Agilent Quaternary Pump (e.g. G1311A ) "Secret" Operator Tip to FLUSH the HPLC Pump in 1/2 the time!

One of the most popular "tips" taught in our Agilent 1100 and 1200-series HPLC training classes shows users how to speed up the daily priming and flushing process of the Quaternary Pump. Many people use these pumps without taking advantage of the Quaternary pump's higher flow capability. If you are not currently using the higher 10mL/min flow rate capability offered by this pump (vs. the Binary pump's 5 mL/min), then you are missing out on a free time saving feature. Please read on to learn how to use this feature.

Based on the HP 1050 pump and introduced in 1995 as the "1100-series" version, the G1311  "Quat" pumps are one of the most popular research grade HPLC pumps found in laboratories today. They are extremely reliable, rugged, easy to operate and service. The Quat pump is driven by an easily accessible, single pump head with an in-series, servo controlled dual plunger and Multi-channel Gradient Valve ('MCGV') for 4-channel solvent proportioning with an active inlet valve (known as the 'AIV', first used in the HP 1050 pump and the reason for this pump's high reliability. No more "sticking" inlet valve issues!). Unlike the Agilent Binary pump (G1312), which uses two separate dual plunger pumps (2-channel) at up to 5.0 mL/min (maximum), the Quat pump offers an extended flow range, up to 10.0 mL/min (maximum). However, most users are not aware of this or do not know how to utilize this higher flow rate feature because the Quat pump defaults to a maximum flow rate of 5 mL/min at initialization. The ability to program the pump to operate at flow rates greater than 5 mL/min requires a "trick" to activate it (which apparently is a secret as we rarely encounter customers who are aware of how to use it). 

Let me share with you why you would want to use this feature, why the feature is hidden to most and of course HOW TO ACTIVATE IT on the Quat pump.

• Q: Why would you want to run the pump at 5 to 10 mL/min? Semi-prep columns can be run within this flow rate range, but a more common reason to operate at 10 mL/min is for daily system start-up. Anytime you replace or change the mobile phase bottle/solution OR when you startup the HPLC system (each day) one of the very first things you need to do is prime or flush each of the mobile phase channels, one-at-a-time through the system to waste. Air bleeds into the system when it is not used and this procedure primes the lines and pump head with fresh mobile phase preparing it for use. The system's flow path is directed to waste (via the open, prime-purge valve) during this step so back-pressure is not a concern. The higher the flow rate you can use for this flushing step, the sooner you can complete it. If you run the pump at 10 mL/min vs 5 mL/min, then flushing can be completed in half the time. This is especially useful if you have a model G1322A degasser module installed as the internal volume of each degassing channel in the G1322A is 10-12 mLs, requiring extended flushing times (4x channels = 30+ mLs flush per channel) before moving on to the next channel.

• Q: Why does the Quat pump initialize with a reduced, 5 mL/min maximum flow rate? The Quat pump was designed to meet two different operating pressure ranges. From 0 to 5 mL/min the permitted operating pressure range is 0 - 40 MPa (0 - 400 bar). Above 5 mL/min, the operating pressure range is reduced, 0 - 20 MPa (0 - 200 bar). As most analytical chromatography is performed at flow rates below 5 mL/min, the system initializes using the more practical, 0 - 400 bar range, limiting flow rates to 5 mL/min maximum. The default maximum pressure field is set to 400 bars. You should always change the maximum pressure value from 400 bars to a more realistic maximum pressure (lower value) for your method. Use a maximum value that is appropriate for your own method. *The only time you will want to set it to the maximum value is when conducting a Pump Pressure/Leak test (it must be set to max pressure for testing).
  

• Q: When I try and enter a pump flow rate larger than 5 mL/min, the system does not accept it. How do I program the pump to increase the flow rate past 5 mL to 10 mL/min? In order for the system to accept a flow rate of greater than 5 mL/min, you must FIRST set the maximum pressure limit to a value that is 200 bars or less (within the allowed "0 - 20 MPa (0 - 200 bar)" range). Once the maximum pressure limit has been reduced in the method, the system will then allow you to enter a higher flow rate such as 9.999 mL/min (10 mL/min). As long as the maximum pressure alarm is set within this window (200 or less), the pump will allow flow rates above 5 mL/min to be used. Now you can program the pump to flush lines or prime the system at twice the speed of the Binary pump equipped systems (10 mL/min).

