How to Calculate NPSHa for Systems Under Vacuum

In the first four parts of this five-part series, we covered the calculation of NPSHa for a flooded suction, a lift condition, a hot water flooded suction and a pressurized hot water flooded example. In this fifth and final working example, we will investigate what happens to NPSHa when the system is under vacuum.

Vacuum

The concept of vacuum is frequently misunderstood and is a source of confusion to many in the pump world. In general, people that manufacture, sell, maintain and operate vacuum pumps and other related vacuum equipment know the terms, units and principles very well, but the rest of us are often confused and dismayed by the subject. Nomenclature in the world of vacuum applications can be confusing and is often counterintuitive; for example, the term “high vacuum” simply implies low pressure. The higher the vacuum, the lower the remaining pressure, and vice versa. What if I told you that vacuum is pressure? Most people would surely dismiss that statement as silly, but please think about it. In a vacuum, there remains an amount of pressure that is below atmospheric pressure, but is also above absolute zero. Even in a container at “middle to high vacuum” there is some pressure remaining. The application example for this article is a steam condenser. Condensers operate in a vacuum by design because this approach maximizes efficiency for the steam system. If you are applying pumps in commercial or industrial applications, you will eventually encounter a situation where the liquid on the suction side of the pump is under vacuum. Condensers are not the only applications concerned with vacuum. The pressure in the suction line of a centrifugal pump operating in a lift application will most often be in a vacuum—that is, at a pressure less than atmospheric. To be clear, when we state a pressure, we should add the mode to differentiate the pressure measurement we are referencing. That is, we should state with the units and measurement quantity the correct mode; either vacuum, atmospheric, gauge or absolute. For this article, we will refer to the area of vacuum as that pressure range (mode) below atmospheric pressure and above zero pressure absolute. Note that atmospheric pressure changes with the weather (barometric pressure) and the elevation above or below sea level.

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

To help in understanding the next part of this example, I will add a few comments. Atmospheric pressure at sea level equals 14.7 pounds per square inch (psi) and that equates to a pressure of 29.92 inches of Hg (mercury). To convert inches of mercury to units of feet, multiply by 1.1349. For those that deal in SI units or work professionally in the vacuum arena, note that a Torr is defined as 1/760 of an atmosphere and may be expressed as 1 mm-Hg, where 760 mm-Hg also equals 29.92 inches Hg. Also in what appears to be an evil plot just to confuse the neophytes, we reverse the scale when we switch from pressure to vacuum. When we use the expression “full vacuum,” we are referring to the vacuum level of 29.92 inches of Hg. Note we state full vacuum and not a perfect vacuum. At full vacuum, there is no pressure remaining for the NPSHa calculations.

The Mistake

The mistake most often made in vacuum applications is thinking the level of vacuum is the same as the pressure and that the units just need to be converted. Further, when the person calculating the NPSHa for the system is looking to determine the value of the first component in the NPSHa equation (which is h_a or h_absolute) many people just convert the vacuum measurement to feet of water and use that result in the equation. That approach will yield the wrong answer. For example, 28 inches of mercury vacuum converts to approximately 32 feet. The correct answer is discussed later. [28 x 1.1349 = 31.7772 ≈ 32] Equation 1

