rewrite equation (2) taking into account equation (3):
(5)

and since v_{2} = v_{1}A_{1}/A_{2 }equation (5) becomes:
(6)

and after simplification:
(7)

This is the point at which we have to shift gears and adapt equation (7) to the system which we really want to study, that is one where the velocities v_{1} and v_{2} are constantly changing as well as the height z_{1}. At each instant in time, we know that equation (7) is valid, therefore if we take the differential with respect time we will be able to take into account the variation of v_{1} and z_{1} with time.
If we differentiate both sides of equation (7) we get:
(8)

since we know that v_{1} = dz_{1}/dt and then
(9)

which means that we can divide both sides of the equation by dz_{1}/dt and equation (9) becomes:
<(10)

We will select our vertical coordinate z to start at the level of point 2, and z_{1} becomes the variable z which will vary from 0 to h.
(11)

Equation (11) is a simple 2^{nd} order differential equation which after integrating twice will lead to the solution for z. However, integrating twice will force us to introduce two constants. The values of these constants depends on the initial conditions. The initial conditions are: at time t = 0, z = h and at time t = 0, v = 0 or dz/dt = 0.
After the first integration we get:
(12) 
since dz/dt = v_{1} = 0 at time t = 0, A = 0. After a second integration equation (12) (with A=0) becomes:
(13) 
since z = h at time t = 0 then B = h, and
(14)

assuming we have a round tank which is typical then and, therefore and equation (14) becomes:
The graph below shows the time required to empty a 3 feet diameter tank with 3 feet of fluid with either a 2" discharge pipe or a 2.5" pipe.
1.6 How to calculate the pump flow, total head or efficiency based on power consumed by the motor.
This procedure will provide a method by which one can use the power generated by the motor to determine the total head, flow or efficiency of a pump. The power generated by the motor can be calculated by measuring the motor amperage taking into account the power factor of the specific motor.
Total Head (H_{P}) and pump flow (Q) in an existing system are measurable quantities. However, sometimes one of these terms may be difficult to determine. Why? The devices required for the measurements may be difficult to install and or expensive, or the equipment may not be shut down long enough to install the devices. However, the power consumed by the motor can be easily measured based on the current flow (amperes).
The power consumed by the pump (at the pump shaft) is:
where P_{pump}: power consumed at the pump shaft
SG: specific gravity of the fluid
H_{P}: Total Head
Q: flow through pump
_{pump} : pump efficiency>
An induction motor has a reactive component which uses power to generate a magnetic field, this power cannot be used at the shaft. The power factor determines how much of the total power input to the motor can be transferred t the shaft. The power factor and motor efficiency is given by the motor manufacturers in the form of tables for various loads and different motor sizes (see table). The power delivered to the pump shaft based on the flow of current to the motor is:
where V: motor supply voltage, often 575volts for motors 250 hp and less
A: motor supply amperage
_{motor} : motor efficiency
P.F.: power factor
By combining the 2 equations above, we can determine the Total Head, the flow or the pump efficiency.
How is Total Head measured?
Total Head can be measured by installing pressure gauges at the outlet and inlet of the pump. The pump inlet pressure measurement can be eliminated if we can be sure what the pressure head is at that point. For example, if the pump suction is large and short and the inlet shut off valve is fully open and is the type of design that offers little restriction, then we can assume that the pressure head at the inlet of the pump is equal to the static head.
What is the best way to measure flow?
Tables of power factor and motor efficiency for standard induction motors are available from the major manufacturers (GE, Westinghouse, Toshiba, ABB). However for those who do not have access to this information, here is a typical table courtesy of Canadian General Electric for TEFC (Totally Enclosed Fan Cooled) severe duty induction motors for frame sizes from 143 to 447, type K, normal starting torque, continuous, 40C ambient, 60 hertz, 575 volts, August 1985.
Horse  Frame  Full Load rpm 