Please share this "trick" with other users of the G1311A, G1311B, G1311C versions of this pump so they can maximize their time and productivity. Let us know if you find this tip useful.

Adjusting the HPLC Gradient Time For Changes in Column Diameter and/or Length (same particle size)

Changes to the column diameter (to scale the method up or down) can be calculated. For an established HPLC method using the same support type (same exact material and particle size) where the column dimensions and flow rate are known. Note: If only the diameter changes and the lengths remain the same (proper linear flow rates used in both cases), then the resulting gradient times will also be similar. If the column lengths change, then the gradient time will change.

Changes to the Gradient Time (Tg2) used for a second column which has a different diameter, "Dc2" and/or length, "Lc2" can be calculated if you know: 

• Tg1 [Time, of initial Gradient on Column #1];
• Tg2 [Time of second Gradient on Column #2];
  
• Fc1 [Flow Rate of Column 1] ;
• Fc2 [Flow Rate of Column 2];
• Dc1 [Diameter of Column 1]
• Dc2 [Diameter of Column 2];
• Lc1 [Length of Column 1];
• Lc2 [Length of Column 2].

        Tg2 = Tg1 x (Fc1 / Fc2) x (Dc2² / Dc1²) x (Lc2 / Lc1)

 

Example: Initial Method utilizes a 4.6 x 150 mm, 5u column run at 1.00 mL/min with a 10 minute gradient program and we wish to transfer this gradient method over to a column with a 2.1 mm diameter (ID) x 100 mm column run at 200 ul/min.

   Tg2 = 10 x (1 / 0.2) x (2.1² / 4.6²) x (100 /150)

   Tg2 = 10 x (5) x (4.41/21.16) x (0.67) 

   Tg2 =  50 x 0.208 x 0.67

   Tg2 =  6.97 minutes.

The gradient time used on the 2.1 x 100 mm column run at 0.200 mL/min would be ~ 7 minutes (vs 10 minutes on the 4.6 x 150 mm column at 1 mL/min).

 

NOTE: A note about optimized flow rates. If the Column PARTICLE SIZE changes, esp from greater than 3.5 u to less than 3.5 u, then the optimized flow rate may also change too. Please refer to my article; 

• "Speed Up HPLC Analysis Time Using Higher than "Normal" Flow Rates with SMALLER Particles" for more information.

Speed Up HPLC Analysis Time Using Higher than "Normal" Flow Rates with SMALLER Particles

Column efficiency (as described by Van Deemter) in HPLC is largely a function of dispersion, column particle size and the flow rate of the mobile phase.After a column has been selected, the Flow rate should be optimized for all methods (start with the nominal linear velocity). Once the optimum flow rate range is achieved, little to no advantage in analysis time or solvent savings is found by increasing it (as column efficiency normally decreases at higher flow rates).

From a practical point of view, columns packed with porous 3 to 5 micron diameter supports show only small differences in efficiency as the flow rate is varied above the initial, optimum level (linear velocity). Running at too low a flow rate serves no purpose, increases dispersion/diffusion and delays the peaks from eluting off the column in a timely manner. Higher rates often decrease column efficiency. Once the flow rate has been set within the 'optimized zone', it no longer becomes a variable in HPLC method development. 

Many ~ 3 micron supports do demonstrate some ability to maintain optimum efficiency at slightly higher flow rates (e.g. with linear velocities > 1 mm/second), but significant advantages in using higher flow rates to save time and solvent are not obvious unless the particle size is reduced further. 

With the much smaller diameter ~ 2 micron particles, column efficiency can be further optimized using higher than "normal" flow rates on standard columns. Columns packed with these smaller porous particles show optimized flow rates at much higher linear velocities (e.g. 2x normal or ~ 2 mm/second for standard analytical sized columns, but experiment using 2 to 5x the normal linear velocity to compare results). 

• For example: If your method currently runs at 1.000 mL/min, you may be able to run the same method at 2.000 mL/min OR if your method currently runs at 0.200 mL/min, you may be able to run the same method at 0.400 mL/min or higher using one of the 2.5 or smaller particles. 