The Formula

For the correct answer, we first need to determine the amount of residual pressure in the condenser. Then use the formula to calculate the resultant NPSHa. I know many of you hate formulas, and I will remain insistent they are your friends. Refer to Image 1, which depicts the condenser application for this example. The application is at sea level. The condenser is operating at a vacuum of 28.42 inches of mercury (28.42”-Hg). Note we are measuring vacuum so the scale is now reversed from our normal perception of pressure. The higher the vacuum, the closer we approach the maximum or full vacuum of 29.92” Hg. At zero or low vacuum, the measurement would be 0” Hg. NPSHa = h_a – h_vpa + h_st – h_f Where: h_a = the absolute pressure. Absolute pressure as measured in feet of head of the liquid being pumped at the surface of the liquid. This will be barometric pressure if suction is from an open tank; or the absolute pressure existing in a closed tank such as a condenser hotwell or deaerator. h_vpa = the vapor pressure. The head in feet corresponding to the vapor pressure of the liquid at the temperature being pumped. h_st = the static head of the liquid over the pump centerline or impeller eye for a flooded suction in feet (positive value for flooded suction). Not all impeller centerlines correspond to the pump centerline. h_f = the total friction loss in feet of head for the suction side system. Equation 2 Using the information I provided above, you now know there is still a small amount of pressure remaining in the condenser. You also know that a full vacuum is accepted to be 29.92”-Hg. Consequently the difference between the full vacuum and the measured vacuum is therefore 1.5” Hg or 1.7 feet [29.92 – 28.42 = 1.5”-Hg]. The 1.5” Hg converts to 1.7 feet of head absolute (1.5 x 1.1349 = 1.7 and note the units are now feet). Now you have the first component in the NPSHa formula as 1.7 feet. The second component in the formula is the vapor pressure (h_vpa). I provided the information that the water was at approximately 92 F. Water at this temperature has a vapor pressure of 0.741457 pounds per square inch absolute (psia) and that pressure converts to a head of 1.73 feet which rounds to 1.7 feet. Caution: remember from the definition of NPSHa formula the vapor pressure is not simply a conversion, but is defined as the head in feet corresponding to the vapor pressure of the liquid at the temperature being pumped. Another way to calculate would be [1.5” Hg x 1.1349 = 1.7 feet]. The third component in the formula is the head due to static height (h_st), which was provided in the figure as 10 feet. The fourth component in the equation is the head due to friction (h_f), which was provided by the author as 3.2 feet. Now you simply need to insert the values in the equation and complete the math steps (see Equation 3). NPSHa = h_a – h_vpa + h_st – h_f NPSHa = 1.7- 1.7 + 10 – 3.2 = 6.8 NPSHa = 6.8 feet Equation 3 When you conduct your calculations for your own applications, you may have results that differ slightly due to temperature conversions, rounding and conversions between units. Another explanation for result variance can be different techniques such as using specific weights versus specific gravities when converting between pressure and head; both methods are correct, but may yield slightly different answers. You can see from the example that the positive component of static head minus the friction becomes the main contributor to the NPSHa total. The head due to absolute pressure and the vapor pressure components cancel each other out because the system is at, or near, equilibrium. This condition is also referred to as saturation. The friction component takes an additional toll on the total leaving some portion of the static head as the main factor. Pumps applied in low NPSHa situations such as condensate service are always going to be in the lowest level of the plant for the aforementioned reasons. In a refinery application, the tower will need to be at a higher elevation so the pumps have adequate NPSHa. At this value of 6.8 feet, you can also see why condensate pumps operate at slow speeds, are physically placed well below the condenser, often have special impellers, enlarged eyes or inducers on the first stage and are frequently dual suction. The NPSHa in this example is 6.8 feet, but also think of it as the net static submergence. If you refer to the Cameron Hydraulic Data Book and view the NPSHa calculation for condenser applications, the editor also points out the vacuum application is similar to, and can also be equated as, a lift situation. The equivalent suction lift is equal to the difference between the “vacuum effect” and the net submergence. In this case it would be 25.45 feet. That is, this vacuum application can be equated to a lift situation of 25.45 feet. The text example is a different result because the friction factor was lower. 28.42 Hg of vacuum x 1.1349 = 32.25 feet Static submergence = 10 feet Friction losses = 3.2 feet Net static submergence = 6.8 feet Equivalent suction lift = 32.25 – 6.8 = 25.45 feet Equation 4

Conclusion

Remember, static height and the NPSHa formula are your friends, vapor pressure is not. Next month I will summarize the subject and lessons learned over the last five months in combination with a discussion on how to address the issue if you do not have sufficient NPSHa. References Cameron Hydraulic Data Book 19th Edition