Full Load  Locked Rotor  lbft
Full Load 
%
Start EEMAC 
%>
Break Down EEMAC 
Full Load  ¾ Load  ½ Load  Full Load  ¾ Load  ½ Load  
1  143T  1735  1.55  9.5  3.04  275  300  72  72  68  78  70  58  
1  145T  1150  1.6  8.3  4.64  170  265  72  68  64  67  59.5  47.5  
1  182T  870  2  12  6.1  135  215  70  60  60  56  47.5  39.5  
1.5  143T  3445  1.8  12  2.27  175  250  75.5  72  68  87.5  82  73  
1.5  145T  1710  1.9  11  4.61  250>  280  75.5  75.5  72  79  72  60  
1.5  182T  1165  2.3  12  6.84  165  50  75.5  72  68  70  62  50  
1.5  184T  865  2.6  16  9.2  130  210  71.5  69  62.5  61.5  54  49  
2  145T  3470  2.3  14  3.03  170  240  78.5  75.5  72  89  86  78  
2  145T  1730  2.4  17.8  6.1  235  270  75.5  75.5  72  78.5  69.5  56.5  
2  184T  1155  2.8  16  9.16  160  240  78.5  75.5  72  72  64  52.5  
2  213T  865  3.6  20  12.2  130  210  75  71.5  66  58.5  51.5  40  
3  182T  3500  3.6  20  4.5  160  230  78.5  75.5  72  85  80.5  72  
3  182T  1740  3.5  21  9.08  215  250  81.5  78.5  75.5  82  76  65  
3  213T  1150  4.1  21  13.8  155  230  72.5  72.5  69  70  62.5  51  
3  15T  870  4.9  25.6  18.4  130  205  76  74  69.5  59.5  51  40  
5  184T  3500  5.4  34  7.49  150  215  84  81.5  78.5  87  83  6  
5  184T  1745  5.5  35  15.1  185  225  81.5  81.5  78.5  86.5  81.5  71.5  
215T  1160  6.3  36.7  23  150  215  81.5  81.5  81.5  75  68.5  56.5  
5  254T  865  7  36.8  30.2  130  205  79.5  79.5  77  67  59  46.5  
7.5  213T  3510  8.3  46  11.2  140  200  84  84  81.5  88  87  80.5  
7.5  213T  1760  8.7  50.8  22.5  175  215  84  81.5  78.5  80  73  62  
7.5  254T  1160  9.5  48  33.8  150  205  81.5  81.5  81.5  75  68  57  
7.5  256T  870  10  50.8  45.3  125  200  80  80  78  73  66  55  
10  215T  3510  10.3  64  14.9  135  200  81.5  81.5  81.5  88.5  86.5  81  
10  215T  1750  11.5  64.8  30  165  200  84  84  81.5  85.5  80.5  75  
10  256T  1160  12  62  45.2  150  200  81.5  84  81.5  76  71  60  
10  284T  870  12.5  64.8  60.2  125  200  82.5  83  82.5  74  68  57  
15  254T  3540  15  81  22.3  130  200  86.5  86.5  86.5  87  85  78  
15  254T  1755  16  90  44.9  160  200  88.5  88.5  88.5  82.5  78.5  69  
15  284T  1175  16  92.8  67  140  200  88.5  86.5  86.5  79.5  74.5  63.5  
15  286T  870  18  92.8  90.1  125  200  83.5  84.5  84  74.5  68  58  
20  256T  3545  20  110  29.7  130  200  88.5  88.5  88.5  86.5  84  77  
20  256T  1750  20.5  116  59.8  150  200  88.5  88.5  88.5  84  82  74  
20  286T  1175  20  116  89.3  135  200  88.5  88.5  88.5  82  78.5  69  
20  324T  880  23  116  119.4  125  200  87  88  87  73.5  67.5  56  
25  284TS  3535  24  146  37  130  200  86.5  86.5  84  90  88.5  84  
25  284T  1765  24  146  74.6  150  200  90.2  90.2  90.2  86.5  85  79  
25  324T  1170  24.4  146  112.2  135  200  90.2  90.2  90.2  86  84  77  