This increased efficiency coupled with proper optimization of the HPLC's flow path to reduce dispersion, allows for a doubling of the flow rate without a loss of efficiency (or loss of resolution). Depending on the scaling used, a two-fold savings in analysis time over conventional methods using larger particles may be observed. There may be a corresponding increase in system back-pressure too (* if only the particle size is changed and the column dimensions are unchanged). *Some of this can be countered using proper scaling of the column dimensions too). 

NOTE: Do Not Optimize HPLC Methods for "Pressure". This goes against basic chromatography fundamentals. Back Pressure is a result of pushing mobile phase through the tubing and column and is not a method development tool or variable. As mobile phase composition changes, so does the pressure. Flow rates should be stable. Work within a pressure range that is high enough to permit the pump(s) to function properly, but below the point in which frictional heating interferes with the method.

Optimization of method resolution, overall analysis time and solvent usage should be considered. The increased efficiency gained from the smaller particle size supports also allows for scaling down the column dimensions (i.e. length, ID or both) too, though a trade-off between overall column efficiency vs. analysis time and/or too high a back-pressure must be addressed to optimize the method and meet the application goals.

Summary: HPLC analytical column flow rate is often ignored in method development (* esp after it has been adjusted to the initial optimum, often 1.0 mL/min for a 4.6 mm ID column), but IF you are using porous HPLC particles that are smaller than 3.5 micron diameter, please be sure to investigate if you should re-optimize the flow rate used in your method / application so you can take advantage of any increases in column efficiency and/or scaling. As with ALL applications using these very small particles, pre-optimization of the HPLC flow path is often needed to achieve many of the available benefits.

HPLC Column Cross-Sectional Area and Scaling

Here is a simple formula to use when scaling up or down Internal Column Diameter to maintain retention values (under constant linear velocity). Flow rate must be adjusted to account for any changes made to the column's cross-sectional area. We usually refer to these types of changes as the "Scaling Factor". To determine the scaling factor, we need to know the internal column diameters of the two columns we are scaling from (actually, we need to know the radius, but once we have the diameter, we simply divide the diameter by 2 to obtain the radius). *In this discussion, changes in cross-sectional area are the only parameters we are concerned with as column length does not affect scaling.

• Scaling Factor = (S);
• Column #1 Radius =  (R1);
• Column #2 Radius =  (R2).

     S = R2² / R1²

Example #1: 250 x 4.60 mm column scaled down to a 250 x 2.10 mm column. 

          Answer = 0.208. 

• If the original flow rate was 1.000 mL/min, the the scaled down flow rate would be 0.208 of the original or 0.208 mL/min for the 2.10 mm ID column. *For practical use and application, we often use either 200 ul/min or 210 ul/min to simplify the value.

Example #2: 250 x 4.60 mm column scaled up to a 250 x 10.00 mm ID semi-prep column.

          Answer  = 4.726. 

• If the original flow rate used was 1.000 mL/min with the 4.60 mm ID column, then we would increase the flow rate to 4.726 mL/min on the 10.00 mm ID column to maintain the same relative velocity (and relative retention). *For practical use and application, we often use 5 mL/min to simplify (round off) the value. 

Notes:

1. Flow rate optimization should always be carried out by running a standard at different flow rates and plotting the plate height (N) vs the flow rate. Test flow rates that are slightly below the predicted linear velocity and up to 2 times higher than that rate to find and optimize the flow rate for your sample (it must be determined through experimentation for your specific method). 
    
2. HPLC Columns packed with sub 2 micron supports may have optimum flow rates 2 to 5 times more than the predicted std linear flow rate so actual testing is critical to determining the most efficient flow rate. I recommend optimizing the flow rate used with analysis methods which use any particles which are 2.5 microns or smaller in diameter.
   

Air Bubbles Exiting the HPLC PUMP, Reasons Why.

Reasons For Air Bubbles Exiting The HPLC Pump:

• Pump Cavitation: When the pump pressure fluctuates wildly up and down, at very low pressures, this is often due to 'pump cavitation'. It is caused by a loss of priming inside the pump (Air, instead of liquid is in the pump's flow path). The HPLC pump should be primed with fresh, degassed mobile phase (following proper procedures) to restore smooth, stable flow. Often, this can be accomplished using the pump, set to a high flow rate, to draw liquid from the bottles. In cases where the pump is not strog enough, manually priming the low pressure lines using a syringe (~ 20 mL) filled with mobile phase and opening (or disconnecting) a fitting at the pump's outlet may aid in priming the system. Note: Depending on the configuration of your HPLC system, to fully prime an HPLC pump, you may need to run 20 or more mLs of solution through EACH channel. Please keep this in mind every time you use the system and every time you prepare or change a mobile phase solution. This article on baseline/pressure fluctuations may assist you in troubleshooting.

• Loose Connections: If one or more of the low-pressure fittings (nuts and ferrules)  which secure the Teflon tubing to the pump (or vacuum degasser) are damaged or loose, air may enter the system resulting in bubbles. Most pumps use plastic finger-tight style fittings 1/4-28 (or 5/16-24). The threads are soft and can be deformed. When access to these fittings is difficult, sometimes the fittings are left loose and will allow small amounts of air to be drawn in. A build up of salts and/or buffers on the exposed fittings can also allow air into the system (and the presence of deposits on the fittings indicates poor maintenance and a LEAK !). Inspect the tubing and fittings used for proper type, seating depth, wear/condition, cleanliness and/or damage. Replace parts as needed and re-install using the correct amount of torque.

• Flow Rate Too High, Too Low or Not Enough Degasser Equilibration Time: Degassing efficiency is directly related to the flow rate. Lower flow rates increase the residence time of the mobile phase in the degassing membrane or tubing, improving the gas removal. Higher flow rates provide less time for gas extraction and result in lower degassing efficiency (which equals bubbles in the outlet line). Check with the manufacturer regarding the optimal flow rate range for your degasser to insure you are working  within an acceptable range. Allow enough time for the degasser to reach its set-point and stabilize before use. If the degasser is not operating properly or is unable to "keep up" with the flow rate, then bubbles may be frequently observed in the outlet lines. 

• Choice of Mobile Phase Liquid: The miscibility of the liquid is also important. If the new mobile phase is not compatible with the previously used mobile phase, pump cavitation may result. Always flush the pump with an intermediate liquid that will dissolve in both the old and new fluids to flush them out before introducing the new mobile phase solution. (such as pure water or IPA, as applicable). The solubility of air (gas) in the specific solution used also affects the efficiency of the vacuum degasser. Aqueous solutions usually hold less gas than popular organic solvents (though air bubbles can be harder to "push" through in water). The amount of dissolved gas inside the liquid relates directly to the time needed to reduce it to acceptable levels for use in HPLC. Be sure to allow enough time to properly degass the new solution.

• Dirty or Obstructed Solvent Pickup Filters (Bottle filters): Bottle filters should be cleaned or replaced at regular intervals, following routine maintenance SOPs. When they become fouled or obstructed, a vacuum may form as the liquid is drawn into the system. This may result in air being sucked into the tubing or through a fitting (remember that the low pressure Teflon tubing used to connect the bottles to the degasser and pump is porous and allows gas to diffuse through it). The pickup filters should not obstruct the normal flow of solvent (typically they are 10-20 u in porosity). * a quick troubleshooting tip to rule out an obstructed solvent pickup filter is to temporarily remove the filter from the bottle. Observe the back-pressure on the pump to see if it increases and priming is restored. If so, the filter may be clogged. Always replace the filter with a fresh, clean filter and never operate the HPLC without the solvent filters installed.

• A Sticking Check Valve: The pump's inlet and outlet check valves must function perfectly, all of the time, to maintain proper flow and pump function. If an inlet check valve is not fully closing properly to seal off the high pressures generated inside the pump, then the pump will not be able to maintain pressure or flow. Inspect the check valve. Remove and clean it, per the manufacturer's guidelines (often this involves placing the check valve assembly in a beaker with solvent such as IPA and sonicating for 20 minutes to remove any residues. If cleaning fails to restore proper valve function, then replace the check valve with a new one.

• Worn Pump Piston Seals (or Pistons): When the piston seals begin to leak, air is allowed into the system. Pump piston seals require regular replacement (they are normal wear items). Scratched or worn pistons may also result in leaks with air getting into the system. Inspect and Test them both for pressure tightness on a scheduled basis or anytime you suspect a problem. Flush the pump with a suitable liquid, then run a high-pressure test to determine if they pass or fail the manufacturer's leak tightness and high pressure tests. Be sure to perform a physical inspection too.