25  326T  880  29  143  149.3  125  200  88  89  88  74.5  69  58  
30  286TS  3540  28  174  44.4  130  200  88.5  88.5  86.5  90  89.5  85  
30  286T  1765  29  174  89.3  150  200  90.2  90.2  90.2  87  85.5  79  
30  326T  1175  29.4  174  134.3  135  200  90.2  90.2  90.2  85.5  82.5  74.5  
30  364T  885  34  174  178.3  125  200  87.5  88.5  88.5  76.5  72  61  
40  324TS  3555  40  210  59.1  125  200  88.5  88.5  86.5  86.5  84.5  78.5  
40  324T  1775  42  32  118.4  140  00  90.2  90.2  88.5  83  79  70  
40  364T  1180  40  232  177.9  135  200  90.2  90.2  90.2  85  82  74  
40  365T  885  46  232  237.1  125  200  8  88.5  87  73.5  68  56  
50  326TS  3560  47  280  3.7  120  200  90.2  0.2  88.5  89  87  81.5  
50  326T  1775  51  290  147.9  140  200  91.7  91.7  90.2  84  81  71.5  
50  365T  1180  50  290  22.4  135  00  90.2  90.2  90.2  85  83  76  
50  404T  885  58  90  297.2  125  200  9  89.5  88.5  72  67  56  
0  364TS  560  57  320  88.5  120  200  88.5  88.5  86.5  8.5  86.5  81.5  
60  364T  1780  2  340  177.2  140  200  0.2  90.2  90.2  80.5  7.5  68.5  
60  404T  1180  59  348  266.9  135  200  90.2  90.2  90.2  84  80.5  71.5  
60  405T  885  69  348  356.1  125  200  90  90.5  90  72  66  54.5  
75  365TS  3565  68  434  110.4  105  200  91.7  90.2  90.2  91  90  86  
75  365T  1780  76  434  221.3  140  200  91.7  91.7  90.2  81  77  68.5  
75  405T  1180  72  434  331.5  135  200  91.7  91.7  91.7  86.5  84  76.5  
75  444T  885  74  434  446.2  125  200  91  91.5  91  82  77.5  68  
100  405TS  3560  91  580  147.4  105  200  91.7  90.2  88.5  90.5  89  83.5  
100  405T  1780  99  580  295  125  200  91.7  91.7  90.2  83.5  80.5  73  
100  444T  1180  96  580  445.3  125  200  91.7  91.7  91.7  85.5  82  74.5  
100  445T  880  98  580  596.3  125  200  91.2  92  91.5  83  80  71.5  
125  444TS  3565  112  700  184.2  100  200  91.7  90.2  90.2  92.5  92  90  
125  444T  1780  112  726  368.6  110  200  91.7  91.7  90.2  90  89  84  
125  445T  1175  117  726  557.7  125  200  91.7  91.7  91.7  87  85  79  
125  447T  880  116  830  743.2  120  200  92  92.5  92  84  80  71.5  
150  445TS  3565  135  868  221  100  200  91.7  91.7  90.2  92.5  92  89.5  
150  445T  1780  132  868  442  110  200  91.7  91.7  90.2  91  89.5  85  
150  447T  1180  140  925  667.2  120  200  93  93  91.7  86.5  84  77  
150  447T  880  140  1000  893  120  200  91.7  92.3  92  83.5  80  71.5  
200  447TS  3570  168  1345  294.2  100  200  93  93  91.7  94  93.5  91.5  
200  445T  1780  180  1280  589.1  100  200  93  93  91.7  88.5  86.5  80  
200  447T  1185  180  1250  885.2  120  200  94.1  94.1  93  86.5  84  77.5  
250  447T  1780  220  1600  736.5  70  175  93.6  93.6  93  89  87  81  
average expected values