• Contaminated or Obstructed Pump Outlet Filter: Most HPLC pumps have a small disposable outlet filter installed at or near the pump outlet line (Note: In the case of most Agilent brand HPLC pumps, a small PTFE filter may be found at the outlet valve or inside of the prime-purge valve). These filters should be replaced at regular intervals (monthly is strongly recommended), especially if any aqueous buffers or solutions are used (a they contribute to contamination). Contaminated pump outlet filters may result in a number of pressure instability problems. Abnormally high back-pressure during operation OR when vented to waste are indications it is obstructed. Regular scheduled replacement is the best way to prevent lost time and reduce system contamination.

 Any of the above causes may contribute to valves not functioning properly or air being drawn into the HPLC system. Troubleshooting should begin with the easiest and obvious areas first. Check the condition of the low pressure tubing used to make the connections to and from the mobile phase bottles and pump. If it is kinked, twisted or damaged, replace it with new tubing. Check the fittings used (nuts and ferrules) for tightness and to insure they have been installed properly and are not leaking. Repair all leaks. Keep the system clean (it is easier to monitor and troubleshoot problems when it is clean). Replace any damaged fittings with new ones. Check the solvent pickup filters monthly to insure they are clean and not obstructed. Make sure the flow rate you are using is within the acceptable range for your degasser. 

Has your degasser module been professionally cleaned and serviced within the last 5 years? Are any degasser errors being generated? Is the vacuum degasser making any unusual sounds? Is liquid being emitted from the vacuum pump exhaust port? If any of the answers to these questions are 'yes', then have the HPLC vacuum degasser professionally diagnosed for problems so that repairs can be made to restore function.

Air Bubbles Exiting the HPLC Vacuum Degasser. Reasons Why

A common question we are asked to solve relates to why air bubbles might be observed exiting out of an HPLC vacuum degasser module  (where the mobile phase leaves the degasser ports to go to the pump heads and/or gradient valve)? Troubleshooting and answering this question is most easily accomplished if you first have a solid understanding of the HPLC flow path, how to make proper connections and are familiar with performing routine maintenance on the HPLC system. 

• Key Point: HPLC systems utilize Teflon low-pressure tubing to transfer the mobile phase (solvents) from the mobile phase bottles to the HPLC pump. The Teflon lines are permeable to gas in the atmosphere. Gas is diffusing through the plastic tubing used to transport your solvents. This is one of the reasons why we purge the entire flow path of the HPLC system before use, each day. Overnight, gas has diffused into the system so we start by flushing (purge) the mobile phase from each bottle, through the degasser, through each channel all the way to the pump head, to waste.

To find the reason why air bubbles may be observed exiting the HPLC vacuum degasser module, we examine the flow path.
 
Common Reasons For Air Bubbles Exiting The HPLC Vacuum Degasser Include:

• Loose Connections: If the low pressure fittings (nuts and ferrules)  which secure the Teflon tubing to the degasser are damaged or loose, air may enter the system resulting in bubbles. Most vacuum degassers use plastic finger-tight style fittings 1/4-28 (or 5/16-24). The threads are soft and can be deformed. When access to these fittings is difficult, sometimes the fittings are left loose and will allow small amounts of air to be drawn in (such as found on many of the generic small benchtop degasser which use the micro-chambers or the HP/Agilent model G1379-series). Inspect the tubing and fittings used for proper seating depth, wear and/or damage. Replace parts as needed and re-install using the correct amount of torque.

• Flow Rate Too High or Not Enough Degasser Equilibration Time: Degassing efficiency is directly related to the flow rate. Lower flow rates increase the residence time of the mobile phase in the degassing membrane or tubing, improving the gas removal. Higher flow rates provide less time for gas extraction and result in lower degassing efficiency. Check with the manufacturer regarding the optimal flow rate range for your degasser to insure you are working  within an acceptable range. Allow enough time for the degasser to reach its set-point and stabilize before use.

• Choice of Mobile Phase Liquid: The solubility of air (gas) in the specific solution used also affects the efficiency of the vacuum degasser. Aqueous solutions usually hold less gas than popular organic solvents (though air bubbles can be harder to "push" through in water). The amount of dissolved gas inside the liquid relates directly to the time needed to reduce it to acceptable levels for use in HPLC.

• Dirty or Obstructed Solvent Pickup Filters (Bottle filters): Bottle filters should be cleaned or replaced at regular intervals, following routine maintenance SOPs. When they become fouled or obstructed, a vacuum may form as the liquid is drawn into the system. This may result in air being sucked into the tubing or through a fitting (remember that the low pressure Teflon tubing used to connect the bottles to the degasser and pump is porous and allows gas to diffuse through it). The pickup filters should not obstruct the normal flow of solvent (typically they are 10-20 u in porosity).

• Vacuum Degasser Damage: HPLC Vacuum degasser modules, like most other component parts of your HPLC system break down over time and require professional diagnostic testing, cleaning and repair. Under ideal conditions, most inline electronic vacuum degassers require diagnostic testing and cleaning or repair every 4 to 5 years. *Many show signs of contamination or failure before that time. The internal vacuum tubing becomes contaminated and worn over time. The vacuum pump is an electromechanical part which is exposed to all of the mobile phase additives and solvent vapors during use. Other internal component parts such as vacuum valves or restrictors may also become contaminated or worn over time. The vacuum degassing membranes (or tubing) themselves can stretch from use and wear out over time. The vacuum chambers may be exposed to incompatible chemicals or over-pressured resulting in internal leakage. Certain chemicals may also attack and even dissolve the degassing membranes causing more internal damage and contamination of the mobile phase. These devices do not have any "contamination" detection alarms and the vacuum sensors sometimes become damaged over time leading to false vacuum levels being reported. Never rely on the module's built-in error alarm system as proof of compliance (no more than you would the reported flow rate shown on the computer screen. It must be measured to be known). Regular professional HPLC degasser testing and service are required to maintain the modules and meet compliance requirements.

 Any of the above causes may contribute to air being drawn into the degasser system. Troubleshooting should begin with the easiest and obvious areas first. Check the condition of the low pressure tubing used to make the connections to and from the mobile phase bottles and degasser. If it is kinked, twisted or damaged, replace it with new tubing. Check the fittings used (nuts and ferrules) for tightness and to insure they have been installed properly. Replace any damaged fittings with new ones. Check the solvent pickups to insure they are clean and not obstructed. Make sure the flow rate you are using is within the acceptable range for your degasser. Has your degasser module been professionally cleaned and serviced within the last 5 years? Are any degasser errors being generated? Is the degasser making any unusual sounds? If any of the answers to these questions are 'yes', then have the HPLC vacuum degasser professionally diagnosed for problems so that repairs can be made to restore function. 

Additional Information:

• "Agilent / HP Brand Vacuum Degasser Troubleshooting Tips, Errors and Repairs"; https://www.hplctools.com/agilent_degasser_error_troubleshooting.htm

• "Waters Alliance and Acquity Brand UPLC Vacuum Degasser Troubleshooting Ti[s and Errors"; https://www.hplctools.com/waters_degasser_error_troubleshooting.htm

USP Guideline Note: HPLC Column Diameter Changes to Maintain Flow Rate Linear Velocity

USP Allowed Variations in HPLC Column Diameter (*USP 32, Second Supplement, Dec 1, 2009). In the previous USP version, a change of up to 50% of the flow rate was allowed. This has been changed in the more recent version. A wide range of column diameter changes are now allowed, provided that the linear velocity is kept constant. *We addressed the effect of changing column diameter on flow rate in a previous blog post, but this time I have also expanded on the calculation by including the extra variable for column length (L1 and L2) as well.

*Adjusting the Column Flow Rate for Changes in the HPLC Column Diameter.

Linear Velocity Formula:

   New Linear Flow Rate₂ = Flow Rate₁ x (L2 x D2²) / (L1 x D1²)

Flow Rates are in ml/min.

L1 = Column Length (original) in mm.

L2 = Column Length (proposed) in mm.

D1 = Column Diameter (original) in mm.

D2 = Column Diameter (proposed) in mm.

Example #1:

Original column is a 150mm x 4.6mm (L x ID) used at 1.000 ml min. We would like to determine what the equivalent flow rate (F₂) would be for a column which is 150mm x 2.1mm (L x ID) to maintain the same linear velocity. This is a proposed change in column diameter of > 50% so it would not have been allowed under the old guidelines. The newer guidelines take into account that with the same particle size, changing the column diameter will not change the chromatography if the linear velocity is maintained as before. Let’s calculate the new flow rate using the formula above.

1.000 x (150 x 2.1²) / (150 x 4.6²) = F₂

                    1 x (661.50 / 3,174) = F₂

                              0.208 ml/min = F₂